peripheral refraction: significance, current limitations and a

$: Peripheral refraction: significance, current limitations and a$
PERIPHERAL REFRACTION: SIGNIFICANCE, CURRENT

LIMITATIONS AND A NEW APPROACH

Cathleen Fedtke, Dipl.‐Ing. (FH)

A thesis submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Optometry and Vision Science

The University of New South Wales, Sydney, Australia

and

Brien Holden Vision Institute

Sydney, Australia

and

Vision Cooperative Research Centre

Sydney, Australia

April 2011

Certificate of Originality

i

CERTIFICATE OF ORIGINALITY

‘I hereby declare that this submission is my own work and to the best of my knowledge it

contains no materials previously published or written by another person, or substantial

proportions of material which have been accepted for the award of any other degree or

diploma at UNSW or any other educational institution, except where due acknowledgement is

made in the thesis. Any contribution made to the research by others, with whom I have

worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the

intellectual content of this thesis is the product of my own work, except to the extent that

assistance from others in the project's design and conception or in style, presentation and

linguistic expression is acknowledged.’

Cathleen Fedtke

April 2011

Acknowledgements

ii

ACKNOWLEDGEMENTS

First and foremost, I would like to thank my supervisors Brien Holden and Klaus Ehrmann for

giving me the opportunity to pursue this PhD. Thank you for your long‐lasting support and

loyalty throughout. I have been very privileged to work with both of you. Brien, your research,

dedication and enthusiasm to the world of optometry have kept me motivated and

driven. It has truly been an honour and I look forward to working with you and the staff at the

Brien Holden Vision Institute into the future. Klaus, thank you for introducing me to the world

of research and for being my mentor throughout this journey, a journey made possible with

your brilliant ideas and technology expertise. I am very grateful for your continuous incredible

support.

This project would also not have been possible without the financial support from various

sources; an UIPA scholarship funded through the University of New South Wales, a scholarship

funded by the Brien Holden Vision Institute and travel grants for the attendance of

international conferences from the University of New South Wales, the American Academy of

Optometry and the Brien Holden Vision Institute. Thank you.

A special thank you goes to Darrin Falk, who has greatly contributed to the instrumental work

presented in this thesis. Thank you for your incredible help and for reassuring me that there is

a light at the end of the tunnel. Another person that has provided much wealth of expertise to

this project was Arthur Ho. Thank you for sharing your amazing knowledge and for giving me

the opportunities to grow as a researcher.

I would also like to thank many other important helpers of this project. Colm Dolphin for

manufacturing the instrument parts, Thomas Naduvilath and Varghese Thomas for statistical

advice, Judith Flanagan for reading the manuscripts and for providing valuable advice on

scientific writing, Ravi Bakaraju for sharing his valuable knowledge on Zemax and Elsbeth Biβ‐

Harms for helping with analysis of the pupil images. Thank you also to all the participants for

their precious time to take part in my studies.

I am also very grateful for the help provided by staff of many other departments within the

Brien Holden Vision Institute, particularly: Eric Papas and Vivienne Miller for taking care of all

the administrative matters, the Myopia team, including Padmaja Sankaridurg, Percy Lazon de

Acknowledgements

iii

la Jara, Judy Kwan, Les Donovan, Rebecca Weng and Belinda Ford, for being a great clinical

team to work with, the i‐media team for helping me produce great posters and each of my

fellow‐postgraduate students, in particular Maria, Ravi, Fabian, Negar, Krupa, Kalika, Ulli and

Usha, who always provided support and encouragement. I appreciate all your help and

friendship.

I would not have made it through some of the tough times without a few very special people.

Maria, you have given me so much support, not just as an amazing friend on the personal

level, who was there when times were very difficult, but also as a fellow student on the

professional level for helping me with proof‐reading, statistics and critical thinking – thank you,

I have learnt so much from you. Claudia, thank you for your friendship and all the support you

have given me during the last four years. This PhD has been a long‐lasting odyssey with many

ups and downs and I deeply appreciate your friendship through all phases. I would also like to

thank the many other friendships which have formed during this PhD journey. In particular I

would like to thank my friends and colleagues Judy, Beth, Aurelia, Melina, Stephanie and

Elsbeth, who each in their own way made working in the clinic so enjoyable.

Most of all I would like to thank my wonderful family, my Mum & Dad, Loreen, and Manu, who

have been of enormous support to my studies and who have been a constant source of

encouragement. Words cannot describe how much that has meant to me. Thank you so much

for your unconditional support and love.

Abstract

iv

ABSTRACT

Peripheral refractive error has assumed considerable importance with the discovery that

it can influence eye growth. The link between the peripheral state of the eye and myopia

development demands rapid and accurate measurements at individual and population

levels. Currently, the use of conventional refraction techniques requires time‐consuming

sequential re‐alignments.

The aims of this thesis were to identify and assess methodological limitations of current

techniques, test new concepts and develop a method of obtaining more rapid and

accurate peripheral refraction measurements.

At first, the impact of pupil misalignment was investigated using a conventional

autorefractor. As visual field angle increased, tolerance to pupil misalignment decreased

significantly, making peripheral measurements particularly susceptible to this

measurement error. It was also shown that the peripheral entrance pupil shape is not

elliptical as currently assumed, adding further potential for pupil misalignment. Based on

these findings, means to rectify pupil alignment‐related errors when using conventional

instruments were established and validated.

Having ascertained limitations of current peripheral refractometry, a novel instrument

concept was proposed, the EyeMapper. The EyeMapper was designed to perform a rapid

peripheral (and central) refraction scan, from ‐50° to +50°, using 10 stationary deflecting

prisms and a scanning mirror. Like most autorefractors, the operation was based on the

ring‐autorefraction principle. The optical design, consisting of 5 intertwined optical sub‐

systems was developed. Safety aspects and criteria for instrument components were

assessed and the operation principle was verified experimentally. Experimental testing

identified an obstacle relating to the ring‐image analysis and it revealed that peripheral

higher order aberrations have the potential to interfere with the sphero‐cylindrical

refraction readings obtained when applying this ring‐autorefraction principle. A

technique that segregates higher and lower order aberrations was thus deemed more

suitable for measuring peripheral refraction. Hence, the EyeMapper design was updated

to include wavefront measurements. The prototype instrument was then built and

experimentally tested over a range of refractive errors. The EyeMapper uses an array of

beam steering mirrors and a scanning mirror to perform a rapid peripheral refraction

scan in one meridian. Three‐dimensional power maps of the eye can be obtained by

pivoting the instrument around its optical axis.

Table of Contents

v

TABLE OF CONTENTS

CERTIFICATE OF ORIGINALITY ...................................................................................... i

ACKNOWLEDGEMENTS .............................................................................................. ii

ABSTRACT ................................................................................................................ iv

TABLE OF CONTENTS .................................................................................................. v

LIST OF FIGURES ........................................................................................................ x

LIST OF TABLES ...................................................................................................... xvii

GLOSSARY OF ABBREVIATIONS ................................................................................ xix

CHAPTER 1

LITERATURE REVIEW .................................................................................................. 1

1.1 Introduction ......................................................................................................... 1 1.2 Peripheral Vision .................................................................................................. 4

1.2.1 Methods of Testing Peripheral Vision ........................................................ 5 1.3 Peripheral Refractive Error Measurement Techniques .......................................... 6

1.3.1 Subjective Peripheral Refraction ............................................................... 9 1.3.2 Retinoscopy ............................................................................................ 11 1.3.3 Manual Refractometer – Optometer ....................................................... 14 1.3.4 Double‐Pass Technique ........................................................................... 17 1.3.5 Autorefraction ........................................................................................ 20 1.3.6 Photorefraction....................................................................................... 27 1.3.7 Aberrometer ........................................................................................... 30

1.4 Alignment Criteria for Peripheral Refractometry ................................................. 34 1.5 Summary and Conclusion .................................................................................... 38 1.6 Thesis Overview .................................................................................................. 40

1.6.1 Rationale for Research ............................................................................ 40 1.6.2 Hypotheses ............................................................................................. 40 1.6.3 Aims ........................................................................................................ 41

CHAPTER 2

INVESTIGATION OF OPERATOR‐RELATED ALIGNMENT INTRICACIES IN CURRENT PERIPHERAL REFRACTOMETRY ................................................................................. 42

2.1 Overview ............................................................................................................ 42 2.2 Investigation of Pupil Alignment Tolerance ......................................................... 42

2.2.1 Introduction ............................................................................................ 42 2.2.2 Methods ................................................................................................. 44

2.2.2.1 Participants ............................................................................................ 44 2.2.2.2 Instrumentation ..................................................................................... 44 2.2.2.3 Participant Alignment ............................................................................. 45 2.2.2.4 Entrance Pupil Alignment ........................................................................ 46

2.2.3 Results .................................................................................................... 49 2.2.3.1 Central and Peripheral Refraction – Pupil Alignment ............................... 49 2.2.3.2 Pupil Misalignment Threshold of Clinical Significance .............................. 52

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vi

2.2.4 Discussion .............................................................................................. 53 2.2.4.1 Peripheral Refraction and its Tolerance to Lateral Pupil Misalignment .... 53 2.2.4.2 Factors Contributing to Misalignment Errors during Peripheral Refraction

Measurements ....................................................................................... 55 2.2.4.3 Improving Pupil Alignment ...................................................................... 56

2.2.5 Conclusion .............................................................................................. 57 2.3 Three‐Dimensional Model of the Entrance Pupil ................................................ 57

2.3.1 Introduction ........................................................................................... 57 2.3.2 Methods ................................................................................................. 58

2.3.2.1 Model of the Entrance Pupil for Different Viewing Angles ....................... 58 2.3.3 Results .................................................................................................... 60

2.3.3.1 Entrance Pupil Relative to the Actual Pupil.............................................. 60 2.3.3.2 Entrance Pupil Relative to the Viewing Direction ..................................... 60

2.3.4 Discussion .............................................................................................. 67 2.3.4.1 Comparison of the Entrance Pupil Model with in Vivo Pupils ................... 68 2.3.4.2 Implications of the Entrance Pupil Model ................................................ 69 2.3.4.3 The Wide‐Field Eye ................................................................................. 72 2.3.4.4 Recommendations for Future Models ..................................................... 72

2.3.5 Conclusion .............................................................................................. 73 2.4 Summary ............................................................................................................ 73

CHAPTER 3

MEANS TO RECTIFY PUPIL ALIGNMENT ERRORS IN CURRENT PERIPHERAL REFRACTOMERTY .................................................................................................... 75

3.1 Introduction ....................................................................................................... 75 3.2 Methods ............................................................................................................ 76

3.2.1 Phase 1 ................................................................................................... 76 3.2.1.1 Participants ............................................................................................ 76 3.2.1.2 Instrumentation and Alignment Procedure ............................................. 76

3.2.2 Phase 2 ................................................................................................... 78 3.2.2.1 Participants and Instrumentation ............................................................ 78 3.2.2.2 Entrance Pupil: Image Capture and Analysis ............................................ 78

3.3 Results ............................................................................................................... 78 3.3.1 Phase 1 ................................................................................................... 78

3.3.1.1 Establish Correction Models ................................................................... 78 3.3.1.1.1 Refractive Vector Component M ......................................................... 79 3.3.1.1.2 Refractive Vector Component J180 ....................................................... 83 3.3.1.1.3 Refractive Vector Component J45 ......................................................... 85 3.3.1.1.4 Sphero‐Cylindrical Notation ................................................................. 88

3.3.1.2 Investigation of Instrument Binocularity with Pupil Alignment ................ 88 3.3.1.3 Validation of the Correction Algorithm ................................................... 91

3.3.2 Phase 2 ................................................................................................... 93 3.3.2.1 Implementation of the Correction Algorithms ......................................... 93

3.4 Discussion .......................................................................................................... 97 3.4.1 Functions of Pupil Alignment .................................................................. 97

3.4.1.1 Functions of Pupil Alignment for Different Visual Field Angles ................. 97 3.4.1.2 Functions of Pupil Alignment for Different Ocular Parameters ................. 99 3.4.1.3 Functions of Pupil Alignment for Nasal and Temporal Measurements .... 102 3.4.1.4 Instrumentation used to Establish Pupil Alignment Functions ............... 102

3.4.2 Pupil Alignment Correction Models ....................................................... 103 3.4.3 Implementation of Compensation Factor ............................................... 104

3.5 Summary and Conclusion .................................................................................. 105

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CHAPTER 4

OPTICAL DESIGN OF A NOVEL PERIPHERAL REFRACTION CONCEPT: THE EYEMAPPER . 106

4.1 Introduction ..................................................................................................... 106 4.1.1 Design Concept and Operation Principle ............................................... 106 4.1.2 Chapter Overview ................................................................................. 109 4.1.3 Introduction into Optical Designing using ZEMAX .................................. 110

4.2 The EyeMapper’s Reference Model Eye ............................................................ 111 4.2.1 Methods ............................................................................................... 111

4.2.1.1 EyeMapper Reference Model Eye ......................................................... 111 4.2.1.2 Computation of Central and Peripheral Refraction via Ray‐Tracing ........ 113 4.2.1.3 Refractive Error‐Dependent Model Eyes ............................................... 116 4.2.1.4 Accommodation‐Dependent Model Eyes ............................................... 119 4.2.1.5 Computation of Peripheral Refraction for Different Ray‐Trace Modes ... 122

4.2.2 Results .................................................................................................. 125 4.2.2.1 Peripheral Refraction Profiles of Schematic Model Eyes ........................ 125 4.2.2.2 Peripheral Refraction Profiles for Different Ray‐Trace Modes ................ 125

4.2.3 Discussion/Conclusion........................................................................... 127 4.3 The Optical Design of the EyeMapper ............................................................... 128

4.3.1 Autorefraction Paths ............................................................................. 129 4.3.1.1 Deflection System ................................................................................. 129

4.3.1.1.1 Methods ............................................................................................. 129 4.3.1.1.2 Results ................................................................................................ 137

4.3.1.2 Illumination Autorefraction Path .......................................................... 141 4.3.1.2.1 Methods ............................................................................................. 142 4.3.1.2.2 Results ................................................................................................ 144

4.3.1.3 Reflection Autorefraction Path ............................................................. 146 4.3.1.3.1 Methods ............................................................................................. 147 4.3.1.3.2 Results ................................................................................................ 150

4.3.2 Pupil Imaging Path ................................................................................ 153 4.3.2.1 Methods ............................................................................................... 153 4.3.2.2 Results ................................................................................................. 154

4.3.3 Fixation Path ......................................................................................... 156 4.3.3.1 Methods ............................................................................................... 156 4.3.3.2 Results ................................................................................................. 158

4.4 Summary .......................................................................................................... 160 4.5 Conclusion ........................................................................................................ 160

CHAPTER 5

RING‐SCAN‐AUTOREFRACTION PRINCIPLE: COMPONENT CRITERIA, SAFETY ASSESSMENT AND EXPERIMENTAL VALIDATION .......................................................................... 163

5.1 Introduction ..................................................................................................... 163 5.2 On‐ and Off‐Axis Ring Scan Illumination ............................................................ 164

5.2.1 Component Criteria ............................................................................... 164 5.2.1.1 Infrared Light Source – Super Luminescent Diode ................................. 164 5.2.1.2 Dual Axis Galvanometer Scanner ........................................................... 165 5.2.1.3 Single Axis Galvanometer Scanner ........................................................ 165

5.2.2 Safety Assessment ................................................................................ 166 5.2.2.1 Introduction ......................................................................................... 166 5.2.2.2 Methods ............................................................................................... 167

5.2.2.2.1 Single and Repetitive Pulse Exposures ............................................... 167 5.2.2.2.2 Ocular Scanning ................................................................................. 169

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viii

5.2.2.3 Results ................................................................................................. 170 5.2.2.3.1 Retinal Image Size – Visual Angle ....................................................... 170 5.2.2.3.2 Maximum Permissible Exposure as a Function of Exposure Duration172 5.2.2.3.3 Repeated Refraction Measurements ................................................. 175

5.2.2.4 Discussion ............................................................................................ 175 5.2.2.4.1 ANSI Exposure Limits and Ocular Scanning ........................................ 175 5.2.2.4.2 Illumination of Peripheral Retinal Locations ...................................... 177 5.2.2.4.3 Scanner Safety ................................................................................... 179

5.3 Component Criteria for Image Detection ........................................................... 179 5.3.1 Reduction of Interfering Reflections ...................................................... 180 5.3.2 Translation Stage and CCD Sensor ......................................................... 181

5.4 Experimental Validation of the Ring‐Autorefraction Principle ............................ 181 5.4.1 Methods ................................................................................................ 181

5.4.1.1 Experimental Set‐Up and Procedure ..................................................... 181 5.4.1.2 Investigation of Shin‐Nippon Detector and Retinal Images .................... 183

5.4.2 Results ................................................................................................... 185 5.4.2.1 Cross‐Validation of the Autorefraction Principle with optical ZEMAX design

............................................................................................................ 185 5.4.2.2 Cross‐Validation of the Autorefraction Principle with the Shin‐Nippon

Autorefractor ....................................................................................... 186 5.4.3 Discussion ............................................................................................. 187

5.4.3.1 On‐Axis Optical Bench Experiment ........................................................ 187 5.4.3.2 Major Obstacles Encountered During Experimental Testing ................... 188

5.4.3.2.1 Image Analysis for Off‐Axis Ring Images ............................................ 188 5.4.3.2.2 Impact of Higher‐Order Aberrations on Peripheral Ring Images ....... 189

5.5 Future Work ...................................................................................................... 193 5.6 Summary and Conclusion .................................................................................. 194

CHAPTER 6

THE EYEMAPPER ‐ A REAL‐TIME GLOBAL ABERROMETER .......................................... 196

6.1 Introduction ...................................................................................................... 196 6.2 Instrument Design ............................................................................................. 197

6.2.1 Optical Design ....................................................................................... 197 6.2.1.1 Wavefront Sensing Paths ...................................................................... 198

6.2.1.1.1 Deflection System .............................................................................. 198 6.2.1.1.2 Illumination Path................................................................................ 199 6.2.1.1.3 Reflection Path ................................................................................... 199

6.2.1.2 Pupil Imaging Path ................................................................................ 200 6.2.1.3 Fixation Path ........................................................................................ 200

6.2.2 Mechanical Design ................................................................................. 201 6.3 Instrument Construction ................................................................................... 204

6.3.1 Tolerance Analysis ................................................................................. 204 6.3.1.1 Aims ..................................................................................................... 204 6.3.1.2 Methods ............................................................................................... 204

6.3.1.2.1 Sensitivity Analysis and Monte Carlo Simulation ............................... 204 6.3.1.2.2 Tolerance Analysis for the Reflection Path ........................................ 205

6.3.1.3 Results ................................................................................................. 207 6.3.1.3.1 Sensitivity Analysis ............................................................................. 207 6.3.1.3.2 Monte‐Carlo Simulation ..................................................................... 209

6.3.1.4 Discussion ............................................................................................ 210 6.3.2 Instrument Components ........................................................................ 211

6.3.2.1 Deflection System ................................................................................. 211

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ix

6.3.2.2 Illumination Path .................................................................................. 211 6.3.2.3 Reflection Path ..................................................................................... 212 6.3.2.4 Fixation Path ........................................................................................ 213 6.3.2.5 Pupil Imaging Path ................................................................................ 213 6.3.2.6 Other Instrument Parts ......................................................................... 214

6.3.3 The EyeMapper ..................................................................................... 216 6.4 Instrument Validation ....................................................................................... 219

6.4.1 Methods ............................................................................................... 219 6.4.1.1 Peripheral Refraction Model Eye ........................................................... 219 6.4.1.2 Human Eyes .......................................................................................... 221

6.4.1.2.1 Participants ........................................................................................ 221 6.4.1.2.2 Instrumentation, Set‐up and Procedure ............................................ 222

6.4.2 Results .................................................................................................. 223 6.4.2.1 Peripheral Refraction: Model Eye .......................................................... 223 6.4.2.2 Peripheral Refraction: Human Eyes ....................................................... 224

6.4.2.2.1 Peripheral Refraction Profiles ............................................................ 224 6.4.2.2.2 Repeatability ...................................................................................... 229 6.4.2.2.3 Reproducibility ................................................................................... 230 6.4.2.2.4 Refraction Map .................................................................................. 232

6.4.3 Discussion ............................................................................................. 233 6.4.3.1 Accuracy: Model Eye ............................................................................. 233 6.4.3.2 Peripheral Refraction Profiles and Repeatability: Human Eyes ............... 234 6.4.3.3 Reproducibility ..................................................................................... 237

6.5 Discussion......................................................................................................... 237 6.5.1 Peripheral Refraction Instruments ........................................................ 237 6.5.2 Limitations and Suggestions for Future Work ........................................ 240

6.6 Conclusion ........................................................................................................ 241

CHAPTER 7: ........................................................................................................... 243

SUMMARY AND CONCLUSIONS .............................................................................. 243

7.1 Significance of Peripheral Refractometry .......................................................... 243 7.2 Current Limitations ........................................................................................... 243

7.2.1 Participant‐Related Alignment Limitations ............................................ 243 7.2.2 Operator‐Related Alignment Limitations ............................................... 244

7.3 A New Approach ............................................................................................... 245 7.4 Conclusions ...................................................................................................... 246

REFERENCES ...................................................................................................................... 248 APPENDICES APPENDIX A: Patent Application: Determination of Peripheral Refraction .................... 261 APPENDIX B: Pupil Misalignment Correction Algorithms ............................................... 302 APPENDIX C: ZEMAX Macro: Calculation of Peripheral Refraction ................................. 304 APPENDIX D: Publications and Presentations ....................................................................... 305

List of Figures

x

LIST OF FIGURES

Figure 1.1: Emmetropic eye with relative hyperopic defocus in the periphery. ............... 2

Figure 1.2: Scheiner disc principle. ................................................................................ 15

Figure 1.3: Alignment of the peripheral measurement angle with respect to the instrument axis via a) eye turn, b) head turn and c) instrument rotation. .... 35

Figure 1.4: Number of studies and their peripheral refraction techniques used over the last 40 years (left) and the last decade (right). ............................................ 39

Figure 2.1: Modifications to the Shin‐Nippon NVision K5001 autorefractor. .................. 46

Figure 2.2: Right eye pupil alignment matrix. ................................................................ 47

Figure 2.3: The pupil alignment scale. ........................................................................... 48

Figure 2.4: RPRE of the mean refractive components M, J180 and J45 as a function of pupil alignment for each refractive error group and three different visual fields. . 50

Figure 2.5: Optical layout for modelling the entrance pupil. ......................................... 59

Figure 2.6: The three‐dimensional entrance pupil for six and nine (Media file online164) actual pupil sizes (1 mm to 6 mm) at various viewing angles relative to the actual pupil position. ................................................................................... 61

Figure 2.7: The three‐dimensional entrance pupil for six and nine (online media file164) actual pupil sizes at various viewing angles as seen by the observer. .......... 62

Figure 2.8: The tangential profile (side‐projection) of the peripheral entrance pupil from the point‐of‐view of the observer for nine viewing angles. .......................... 63

Figure 2.9: Apparent tilt of the tangential entrance pupil meridian as a function of viewing angle and pupil size. ....................................................................... 63

Figure 2.10: Two‐dimensional (frontal) projection of (a) the actual pupil and (b) the entrance pupil at 60° observation angle showing the shape as seen by the observer. ..................................................................................................... 64

Figure 2.11: Entrance pupil decentration as a function of viewing angle and actual pupil diameter. .................................................................................................... 65

List of Figures

xi

Figure 2.12: Entrance pupil diameter (a) and (c) and magnification (b) and (d) along the tangential (a) and (b) and sagittal (c) and (d) meridians as a function of viewing angle and actual pupil size. ............................................................ 66

Figure 2.13: Comparison of the ratio of tangential (horizontal) to sagittal (vertical) entrance pupil diameter as a function of viewing angle determined by in vivo measurements and the current entrance pupil model for 6 mm and 3 mm actual pupil diameters. ............................................................................... 69

Figure 2.14: Tangential and sagittal spot sizes (in mm) for the horizontal proximal and distal pupil margins as well as the vertical superior pupil margin as a function of viewing angle. ......................................................................................... 71

Figure 3.1 The refractive vector component M (in D) plotted as a function of pupil alignment position (in mm) for the vertical and horizontal pupil meridian (n=40). ........................................................................................................ 80

Figure 3.2 The refractive vector component J180 (in D) plotted as a function of pupil alignment position (in mm) for the vertical and horizontal pupil meridian (n=40). ........................................................................................................ 84

Figure 3.3 The refractive vector component J45 (in D) plotted as a function of pupil alignment position (in mm) for the vertical and horizontal pupil meridian (n=40). ........................................................................................................ 87

Figure 3.4: The sphere, cylinder and axis components plotted as a function of pupil alignment position (in mm) for the vertical and horizontal pupil meridian (n=40). ........................................................................................................ 89

Figure 3.5: Right and left eye refraction data as a function of pupil alignment. ............ 90

Figure 3.6: Three pupil alignment correction models. ................................................... 92

Figure 3.7: Standard deviation (in D) for M, J180 and J45 before and after correction. .... 93

Figure 3.8: Pupil alignment positions as measured during peripheral refraction. .......... 94

Figure 3.9: Measured and corrected M, J180 and J45 as a function of horizontal visual field angle........................................................................................................... 95

Figure 3.10: Spread of the repeats for the measured and corrected M (in D) as a function of peripheral visual field angle of the four participants. .............................. 96

List of Figures

xii

Figure 3.11: Central and peripheral (40°) rays traced into the eye for three different pupil alignment positions, i.e. left: 1.5 mm temporal, middle: central and right: 1.5 mm nasal pupil position. ............................................................................. 98

Figure 3.12: The functions of pupil de‐alignment for the RPRE of M at four visual field angles, i.e. the central visual field and 20°, 30° and 40° nasal visual field, for the Escudero‐Sanz & Navarro model eye (a) and the experimental data (b). ............................................................................................................ 100

Figure 3.13: Functions of pupil de‐alignment for changing ocular parameters. ............. 101

Figure 4.1: A basic diagrammatic plan of the optical layout of the EM. ....................... 108

Figure 4.2: Optical design paths and the respective mode and wavelength used for ray‐trace. ........................................................................................................ 109

Figure 4.3: Shaded layout of the EM reference model eye in IERT mode for two visual field angles (0° and 50°). ........................................................................... 113

Figure 4.4: Pyramid of Zernike Polynomials up to the 5th order. .................................. 113

Figure 4.5: Vitreous chamber depth as a function of central M (LEFT) and y‐radius of the anterior cornea as a function of central J180 (RIGHT). ................................. 118

Figure 4.6: The object sided peripheral angles in IERT mode correspond to the visual field angles (LEFT) and the object sided peripheral angles in OERT mode correspond to the retinal angles (RIGHT). .................................................. 123

Figure 4.7: Comparison of the peripheral refractive vector components M (TOP) and J180 (BOTTOM) as a function of horizontal visual field angle of different schematic model eyes. ............................................................................................... 126

Figure 4.8: Comparison of the refractive power vector components M and J180 as a function of horizontal visual field angle between schematic eyes in IERT (visible) and OERT (visible) mode (TOP) and between schematic eyes in IERT (IR) and OERT (IR) mode (BOTTOM). .......................................................... 127

Figure 4.9: Layout of the optical design of the deflection system. ............................... 137

Figure 4.10: The RPRE of M and J180 as a function of horizontal visual field angle for the eye with and without deflecting components in place. .............................. 141

Figure 4.11: The side layout of the different retinal positions for a range of refractive error eyes. ................................................................................................. 146

List of Figures

xiii

Figure 4.12: Graphical illustration of the design of the deflection system (the prisms and the scanning mirror) and the illumination path (SLD, x‐y scanning mirror and L1). ........................................................................................................... 146

Figure 4.13: Graphical illustration of the design of deflection system (prisms and scanning mirror) and the reflection path (L2, L3, A1, movable CCD). The movement of the CCD camera permits the focussing of the retinal ring images. ............. 152

Figure 4.14: Graphical illustration of the design of deflection system (prisms and scanning mirror) and the reflection path (L2, L3, A1, movable CCD) indicating the system’s image spaced telecentricity. ....................................................... 153

Figure 4.15: Graphical illustration of the pupil imaging path (dotted lines) and the autorefraction paths. ................................................................................ 155

Figure 4.16: The two‐dimensional layout showing the fixation path design with all six fixation target positions for the accommodating eye. ............................... 159

Figure 4.17: Graphical illustration of the fixation path, which has been incorporated into the autorefraction paths and pupil alignment path. .................................. 159

Figure 4.18: Summary of the layout of each optical path designs. ............................... 162

Figure 5.1: LEFT: Dual Axis (x‐y) Galvanometer Scanner, RIGHT: Single Axis Galvanometer Scanner ..................................................................................................... 165

Figure 5.2: ANSI Single Pulse Rule as described by Delori et al.205 ............................... 168

Figure 5.3: Three ANSI Repetitive Pulse Rules as described by Delori et al.205 ............. 168

Figure 5.4: Retinal images and corresponding visual angle for single exposure MPФ calculations............................................................................................... 171

Figure 5.5: Pulsed Line Segment (PLS) definition ........................................................ 172

Figure 5.6: Maximum permissible MPФbeam in mW for all sub‐exposures, i.e. spot (red), circle (pink), line (green), PLS – F 100 Hz (blue – dashed), PLS – F 1000 Hz (turquoise – dashed) and PLS – F 10000 Hz (light blue – dotted). .............. 174

Figure 5.7: Graphical illustration on the use of linearly polarised light for the reduction of interfering reflections. .......................................................................... 181

Figure 5.8: Layout of the optical bench set‐up. ........................................................... 183

List of Figures

xiv

Figure 5.9: A calibration model eye with a known induced refractive error (trial lens) was measured with the Shin‐Nippon NVision K5001. ........................................ 184

Figure 5.10: Detector images for a range of refractive error eyes as computed with ZEMAX (TOP) and as captured on the optical bench set‐up (BOTTOM). ..... 185

Figure 5.11: The number of pixels (± SD) that define the radius of the captured ring image as a function of change in refractive error. ................................................ 186

Figure 5.12: Printed detector images of the Shin‐Nippon NVision K5001 for an emmetropic eye and a +15D hyperopic and ‐15D myopic eye. ................... 186

Figure 5.13: The comparison of the retinal ring image diameters (in mm) as a function of refractive error change (in D) between the Shin‐Nippon NVision K5001 and the illumination path design of the EM. ..................................................... 187

Figure 5.14: Modelling of the retinal ring image as a function of visual field angle. ...... 191

Figure 5.15: The ratio between the tangential retinal ring radii which are distal and proximal to the fovea as a function of visual field angle and refractive error. ................................................................................................................. 192

Figure 6.1: Layout of the EM instrument design. ......................................................... 197

Figure 6.2: Three‐dimensional layout of the deflection system. .................................. 198

Figure 6.3: SolidWorks EM design from above. ........................................................... 201

Figure 6.4: SolidWorks EM design from the side and below. ....................................... 202

Figure 6.5: SolidWorks EM design from the front and above. ...................................... 203

Figure 6.6: Flow chart used for the tolerance analysis of the EM using ZEMAX. .......... 205

Figure 6.7: Reflection path set‐up used for the tolerance analysis. ............................. 206

Figure 6.8: Absolute change in performance with respect to the terms defocus and spherical aberration, for axial lens misalignment of ± 0.5 mm. .................. 207

Figure 6.9: Absolute change in performance for the terms defocus, astigmatism, coma and spherical aberration, when the individual lenses were decentred by ±0.5 mm............................................................................................................ 208

List of Figures

xv

Figure 6.10: Absolute change in performance for the terms of defocus, astigmatism, coma and spherical aberration, when the individual lenses were tilted by 1°. .... 208

Figure 6.11: Pictures taken during the manufacturing process of the EyeMapper. ........ 215

Figure 6.12: The EyeMapper instrument without (A) and with cover (B). ...................... 217

Figure 6.13: The user‐interface of the EyeMapper developed by Darrin Falk. ............... 218

Figure 6.14: Peripheral Refraction Model Eye. .............................................................. 220

Figure 6.15: Custom‐made peripheral fixation device for the COAS. ............................. 223

Figure 6.16: Peripheral refraction profiles of the model eye when measurements were performed with the EyeMapper, the COAS aberrometer and the Shin‐Nippon NVision K5001 autorefractor. .................................................................... 224

Figure 6.17: The refractive vector component M (in D) plotted as a function of visual field angle when measured with the EyeMapper, the COAS aberrometer and the Shin Nippon NVision K5001 autorefractor. ................................................ 225

Figure 6.18: The refractive vector component J180 (in D) plotted as a function of visual field angle when measured with the EyeMapper, the COAS aberrometer and the Shin Nippon NVision K5001 autorefractor. .......................................... 226

Figure 6.19: The refractive vector component J45 (in D) plotted as a function of visual field angle when measured with the EyeMapper, the COAS aberrometer and the Shin Nippon NVision K5001 autorefractor. ................................................ 227

Figure 6.20: Coefficients of repeatability for M, J180 and J45 (in D). ................................ 230

Figure 6.21: The peripheral refraction profile for M measured by two independent operators on two different occasions. ...................................................... 231

Figure 6.22: The relative refraction data measured with the EM and plotted as function of visual field meridian and visual field angle (n=1). ...................................... 232

List of Tables

xvi

LIST OF TABLES

Table 1.1: Summary of all authors with their peripheral refraction technique used. ...... 7

Table 1.2: This table shows all authors and their study set‐ups for the measurement of peripheral subjective refraction. ................................................................... 9

Table 1.3: This table shows all authors and their study set‐ups for the measurement of peripheral retinoscopy. ............................................................................... 12

Table 1.4: This table shows all authors and their study set‐ups for the measurement of peripheral refraction using an optometer. ................................................... 16

Table 1.5: This table shows all authors and their study set‐ups for the measurement of peripheral refraction by use of the double‐pass technique. ......................... 19

Table 1.6: This table shows all authors and their study set‐ups for the measurement of peripheral autorefraction. ........................................................................... 21

Table 1.7: Features of autorefractors used for peripheral refractometry. .................... 23

Table 1.8: This table lists all authors and their study set‐ups for the measurement of peripheral photorefraction. ......................................................................... 28

Table 1.9: This table shows all authors and their study set‐ups used for the measurement of aberrometer‐based peripheral refraction. ........................ 31

Table 1.10: Summary of the findings investigating possible refractive changes between eye and head turn as well as instrument rotation. ....................................... 35

Table 2.1: Absolute M, J180 and J45 (in D) measured at the centred entrance pupil position (0CP) for all three visual field angles. Data are means ± SD. ........... 49

Table 2.2: Pupil misalignment threshold (in mm) of clinical significance (≥0.25D for M and ≥0.125D for J180). .................................................................................. 53

Table 3.1: Study demographics for participants in Phase 1. ......................................... 78

Table 4.1: Lens Data Editor tabulating the set‐up for the EM’s reference model eye in IERT (visible) mode. ................................................................................... 112

Table 4.2: LDE and MFE set‐up prior the optimisation of the eye’s refractive state. ... 117

Table 4.3: LDE and MFE following the optimisation of the eye’s refractive state........ 118

List of Tables

xvii

Table 4.4: Set‐up of the three ZEMAX editors prior the optimisation of the accommodation‐ dependent parameters. .................................................. 120

Table 4.5: The three ZEMAX editors following the optimisation of the accommodation‐ dependent parameters. ............................................................................. 121

Table 4.6: Set‐up of the MCE and MFE prior the optimisation of the retinal angles. ... 124

Table 4.7: The MCE and MFE following the optimisation of the retinal angles. ........... 124

Table 4.8: Field angle settings for ray‐trace in IERT and OERT modes, using either visible (555 nm) or IR (830 nm) wavelengths. ....................................................... 125

Table 4.9: Set‐up of the LDE prior the optimisation of the deflection system. ............ 133

Table 4.10: Set‐up of the MCE prior the optimisation of the deflection system. ........... 134

Table 4.11: Set‐up of the MFE prior the optimisation of the deflection system. ........... 136

Table 4.12: LDE following the optimisation of the deflection system............................ 138

Table 4.13: MCE following the optimisation of the deflection system. .......................... 139

Table 4.14: MFE following the optimisation of the deflection system. ......................... 140

Table 4.15: The total path lengths between the anterior cornea surface and the scanning mirror for all 11 visual field angles in the deflection system. ..................... 140

Table 4.16: LDE and MCE prior the optimisation of the illumination path. ................... 143

Table 4.17: MFE prior the optimisation of the illumination path. ................................. 144

Table 4.18: All three editors following the optimisation of the illumination path. ........ 145

Table 4.19: LDE and MCE prior the optimisation of the reflection path. ....................... 148

Table 4.20: MFE prior the optimisation of the reflection path. ..................................... 150

Table 4.21: LDE and MCE following the optimisation of the reflection path. ................ 151

Table 4.22: MFE following the optimisation of the reflection path. .............................. 152

Table 4.23: LDE and MFE prior the optimisation of the pupil imaging path. ................. 154

List of Tables

xviii

Table 4.24: LDE and MFE following the optimisation of the pupil imaging path. .......... 155

Table 4.25: LDE and MCE prior the optimisation of the fixation path. .......................... 157

Table 4.26: MFE prior the optimisation of the fixation path. ........................................ 157

Table 4.27: All three editors following the optimisation of the fixation path. .............. 158

Table 4.28: Summary of the ray‐trace mode, ray‐trace wavelength, optical components and individual design criteria of each optical path. .................................... 161

Table 5.1: ANSI ocular exposure definitions (α=visual angle subtended by the retinal image to the centre of pupil (mrad)) ......................................................... 167

Table 5.2: MPФ calculation for all single pulse simulations (spot, circle and line) as well as PLS exposure when the measurement of one of the 11 retinal positions takes 0.05 seconds. ................................................................................... 173

Table 5.3: Maximum permissible exposure in mW. .................................................... 175

Table 6.1: Results of the ZEMAX Monte Carlo simulation shown as a change in merit function degradation. ................................................................................ 209

Table 6.2: Maximum permissible exposure limits (mW) for the EyeMapper. .............. 212

Table 6.3: Study demographics .................................................................................. 221

Table 6.4: Summary of the coefficients of reproducibility (in D). ............................... 231

Table 6.5: Features of current peripheral refraction instruments. ............................. 238

Glossary of Abbreviations

xix

GLOSSARY OF ABBREVIATIONS

ANOVA Repeated‐Measures Analysis of Variance

C Cylinder

CAD Computer‐Aided Design

CB Coordinate Break

CCD Charge‐Coupled Device

Conf = Config Configuration

COAS Complete Ophthalmic Analysis System

CP Central Pupil Alignment

CW Continuous Wave

D Dioptres

EM EyeMapper

FC Fibre Channel

I Inferior

IERT Into‐the‐Eye Ray‐Trace

IR Infra‐Red

J45 Oblique astigmatism

J180 With/against the rule astigmatism

L1, L2, L3, L4, L5 Lens 1, 2, 3, 4, 5

LASIK Laser‐Assisted In Situ Keratomileusis

LDE Lens Data Editor

LED Light‐Emitting Diode

LSF Line Spread Function

M Spherical Equivalent

MCE Multi Configuration Editor

MCF Monte Carlo File

MFE Merit Function Editor

MPФ Intrapupillary Radiant Power

N Nasal

NA Numerical Aperture

NP Nasal Pupil De‐Alignment

Glossary of Abbreviations

xx

OD and OS Right and Left Eye

OERT Out‐of‐the‐Eye Ray‐Trace

P Pick‐up solve

PBS Pellicle Beam Splitter

PCBS Polarising Cube Beam Splitter

PLS Pulsed Line Segment

PP Pupil Position

PSF Point Spread Function

RMSE Root Mean Square Error

RP Repetitive Pulse

RPRE Relative Peripheral Refractive Error

S = Sph Sphere

S Superior

SD Standard Deviation

SLD Super Luminescent Diode

SLO Scanning Laser Ophthalmoscope

SP Single Pulse

T Temporal

TDE Tolerance Data Editor

TP Temporal Pupil De‐Alignment

V Variable

ZPL ZEMAX Programming Language

CHAPTER 1: LITERATURE REVIEW

1

CHAPTER 1:

LITERATURE REVIEW*

1.1 Introduction

Clear central vision is essential for many activities in life, be it for close, intermediate or

far distances. As such, the majority of research work on refractive errors, their

development and best correction, has focused on on‐axis refraction. Study into the

extent to which peripheral refractive error plays a role in the development of the eye

and vision has long been neglected. However, recent research findings have shown that

the peripheral refractive state of the eye can affect eye development, particularly

progression of myopia.1-4 With the rapidly increasing prevalence of myopia in many

countries, the discovered link to peripheral vision has stimulated much interest in the

precise measurement of peripheral refractive errors.

Animal models have played an important role for many years in understanding refractive

error development. Such models have shown that central retinal defocus or form

deprivation can cause eye shape changes and axial elongation resulting in myopia.1-4

Animal models have also helped in establishing a link between peripheral refractive error

and myopia development. Form deprivation of partial areas of the peripheral retinal

image using lenses or diffusers demonstrated local retinal, growth‐altering mechanisms

in the affected areas.5-8 By obstructing the peripheral vision of monkeys’ eyes and

keeping clear central vision Smith et al.9, 10 demonstrated that peripheral vision in rhesus

monkeys has an impact on axial length development. In an additional experiment, the

macula of one eye of each monkey was photocoagulated using an argon laser. These

laser‐treated eyes recovered as quickly from form vision deprivation or refractive‐

induced myopia as the non‐macula ablated eyes, indicating that the peripheral retina can

mediate emmetropising responses. Hence, it is hypothesised that peripheral vision can

influence axial length in human eyes, potentially altering the central refractive error and

its development.

* A large part of this chapter has previously been published.11


2

In humans, the first link between peripheral refraction and myopia was found in 1971 by

Hoogerheide et al.12 Seventy‐seven percent of young emmetropic pilots with relative

hyperopic shifts in the periphery developed myopia during their training. At that time it

was not acceptable for pilots to have any myopia when commencing their pilot training.

This peripheral refraction test was therefore the first method used in association with

refractive error development to predict the risk of late‐onset myopia for young pilots.

In general, peripheral refractive errors have been measured for more than 70 years. It

was shown that myopic eyes usually have relative hyperopic defocus in the periphery

and hyperopic eyes are usually myopic in the periphery relative to the centre.13-23 One

hypothesis is that peripheral rays focused behind the retina may trigger compensatory

growth, resulting in an elongated eye and axial myopia (Figure 1.1). It was also shown

that the degree of astigmatism increases steadily with field angle.14, 24-28 Typically at a

40° field angle, the degree of astigmatism is about 4 dioptres (D) and rises to about 7D

for a 60° field angle.25 The amount of astigmatism is usually at a minimum in the nasal

retina.15, 22-25, 29-41 This asymmetry across the horizontal visual field was also found to be

present for monochromatic aberrations, which were generally greater in the temporal

visual field.31 It was hypothesised that this asymmetry is caused by the mismatch

between the eye’s optical and visual axes, but only poor association was found between

the peripheral astigmatic minima and angle alpha.37

Figure 1.1: Emmetropic eye with relative hyperopic defocus in the periphery.

Although, the recent interest in peripheral refraction is linked to refractive development,

there are numerous other aspects and research areas that have dealt with off‐axis

functions of the eye, including:

ocular and retinal shapes,13, 19, 22, 42-45

impact on peripheral optics of the eye after refractive surgery such as laser‐


3

assisted in situ keratomileusis (LASIK),46, 47 photorefractive keratectomy,48 or

intraocular lens implantation,47

improvement and better understanding of psychophysical tasks (visual field

perimetry, contrast detection tasks) through correction of the peripheral

refractive errors of the eye,27, 49-53

improvement of off‐axis vision in patients with central visual field loss,54-56

development of theoretical model eyes,57, 58

association between age and peripheral refraction/aberrations,35, 59-62

measurement of peripheral refraction in different ethnicities,63

measurement of angle alpha,37, 58 and angle kappa,54

measurement of refractive changes for different gazes,23, 64-69

measurement of peripheral refractive changes for different accommodation

states,34, 44, 67, 70-75

comparison of peripheral refraction between phakic and with intraocular lens‐

corrected eyes,76

determination of peripheral refraction in keratoconus patients,77

assessment of the risk of onset of myopia,78

impact of orthokeratology lenses on peripheral vision and/or the peripheral

refraction profile 36, 79, 80 and

measurement of peripheral refraction with radial refractive gradient

spectacles,52 soft and rigid contact lenses81 and other custom‐designed spectacle

lenses.82, 83

In general, refraction is a well‐known clinical and optometric procedure used to prescribe

spectacle lenses or contact lenses that deliver clear central vision. Due to its clinical relevance,

numerous objective refraction instruments have been developed over the last years to ease

and streamline clinical vision work. Technological improvements have resulted in many

accurate, reliable methods, such as autorefractors and aberrometers. With the interest in

researchers also wanting to perform peripheral refraction, these commercially available

instruments were generally modified so that they permit the measurement of the peripheral

optics of the eye. As yet no instrument is commercially available which has been designed

with the designated purpose of measuring peripheral refractive errors rapidly and precisely.


4

In this review, previous investigations into peripheral vision of the human eye and methods of

peripheral refractive error measurement will be discussed and obstacles relating to current

measurement techniques ascertained. Information on preference and usefulness of certain

peripheral refraction techniques and suggestions for future technology and research work will

also be given.

1.2 Peripheral Vision

For the measurement of peripheral vision it is important to understand the optical and

physiological factors in the periphery of the eye and to identify stimuli that are most

useful for peripheral vision testing.

Optical factors affecting quality of peripheral vision are refractive error, diffraction,

scatter and aberrations such as high levels of oblique astigmatism, curvature of the field

and horizontal coma. Existence of oblique astigmatism induced by the oblique angle of

the incident light has been known for many years. As early as 1801, Thomas Young

stated that the eye’s “imperfection is partly owing to the unavoidable aberration of

oblique rays, but principally to the insensibility of the retina”.84

Insensitivity of the peripheral retina can be explained by the receptive fields and a

number of neural factors which gradually change from the macula to the periphery,

affecting different aspects of retinal image quality. This includes size, spacing, function,

alignment and distribution of retinal photoreceptors, the rods and cones.85 Whereas the

peripheral retina is dominated by rods, good detectors of motion, the macula area

consists mainly of cones, which are essential for resolution of fine detail, form and

colour detection.

The Troxler effect, discovered in 1804,86, 87 is another factor influencing peripheral vision. This

effect describes an optical cognitive phenomenon whereby a stimulus in the peripheral vision

fades away when a central stimulus is fixated in steady gaze for several seconds. This

phenomenon is due to the adaptation of neurons in the visual system and may form an

obstacle to peripheral vision testing.


5

Physical factors influencing peripheral image quality include peripheral restrictions from

the morphology of eye lids or eye lid abnormalities. The morphology of the eye lids

differs between some ethnic populations, most notably between East Asians and

Caucasians. Studies have shown that a smaller palpebral fissure size, as common in Asian

eye lids, can have an impact on refractive error.88-91

1.2.1 Methods of Testing Peripheral Vision

Central vision is commonly measured by use of a resolution target, such as a logMAR

Bailey‐Lovie chart, in which letters need to be identified. Considering the neural

differences associated with central and peripheral retinal sampling, it has been

suggested to use two different testing procedures for on‐axis and off‐axis vision tests.

Campbell and Gubisch92 showed that resolution in the peripheral visual field is limited

much more by neural factors, due to the reduced density of the retinal ganglion cells

than by optical factors. While detection acuity remains high with increasing eccentricity,

resolution acuity decreases drastically.93-95

There are numerous different peripheral vision tests reported in the research literature,

including motion detection tests such as high‐pass resolution perimetry,54, 96 the

movement of a white square on a black background,97, 98 contrast detection sensitivity

tests using a Gabor stimulus27, 99 or gratings55, 93, 100-103 and resolution tests using the

tumbling‐E letters,21, 100 Landolt C21, 53 or number identification.55 Due to evidence

suggesting peripheral resolution is sampling‐limited, it has been recommended to use

contrast detection sensitivity tests for subjective assessment of peripheral image

quality.27, 101

Several studies have investigated the impact of refractive blur on assessing quality of

peripheral vision using different stimuli.94, 95, 104 Overall, it has been demonstrated that

detection acuity varies strongly with defocus, whereas resolution acuity for high contrast

targets is unaffected by peripheral defocus. The difference between the two acuity

thresholds depends on target properties.101 A decrease in spatial frequencies, as well as

in luminance levels of the stimulus, will reduce detection acuity to a point where it

eventually aligns with resolution acuity, and both will be contrast‐limited.


6

Objective methods such as assessment of point‐spread and line‐spread function using a

double‐pass technique have also been used for evaluation of peripheral image quality.

For larger peripheral angles, the higher order aberrations become more prominent,

impairing the point‐spread or line‐spread function and consequently the peripheral

visual performance.105-107

Correction of peripheral refractive errors is strongly pupil size‐dependent but has shown

to improve image quality and, with that, detection of contrast and movement.38, 54, 55, 93,

97, 108, 109 However, due to the clinical and optometric focus on central refractive error

and only marginal improvement in peripheral resolution acuity, it has often been

discounted, even though peripheral detection acuity can be improved.94 With the current

knowledge that peripheral refraction can influence refractive development, the

assessment of peripheral vision has also become of increased interest to researchers.

Thus, methods and stimuli should be selected carefully when testing peripheral vision.

1.3 Peripheral Refractive Error Measurement Techniques

That visual performance decreases as visual field angle increases has been known for

more than two centuries, when Thomas Young84 indicated that the eye’s “whole extent

of perfect vision is little more than 10 degrees… the imperfections begin within a degree

or two of the visual axis”. First measurements of peripheral refraction were performed

by Ferree and co‐workers in 1931.68

Table 1.1 provides a comprehensive summary on authors and their particular techniques

used for the measurement of peripheral refractive errors. Peripheral refractive errors

were usually measured in steps of 5° or 10°, with techniques such as subjective

refraction, double‐pass technique, manual optometers, retinoscopy, or more common

objective instruments, such as autorefractors, photorefractometers or aberrometers.

Dependent on the instrument modification and study purpose, researchers may either

refer to angles measured with respect to the visual field24, 40, 64 or the retina23, 34, 71 or the

fixation direction.64 The peripheral angles shown in Table 1.1 correspond to the visual

field.


7

Table 1.1: Summary of all authors with their peripheral refraction technique used.

The table fields indicate the direction of the maximum peripheral angles tested. All angles refer to the visual field: N stands for nasal, T for temporal, S for superior and I for inferior. * the participants preferred eccentric retinal locus was measured.

Author Year

Method

Subjective

Refraction

Retinoscopy Manual

Optometer

Double‐Pass

Technique

Autorefraction Photorefraction Aberrometry

Ferree et al. 68 1931 60° N/TFerree et al. 110 1932 60° N/TFerree & Rand 111 1933 60° N/TRempt et al. 18 1971 60° N/THoogerheide et al. 12 1971 60° N/TRonchi 112 1971 60° TLeibowitz et al. 97 1972 80° TLotmar & Lotmar 14 1974 60° N/TMillodot & Lamont 21 1974 60° T 60° T 60° TJohnson & Leibowitz 98 1974 80° TRempt et al. 104 1976 60° NJennings & Charman 38 1978 40° N/TMillodot 15 1981 60° N/TJennings & Charman 105, 113 1981 45° N/TRovamo et al. 102 1982 30° TMillodot 41 1984 40° N/TSmith et al. 70 1988 60° TScialfa et al. 59 1989 40° TDunne & Barnes 114 1990 40° N/TNavarro et al. 106 1993 60° N/TDunne et al. 37 1993 40° N/T 40° N/TArtal et al. 93, 115 1995 40° NThibos et al. 101 1996 30° N 30° NWang et al. 27 1996 40° N 40° N 40° NWilliams et al. 108 1996 40° NNavarro et al. 116 1998 40° TAnderson & Thibos 100 1999 50° TGuirao & Artal 107 1999 45° TLove et al. 39 2000 35° N/TMutti et al. 17 2000 30° NGustafsson et al. 25 2001 60° N/TSeidemann et al. 23 2002 45° N/T 25° N/TAtchison and Scott 31 2002 40° N/TGustafsson et al. 117 2002 *Walker and Mutti44 2002 30° NAtchison 29 2003 40° N/T 40° N/TAtchison et al. 32 2003 40° N/TGustafsson & Unsbo 54 2003 *Schmid 19 2003 15° N/T/S/IJackson et al. 28 2004 20° NLogan et al. 13 2004 40° N/TAtchison 118 2004 40° N/TPaysse et al.119 2004 20°


8

Author Year

Method

Subjective

Refraction

Retinoscopy Manual

Optometer

Double‐Pass

Technique

Autorefraction Photorefraction Aberrometry

Atchison et al. 30 2005 35° N/TChui et al. 103 2005 10° N & 15°TLundström et al.56 2005 * *Ma et al. 40 2005 35° N/TLundström et al. 99 2005 30° N 30° N 30° N 30° NCharman & Jennings 35 2006 35° N/T 35° N/TCharman et al. 36 2006 34° N/TAtchison et al. 24 2006 35° N/T/S/IAtchison et al. 120 2006 5° T 5° N/TAtchison 121 2006 40° N/TMutti et al. 16 2007 30° NRadhakrishnan et al. 65 2007 30° N/TLundström et al. 53 2007 20° NDonovan et al.122 2007 30° N/T 30° N/T 30° N/TLundström et al. 55 2007 20° T/ * 20° T/ *Calver et al. 34 2007 30° N/TRadhakrishnan & Charman 66 2008 30° N/TBerntsen et al. 33 2008 30° N/T 30° N/TMathur et al. 123 2008 21° N/THung et al.60 2008 45° N/T/S/IWhatham et al.71 2009 40° N/TDavies & Mallen73 2009 30° N/THuang et al.124 2009 45° N/TMathur et al.64 2009 34° N/TMathur & Atchison79 2009 34° N/T 21° N/TQueirόs et al.75 2009 20° N/TLundström et al.67 2009 40° N/T 20° S/ILundström et al.125 2009 30° NTabernero & Schaeffel42 2009 45° N/TTabernero et al.52 2009 45° N/TTabernero & Schaeffel74 2009 40° N/TFedtke et al.126 2009 30° N/TMathur et al.127 2009 21° N/THo et al.72 2009 40° N/TLin et al.83 2010 40° N/TMathur et al.61 2010 21° N/TWei & Thibos128 2010 15° N/TChen et al.43 2010 40° N/T 32° S/ISankaridurg et al.82 2010 40° N/TKang et al.63 2010 35° N/TAtchison et al.77 2010 21° N/TQueirόs et al.80 2010 35° N/TMutti et al.78 2010 30° NShen et al.81 2010 30 ° N/TSng et al.129 2010 30° N/TBaskaran et al.130 2011 40° N/T 20° ITabernero et al.131 2011 45° N/TBaskaran et al.62 2011 40° N/T 20° I


9

1.3.1 Subjective Peripheral Refraction

In general, subjective refraction is designated as the “gold standard” for on‐axis

refraction, particularly for the purpose of prescribing optical correction devices. A

literature review by Goss and Grosvenor132 concludes that central subjective refraction

provides reliable refraction measurements within 0.25D to 0.50D and suggests this

technique always be conducted for refinement of objective refraction results.

In general, peripheral refractive errors can be obtained subjectively through

manipulation of the refractive state by introducing trial lenses with different powers into

the peripheral viewing path. The lens that maximises acuity will be determined to

correct the peripheral refractive error of the eye in the appropriate peripheral angle.

Table 1.2 shows all authors who reported on peripheral subjective refraction

measurements. Most of them also compared the results to other instruments.

Lundström et al.99 tried to use subjective refraction as the “gold standard” technique not

only for central but also peripheral measurements.

Table 1.2: This table shows all authors and their study set‐ups for the measurement of peripheral subjective refraction.

Author Year Peripheral Stimulus Acuity Pupil Max. Angle

(°) tested

Test

distance

(metres)

Subjective

refraction was

compared to …

Ronchi 112 1971 Point‐like target

Perception of

point‐like target

Non‐

cycloplegic60 1.00 ‐

Millodot and

Lamont 26 1974

Resolution target –

Landolt C

Resolution acuity

(logMAR)

Non‐

cycloplegic60 1.10

Retinoscopy

Hartinger

optometer

Thibos et al. 101 1996

High frequency

aliased stimuli –

Contrast detection

and resolution task

Spatial frequency

(cycles/degree)

Non‐

cycloplegic30 ‐ Retinoscopy

Wang et al. 27 1996

Contrast detection

target – horizontal

and vertical

sinusoidal gratings

Detection acuity

(cycles/degree)

Non‐

cycloplegic40 distant

Retinoscopy

Canon Autoref R‐1

Lundström et al. 99

2005

Contrast detection

target – changing

contrast

Contrast sensitivity

(logCS)

Non‐

cycloplegic30 3.00

Retinoscopy

PowerRefractor

Hartmann‐Shack

Atchison et al. 120 2006

Contrast detection

target – Gabor stimuli

Detection acuity

(log of grating

detection acuity)

Non‐

cycloplegic5 8.00 COAS


10

The first peripheral subjective refraction measurements were reported by Ronchi112 in

1971, who studied the relationship between absolute luminance threshold and retinal

eccentricity. The participant, who was experienced in visual experiments, was asked to

view and judge a point‐like peripheral target. Correction of oblique astigmatism up to

60° was achieved using cross‐cylinders.

For four participants, Wang et al.27 and Millodot and Lamont21, 27 compared peripheral

subjective refraction results with two other refraction techniques. They found that with

increasing eccentricity, the agreement of peripheral subjective refraction was closer to

peripheral retinoscopic refraction rather than to results obtained with an optometer or

autorefractor, which revealed highest astigmatism results. Lundström et al.’s 99

peripheral subjective refraction data revealed a larger spread compared with the

Hartmann‐Shack sensor, photorefractor and retinoscopy. Atchison et al.’s120 study

investigated refractive error and aberration variations in the central visual field. They

undertook subjective refraction in the temporal visual field at 2.2° and 5°. Comparison

with refractive errors obtained using the Complete Ophthalmic Analysis System (COAS)

wavefront sensor showed that subjective refraction exhibited a smaller refractive change

(0.37D) between central and 5° measurements than using the wavefront sensing

technique (0.71D).

As mentioned previously, there are several different peripheral vision test targets, which

make a direct comparison or assessment of peripheral refractive error results between

studies difficult. Whereas Wang et al., Lundström et al. and Atchison et al. used contrast

detection stimuli to measure the peripheral refractive state of the eye, Millodot and

Lamont used a resolution target, the Landolt C, while Ronchi relied on the participant’s

shape perception of the peripheral target. Thibos et al.101 highlighted a difference in

peripheral acuity results between spatial resolution and contrast detection tasks, which

reinforces the importance of stimuli choice when assessing peripheral vision or when

measuring peripheral subjective refraction.

Since peripheral subjective refraction requires the participant to pay constant attention

in order to try and detect the target stimulus, it is a difficult and exhausting technique to


11

perform, in particular if there are multiple or large peripheral angles to be tested.99 The

difficulties are mainly due to optical factors such as the increase in peripheral

astigmatism, poor paraxial retinal image quality as well as neural factors, which are

stimuli‐dependent. The previously mentioned Troxler effect can also have an impact on

acuity measurements.86 As a possible result of all these factors, subjective peripheral

refraction measurements have been found to yield highly variable results99 and

measurements are often limited to axis approximations of 90° and 180° when

astigmatism is determined.27 No studies were found reporting on repeatability for

peripheral subjective refraction.

1.3.2 Retinoscopy

Retinoscopy, particularly streak retinoscopy, is a refraction technique that has been used

successfully for the precise measurement of central refraction. The relative movement of

the reflex from the participant’s retina is observed and, with the aid of lenses,

neutralised, providing the eye’s refractive error. The main advantage is its accuracy

when used in pediatric participants and performed by a skilled clinician because it

requires no co‐operation from the participant. Since the participant is not actively

involved in the process retinoscopy is considered an objective technique, however

assessment of the retinoscopic reflex requires an experience‐dependent subjective

decision by the practitioner.

Several studies have used this technique to also measure the peripheral optics of the eye

(Table 1.3).

The first peripheral retinoscopic measurements were conducted by Rempt et al.,18 who

on the basis of their results, introduced the skiagram. This is a peripheral refractometric

diagram used for the categorisation of different peripheral refractive error patterns. For

the large sample sized study they preferred the use of a retinoscope rather than the

optometer technique used by Ferree et al.,68, 110, 111 since this method would have been

“too cumbersome” for the peripheral data to be collected on 442 participants.

Hoogerheide et al.12 and Lotmar and Lotmar14 targeted their investigations in reference

to the refractive error results presented by Rempt et al.18 Hoogerheide and co‐workers’

interests were in finding a characteristic pattern that can predict whether one


12

emmetropic person is more prone to develop myopia than another. Their finding showed

that young emmetropic pilots with hyperopic defocus in the peripheral field were at risk

of developing myopia. Lotmar and Lotmar investigated whether the non‐cycloplegic

peripheral refraction data provided by Rempt et al. fit the theoretical model eye

proposed by Lotmar57 in 1971. Close agreement between the measured and calculated

peripheral astigmatism values was only found up to about 30° eccentricities, thereafter

the theoretical eye model did not fit well with the experimental findings.

Table 1.3: This table shows all authors and their study set‐ups for the measurement of peripheral retinoscopy.

Author Year Pupil Max. Peripheral

angle (°) tested

Test distance to

fixation target

(metres)

Retinoscopy was

compared to …

Rempt et al. 18 1971 cycloplegic 60 3 ‐

Leibowitz et al. 97 1972 ‐ 80 0.787 ‐

Millodot and

Lamont 26 1974 cycloplegic 50 1.1

Subjective refraction

Optometer

Johnson and

Leibowitz 98 1974 non‐cycloplegic 80 0.77 ‐

Rempt et al. 104 1976 cycloplegic 60 3 ‐

Rovamo et al. 102 1982 ‐ 30 ‐ ‐

Scialfa et al. 59 1989 ‐ 40 0.83 ‐

Wang et al. 27 1996 non‐cycloplegic 40 distant Subjective refraction

Autorefraction

Anderson and

Thibos 100 1999 non‐cycloplegic 50 3 ‐

Jackson et al. 28 2004 cycloplegic 20 0.4 ‐

Paysse et al.119 2004 cycloplegic 20 0.4 ‐

Lundström et al. 99 2005 non‐cycloplegic 30 3

Subjective refraction

Photorefraction

Wavefront Sensor

Donovan et al.122 2007 cycloplegic 30 ‐ Autorefraction

Wavefront Sensor

Hung et al.60 2008 cycloplegic 45 0.5 ‐

Huang et al.124 2009 cycloplegic 45 0.5 ‐

Interestingly, two studies conducted by Leibowitz et al.97 and Johnson and Leibowitz98

were able to provide results for measurements of up to 80° in three participants. In

contrast, Millodot and Lamont21 were unable to obtain reliable retinoscopic readings

beyond 50°. Furthermore, Leibowitz et al.97 and Johnson and Leibowitz98 measured

peripheral astigmatism that is far below the values of the majority of published data.

Even though both studies reported measuring far off‐axis refractive errors, no comment


13

was made as to whether it was difficult to perform or whether it can be assumed to be

reliable. However, literature has shown that the majority of studies encountered

difficulties when performing peripheral retinoscopy, in particular for large angles.26, 28, 59

The main issue is that, as measurement angles increase, the pupil appears elliptical to

the examiner and aberrations increase in the periphery. As a result the aberrated reflex

at large angles may be split or behave contradictorily in central and peripheral parts of

the pupil and consequently, it is more complex and difficult to precisely define. This

difficulty was found to be most cumbersome for the task of determining the axis of the

astigmatism.18, 21, 28, 99

Jackson et al.28 and Paysse et al.119 performed peripheral retinoscopy under cycloplegia

in angles up to 20° in order to investigate how much impact slight off‐axis retinoscopy

has in clinical practice. They found a clinically important increase in astigmatism by an

average of 3% per degree of eccentricity. Paysse et al. concluded that “even small

degrees of eccentricity can result in significant errors in refractive error determination.”

Zadnik et al.133 reported that the repeatability of the central retinoscopic measurements

under cycloplegia is poor. The effects of paralysing accommodation through cycloplegia,

which inhibit refraction stability and increase aberrations due to the dilated pupil, would

explain the generally poorer repeatability using cycloplegic retinoscopy. Table 1.3 shows

that half the studies conducted peripheral retinoscopy under cycloplegia, making results

not directly comparable to the refraction results measured under natural pupil

conditions.

Wang et al.27 measured eccentricities of up to 40° (n=3) and Millodot and Lamont26 up to

50° (n=4). They reported that the results were in good agreement with those of

peripheral subjective refraction, the Canon R‐1 autorefractor27 and the manual

optometer (Zeiss Hartinger) respectively.26 Compared to other subjective and objective

techniques, Lundström et al.99 found in a study of 50 participants a significant difference

in cylinder axis when peripheral retinoscopy was performed. They also showed

significant differences (mean difference of ‐0.73 D) in 30° spherical equivalent values

between peripheral retinoscopy and subjective refraction, whereby the retinoscopic


14

values tended towards hyperopia. However, carrying out non‐cycloplegic retinoscopic

refraction reduced the pupil diameter, due to the bright light used, and this was thought

to be the reason for the difference to subjective refraction technique, which was

obtained with normal pupil diameter.

In two recent studies, Hung et al.60 and Huang et al.124 conducted peripheral retinoscopy

in monkeys under cycloplegic conditions. Alignment was achieved with the help of an arc

perimeter and by monitoring the position of the first Purkinje images as a reference.

Good agreement was found between the two examiners that measured the refraction in

the peripheral visual field up to 45°. Furthermore, the mean peripheral refraction result

was very repeatable. There was no mention whether they had any difficulties with

respect to the retinoscopic reflex or the alignment of positions of the monkeys.

Overall, it can be concluded that, similar to peripheral subjective refraction

measurements, peripheral retinoscopy has shown difficulties in determining the axis of

the astigmatism.25, 99 Moreover, if numerous peripheral measurements are required, this

technique also appears to be very protracted and inconvenient, for both participants and

examiners.

1.3.3 Manual Refractometer – Optometer

A different principle for the measurement of refraction of the eye was discovered more

than four centuries ago by Christian Jesuit Scheiner.134 The so‐called Scheiner disc is a

disc with two pinholes that enables identification of the point at which an eye focuses

(Figure 1.2). Having the disc aligned in front of the participant’s visual axis and sending

parallel light rays from a distant object light source through the two apertures into the

eye, generates two small bundles of light. A single focus image is formed on the retina if

the eye is emmetropic (Figure 1.2 a). If an ametropic eye is measured, two light spots

will fall on the retina (Figure 1.2 b and c). To measure the refractive error of the eye, the

position of the object has to be adjusted so that the participant can see one light spot.

This can be done by moving the object mechanically, or by placing a convex lens in the

viewing path, as done in the optometer instrument. Whereas first optometers were

purely subjective instruments, requiring the participant to align the target, later so‐


15

called “objective” optometers were operated by the examiner, who adjusted the target

on the participant’s retina. Being performed through assessment by the examiner, this

technique is not truly objective either. Due to improvements in technology with regards

to fully objective instruments, optometers are no longer built. However, this well‐known

basic principle of the Scheiner disc finds application in many improved and automated

current autorefractors and aberrometers.134

Figure 1.2: Scheiner disc principle.

The Zeiss Hartinger optometer and the Topcon refractometer Model III are based on the

coincidence principle, which require vernier adjustment of the test targets (two sets of

three vertical bars and two sets of two horizontal bars) by the examiner. The examiner

observes the retinal images and aligns the test targets to be in coincidence. The use of a

second pair of targets perpendicular to the first also permits the measurement of

astigmatism. Besides coincidence optometers, there are other optometers (Rodenstock)

based on the focus principle, whereby the test target has to be adjusted to sharpest

focus.

Table 1.4 lists authors which reported on peripheral refraction measurements performed

with either the Zeiss coincidence optometer (Hartinger optometer) or the Topcon

refractometer Model III. The peripheral measurement were either achieved via eye or

head turn or instrument rotation.


16

Table 1.4: This table shows all authors and their study set‐ups for the measurement of peripheral refraction using an optometer.

Author Year Type of Optometer Pupil

Max.

Peripheral

horizontal

angle (°)

tested

Eye Turn, Head

Turn,

Instrument

rotation

Ferree et al. 68 1931 Zeiss Hartinger

coincidence optometer

cycloplegic and

non‐cycloplegic 60

Eye turn and

instrument

rotation

Ferree et al. 110 1932 Zeiss Hartinger

coincidence optometer

cycloplegic and

non‐cycloplegic 60

Eye turn and

instrument

rotation

Millodot and Lamont 26 1974 Zeiss Hartinger

coincidence optometer non‐cycloplegic 50 ‐

Millodot 15 1981 Topcon Model III non‐cycloplegic 60 Eye turn

Millodot 41 1984 Topcon Model III non‐cycloplegic 40 Eye turn

Smith et al. 70 1988 Topcon Model III non‐cycloplegic 60 Eye turn

Dunne and Barnes 114 1990 Zeiss Hartinger

coincidence optometer non‐cycloplegic 40

Instrument is

rotated

Dunne et al. 37 1993 Zeiss Hartinger

coincidence optometer non‐cycloplegic 40

Instrument is

rotated

Gustafsson et al. 25 2001 Zeiss Hartinger

coincidence optometer ‐ ‐ ‐

Ferree et al.68, 110, 111 measured refraction along the peripheral visual field using a Zeiss

coincidence optometer. They undertook refraction measurements up to 60°. Further

increasing of the eccentricity angle caused the reflected image to be too dim to be

distinguished. They stated that this method was “reasonably feasible, satisfactory and

accurate”. Their set‐up permitted the rotation of the optometer in front of the eye. The

alignment of the eye was achieved with a movable rest attached to a mouthboard, which

contained the impression of the participant’s teeth in wax. Considering the elaborate

procedure to ensure alignment of the eye position for peripheral measurements, this

technique would not have been very convenient, particularly for large‐sample studies.

Sixty years after measurements of Ferree et al.,68, 110, 111 Dunne et al.37, 114 found

measurements with the Zeiss optometer to be inconsistent for peripheral angles greater

than 40°. Gustafsson et al.25 also attempted to use the Hartinger optometer in 2001 and

found great difficulties in measuring peripheral astigmatism.

Since it was the examiner’s task to vernier align the bar targets to coincidence, similar

obstacles as mentioned for peripheral retinoscopy were observed, such as the impact of

peripheral aberrations, which can have a profound effect on the proper adjustment of


17

the optometer targets. Furthermore, the effect of having an elliptical pupil when

measuring through the periphery of the eye reduces the area for the measurement

targets that are focused onto the retina. This finding was mentioned in Smith et al.’s70

study, in which it was noted that for eccentricities larger than 60°, the diameter of the

elliptical pupil is smaller than the outer areas of the target, which are then partially cut‐

off and make adjustment impossible.

1.3.4 Double‐Pass Technique

The double‐pass technique is an ophthalmoscopic method, which was first introduced by

Flamant135 in 1955, enabling the assessment of central retinal image quality. In 1981

Santamaria et al.136 used this method to record double‐pass images of point‐spread

function.

Different experimental set‐ups of the double‐pass techniques were implemented by

different researcher groups.23, 35, 106, 108 The basic principle is that a laser light beam,

usually Helium‐Neon laser, passes first through a neutral density filter to reduce light

intensity and is then spatially filtered by a microscope objective. The beam that expands

from this point source is collimated before entering a small artificial pupil or a slit of a

slit‐lamp that is conjugate with the pupil of the eye. The optical system of the eye then

forms the aberrated image of the point or line source on the retina. The fundus, acting

as a diffuse surface, reflects a small fraction of light and a camera then captures the so‐

called “double‐pass images”. In order to measure the refractive error of the eye, a

focusing lens scans through the double‐pass images and the images corresponding to the

extremes of the Sturm interval are observed. Refraction can be validated by placing the

corrective lens in front of the participant’s eye and the compact image of the least‐

confusion circle will be observable.

Thirteen years after its first on‐axis use, this double‐pass technique has also been

applied for the measurement and evaluation of the peripheral optics of the eye (Table

1.5).

Navarro and Artal106 investigated retinal image quality of point light sources across a

wide visual field, evaluating double‐pass images. Initially, they found paraxial image


18

quality to be much better than previously indicated. They found this to be due to the

loss of paraxial asymmetric aberrations, such as coma and distortion, in the double‐

pass.115 To circumvent this impediment, two alternatives were suggested and

investigated. The first attempt was a modified version of the double‐pass technique,

using different entrance and exit pupil diameters and the second required reconstruction

of the PSF by phase‐retrieval algorithms.107 Both methods provided an estimate of off‐

axis astigmatism and horizontal coma.

Jennings and Charman used the line spread function (LSF) double‐pass technique to

assess image quality across the retina,38 and to correct peripheral refractive errors for

the measurement of the critical fusion frequency113 and to investigate peripheral

refraction changes with age35. For all measurements, they recorded radial and tangential

LSFs in 5° steps up to eccentricities of 45°. Using this double‐pass technique, cylinder

axis determination was limited to 90° or 180°.

Gustafsson et al.25 used a double‐pass technique to measure peripheral astigmatism in

emmetropic eyes in 10° steps up to 60° and found very large individual differences in

oblique astigmatism between 20 eyes. They also repeated the measurements of one

participant on eight different occasions and found a mean standard deviation of the

measured astigmatism over all angles to be 0.60D. The authors also note that the angle

between the sagittal and tangential foci line was different from 90° and that the circle of

least confusion was not in the midpoint of the two foci lines but rather shifted towards

the more hyperopic line.

Seidemann et al.23 used their double‐pass technique for peripheral refraction

measurements up to 45° on 42 participants. Comparison of the photorefraction results

(PowerRefractor) on six participants showed significant correlation. Using a

multimeridional refraction procedure to calculate the average refractive components,

they showed average differences between the spheres of 0.78D and between the

cylinders of 0.85D.


19

Table 1.5: This table shows all authors and their study set‐ups for the measurement of peripheral refraction by use of the double‐pass technique.

Author Year

Double‐Pass Technique

Pupil

Max.

Angle

(°)

tested

Eye or Head

Turn, or

Instrument

Rotation

Double‐pass

technique

was

compared to

…

Apertures Evaluation

Jennings and

Charman 38 1978 Slit

Horizontal and

vertical line

spread function

Non‐

cycloplegic

and

cycloplegic

40 Instrument

is rotated ‐

Jennings and


Horizontal and

vertical line

spread function

Cycloplegic 45 Instrument

is rotated ‐

Jennings and


Horizontal and

vertical line

spread function


is rotated ‐

Navarro and

Artal 106 1993

Hole in

perimeter

Modulation

transfer function

Non‐

cycloplegic 60 Head turn ‐

Artal et al. 93 1995

Equal 3 mm

diameter

pupils in

both passes

Focus positions:

sagittal, tangential

foci and circle of

least confusion

Non‐

cycloplegic 40

Instrument

is rotated ‐

Williams et

al.108 1996

Equal 3 mm

diameter

pupils in

both passes

Focus positions:


foci and circle of

least confusion

Cycloplegic 40 Eye turn ‐

Guirao and

Artal 107 1999

Unequal

pupil

diameters

Focus positions:


foci, circle of least

confusion and

coma

Non‐

cycloplegic 45 Eye turn ‐

Gustafsson et

al. 25 2001

Equal 3 mm

diameter

pupils in

both passes

Focus positions:


foci and circle of

least confusion

Non‐

cycloplegic 60

Instrument

is rotated ‐

Seidemann et

al. 23 2002

Equal 1.5

mm

diameter

pupils in

both passes

Focus positions:


foci and circle of

least confusion

Non‐

cycloplegic 45

Instrument

is rotated

Power

Refractor

Jennings and


Horizontal and

vertical line

spread function


is rotated

Auto‐

refractometer

For most of these peripheral double‐pass techniques, the participants’ head was fixed by

a bite bar and the instrument was rotated in front of the eye. This rotation of the

instrument for each eccentricity angle requires an additional alignment of the second

aperture,93, 108 making it a difficult peripheral refraction procedure to set up. In most


20

studies only few participants were chosen to be measured, which may be due to the

inconvenience of using a bite bar for the alignment.

1.3.5 Autorefraction

Automatic objective refractors (autorefractors, auorefractometers) are fast and easy to

use instruments, which do not require subjective judgments from operators or

participants. For more than two decades they have been used successfully for on‐axis

refraction measurements in ophthalmologic and optometric practices and research

institutions. Most instruments have an integrated function for the measurement of

corneal curvature, which makes them a valuable objective clinical tool.

General problems with some autorefractors can occur due to pseudomyopia caused by

accommodation and inadequate autofogging mechanisms.46, 137-139 Pseudomyopia is

caused by using “closed‐field” autorefractors in which the fixation target is placed at

optical infinity inside the instrument. To avoid instrument‐induced myopia,

autorefraction may be performed under complete cycloplegia. Alternatively, the use of

“open‐view” autorefractors permits fixation and accommodative responses to real‐world

targets external to the instrument.

Only a few autorefractors have been used to measure peripheral refractive errors (Table

1.6). All of them feature a binocular open‐view arrangement through a large beam‐

splitter, avoiding instrument myopia and enabling the fixation of peripheral targets.

These instruments are the Shin‐Nippon NVision K5001, also marketed as the Grand Seiko

WR‐5100K, Shin‐Nippon SRW5000, also marketed as the Grand Seiko WV‐500, the Grand

Seiko WAM‐5500 and the Canon Autoref R‐1. Whereas, the first three instruments

operate on the ring‐autorefraction principle, the Canon Autoref R‐1 operates on the

grating focus principle. Being based on infrared illumination, they all incorporate a

correction factor that adjusts the refraction results to white light. The output refraction

is presented in conventional terms of sphere (S), cylinder (C) and cylinder axis (θ).


21

Table 1.6: This table shows all authors and their study set‐ups for the measurement of peripheral autorefraction.

Author Year Type of Autorefractor Pupil

Max.

peripheralAngle

(°)

Test distance

(metres) Eye or Head Turn

Dunne et al. 371993 Canon Autoref R‐1 Non‐cycloplegic 30 Distant Eye turn

Wang et al. 271996 Canon Autoref R‐1 Non‐cycloplegic 40 Distant ‐

Love et al. 392000 ‐ Cycloplegic 35 Distant ‐

Mutti et al. 172000 Canon Autoref R‐1 Cycloplegic 30 Distant Eye turn

Walker and Mutti44 2002 Canon Autoref R‐1 Non‐cycloplegic 30 Distant Eye turn

Atchison 29 2003

Shin‐Nippon SRW5000 and Canon

Autoref R‐1 Cycloplegic 40 Distant Eye turn

Schmid 192003 Shin‐Nippon NVision K5001 Cycloplegic 15 0.80 ‐

Logan et al. 132004 Canon Autoref R‐1 Cycloplegic 40 0.50 Eye turn

Chui et al.1032005 Shin‐Nippon NVision K5001 Cycloplegic 15 Distant ‐

Atchison et al. 30 2005 Shin‐Nippon SRW5000 Non‐cycloplegic 35 3.30 Eye and head turn

Ma et al. 40

2005 Shin‐Nippon SRW5000 Non‐cycloplegic 35 3.00 Eye turn

Charman and Jennings 35 2006 Shin‐Nippon SRW5000 Non‐cycloplegic 35 6.00 ‐

Charman et al. 36 2006 Shin‐Nippon SRW5000 Non‐cycloplegic 34 3.00 Eye turn

Atchison et al. 24 2006 Shin‐Nippon SRW5000 Non‐cycloplegic 35 3.30 Eye turn

Mutti 16 2007 Canon Autoref R‐1 & the Shin‐Nippon

NVision K5001 Cycloplegic 30 ‐ Eye turn

Calver et al. 342007 Shin‐Nippon Non‐cycloplegic 30 2.50 and 0.40 Eye turn

Donovan et al.122 2007 Shin‐Nippon NVision K5001 cycloplegic 30 2.5 Head turn

Radhakrishnan and Charman 66 2008 Shin‐Nippon SRW5000 Non‐cycloplegic 30 2.00 Eye and head turn

Berntsen et al. 33 2008 Shin‐Nippon NVision K5001 Cycloplegic 30 1.75 Head turn

Queirόs et al.75 2009 Grand Seiko WAM‐5500

Cycloplegic & Non‐

cycloplegic 20 Distant ‐

Whatham et al.71 2009 Shin‐Nippon NVision K5001 Non‐Cycloplegic 40 2.00, 0.40 and 0.30 Head turn


22

Author Year Type of Autorefractor Pupil

Max.

peripheralAngle

(°)

Test distance

(metres) Eye or Head Turn

Davies and Mallen73 2009 Shin‐Nippon SRW5000 Non‐Cycloplegic 30

Distant, 1.00, 0.50

and 0.33 Eye Turn

Mathur and Atchison79 2009 Shin‐Nippon SRW5000 Non‐Cycloplegic 34 3.30 Eye Turn

Mathur et al.64 2009 Shin‐Nippon SRW5000 Cycloplegic 34 3.30 Eye and Head Turn

Ho et al.722009 Shin‐Nippon NVision K5001 Non‐Cycloplegic 40 2.5 Head Turn

Fedtke et al.1262009 Shin‐Nippon NVision K5001 Non‐Cycloplegic 30 2.5 Head Turn

Lin et al.832010 Shin‐Nippon NVision K5001 Cycloplegic 40 3.0 Head Turn

Sankaridurg et al.82 2010 Shin‐Nippon NVision K5001 Cycloplegic 40 2.5 Head Turn

Chen et al.432010 Shin‐Nippon Cycloplegic 40 ‐ Eye Turn

Kang et al.632010 Shin‐Nippon NVision K5001 Non‐Cycloplegic 35 ‐ ‐

Queirόs et al.80 2010 Grand Seiko WAM‐5500 Non‐Cycloplegic 35 2.5 Eye Turn

Mutti et al.78 2010

Canon Autoref R‐1 & the Shin‐Nippon

NVision K5001 Cycloplegic 30 ‐ Eye Turn

Sng et al.1292010 Grand Seiko WAM‐5500 Cycloplegic 30 0.33 Eye Turn


23

Specifically, the mode of operation of the Shin‐Nippon SRW5000 relies on a near infrared

850 nm ring target that is projected onto the retina. A small fraction of light reflects

from the retina and the reflected ring image containing the error information of the eye

is captured on a charged couple detector (CCD). The images are analysed along multiple

meridians to determine the sphero‐cylindrical refraction output. As the Shin‐Nippon

SRW5000 requires pupil sizes of at least 3.0 mm,140 room illumination should be adjusted

accordingly.30 This autorefractor was shown to be a reliable and valid instrument for on‐

axis measurements in adults137, 141 as well as children.140

The successor of the Shin‐Nippon SRW5000 is the Shin‐Nippon NVision K5001 that uses

three arcs of infrared light arranged around a smaller diameter (Table 1.7). It allows

measurements with pupil sizes of ≥2.3 mm instead of the ≥3.0 mm of the former

version.140 A smaller pupil size can give more accurate results for measurements in small

peripheral angle steps and it also can have advantages when measuring in very large

eccentric angles, whereby the smaller target diameter fits more easily into the horizontal

minor axis of the elliptical pupil. For central refraction measurements, the Shin‐Nippon

NVision K5001 was shown to be more reliable than subjective refraction.139

The most recent "open‐view" autorefractor, the Grand Seiko WAM‐5500, is based on the

same operation principle as the Shin‐Nippon NVision K5001, with the additional

advantage that it permits the dynamic recording of refraction (accommodation) as well

as the measurement of the pupil diameter during accommodation.

Table 1.7: Features of autorefractors used for peripheral refractometry.

Canon Autoref

R‐1

Shin‐Nippon

SRW5000

Shin‐Nippon

NVision K5001

Grand Seiko

WAM 5500

Wavelength of the

instrument (nm) 850 930 Not known Not known

Required pupil

diameter (mm) 3.5 3.0 2.3 2.3

Number of

meridians 3 All All All

Fixation Open‐view Open‐view Open‐view Open‐view

Measuring targets 3 square wave

gratings Ring target 3 arcs 3 arcs


24

The Canon Autoref R‐1 is, along with the other three autorefractors, an open‐field

instrument, but of an earlier generation. Its measurement light source emits in the near

infrared wavelength at 930 nm. Even though the Canon R‐1 is no longer commercially

available, it is still in use in some optometric practices. Its widespread past and present

use for research purposes warrants its inclusion in this discussion. The refraction

principle is different to the other three autorefractors; it is based on the grating focus

principle. Three illuminated square wave grating targets arranged in 60° to each other

are adjusted for best output position via a detector system. Although, central refraction

was found to be reliable and relatively valid, accuracy was reduced for the cylinder

component result. It was assumed that the refractive accuracy, in particular for cylinder

and axis values, could be improved by increasing the number of meridians of the

instrument.142 As the Canon R‐1 requires a minimum pupil diameter of at least 3.5 mm,

aberrations such as spherical aberration may have some impact on refraction results.

Compared to central retinoscopy or subjective refraction, the Canon R‐1 showed to be a

reliable refraction instrument for on‐axis measurements.133

Several research groups compared peripheral refraction measurements obtained with

the Canon Autoref R‐1 to other peripheral refraction techniques. Wang et al.27 compared

this instrument to subjective and retinoscopic peripheral refraction. Even though close

agreements were found between objective and subjective methods, considerable

differences were found between peripheral subjective refraction and the Canon R‐1

results measured for the 40° eccentricity angle in the 90° meridian. In addition, Atchison

et al.29 compared peripheral refraction results of the Canon R‐1 with two other

techniques, the Shin‐Nippon SRW5000 and the Hartmann‐Shack wavefront sensor. The

poorest agreements between all instruments were found in conjunction with the Canon

R‐1, suggesting this to be the least comparable instrument. Dunne et al.37 used the Zeiss

Hartinger coincidence optometer and the Canon R‐1 to investigate an association

between peripheral astigmatic errors and angle alpha. Although, there was no significant

difference found between the two refractor results, the graphed results indicate a shift

towards greater astigmatic error measured with the Canon R‐1. They also reported

problems measuring peripheral refraction on the Canon R‐1 for eccentricities greater

than 30° due to the limitations of this instrument on the required pupil size.


25

Whereas most studies with the Shin‐Nippon SRW5000 performed peripheral refraction

measurements along the horizontal visual field meridian, one study by Atchison et al.24

also measured the vertical meridian. By use of beamsplitters and a light emitting diode

(LED), the participant was able to fixate the target in 5° steps upwards or downwards. By

use of this set‐up, only right eyes could be measured, and when gazing downwards, the

upper eye‐lid required holding up to ensure a valid measurement.

Charman and Jennings35 used a double‐pass technique and the Shin‐Nippon SRW5000 to

investigate the factor of peripheral refractive error changes with age. Whereas, the

baseline data were obtained using a double‐pass technique, 26 years later they used the

Shin‐Nippon SRW5000 for the measurement of peripheral refraction. Measurements

revealed a central hyperopic shift over time. However, using two different measurement

techniques, which are based on different operation principles and under different study

protocol conditions such as performing cycloplegic refraction with double‐pass

technique and non‐cycloplegic refraction with the autorefractor, limits a direct

comparison.

Davies and Mallen73 modified the Shin‐Nippon SRW5000 by attaching a rotating +3.00D

Badal system and an axially movable Maltese cross target, to enable both, central and

peripheral refraction measurements at different accommodative states of 0.00D, 1.00D,

2.00D and 3.00D.

Berntsen et al.33 compared peripheral refraction results of the Shin‐Nippon NVision

K5001 with the COAS aberrometer and found equivalent measurements, but having a

more hyperopic spherical equivalent shift with the Shin‐Nippon NVision K5001. Donovan

et al.122 also compared the Shin‐Nippon NVision K5001 autorefractor with the COAS

aberrometer and streak retinoscope Using head turn, peripheral refraction was

measured in 28 participants. They found much lower values in oblique astigmatism

measured with the aberrometer when compared to the two other methods.

Fedtke et al.126 investigated the impact of pupil misalignment on peripheral refraction

measurements when using the Shin‐Nippon NVision K5001. They showed that refraction


26

measurements became more sensitive to pupil misalignment as visual field angle

increased.

Like Davies and Mallen73, Whatham et al.71 and Ho et al.72 also aimed to understand the

impact of accommodation on peripheral refraction profiles. Using the Shin‐Nippon

NVision K5001, they approached the near viewing of targets for peripheral refractometry

differently. An instrument head was mounted on top of the Shin‐Nippon NVision K5001,

which had not only small laser diodes attached to emit visible red light towards the

selected peripheral field positions (up to 40°), but it also had adjustable near viewing

targets at 0.40 and 0.30 m attached to it. In both studies the participants were asked to

turn the head towards the peripheral targets.

With the increased interest in measuring peripheral refraction with open‐view

autorefractors, the latest model, the Grand Seiko WAM‐5500, has now also been

adopted for this purpose.75, 80, 129

Overall, it has been shown that commercially available autorefractors are great objective

tools and they produce similar peripheral refraction results to other techniques.29

Nevertheless, measurement of peripheral refraction with these instruments remains

time‐consuming as they require continuous re‐alignments by the participant towards the

provided peripheral fixation targets as well as continuous re‐alignment of the instrument

axis with the centre of the pupil by the operator. From the four autorefractors used for

peripheral refraction, the Shin‐Nippon NVision K5001 and the Grand Seiko WAM‐5500

are likely to be the most useful instruments for peripheral measurements. This is mainly

due to their smaller pupil size requirement, which is of particular advantage for the

measurement of large peripheral angles. Moreover, the ring‐autorefraction principle

appears to have advantages over the grating focus principle of the Canon Autoref R‐1,

which showed limitations with respect to only using three meridians for the

determination of astigmatism.

Lastly, it should be noted that there are commercially available hand‐held autorefractor

instruments, such as the Retinomax (Nikon Corp.) and the Welch Allyn SureSight Vision


27

Screener, which have proven to be convenient screening tools in schools and nursing

homes.143 Refraction measurements were reported to be in moderate agreement with

each other, though showing large variability in axis measurements.144 Comparison with a

table‐mounted autorefractor and subjective central refraction has shown that these

hand‐held autorefractor instruments overestimate myopia.145, 146 As such, it was

suggested that portable autorefractors should be used as screening tools only, and not

for research purposes.144, 145 Even though these instruments are easy to handle and do

not require off‐axis fixation, no studies were found reporting on the use of these hand‐

held autorefractors for peripheral refraction.

1.3.6 Photorefraction

In photorefractometry, the eye is illuminated by a point light source and the reflected

image in the pupil plane is observed or photographed. The refractive error of the eye can

then be determined by means of distribution analysis of the illumination in the pupil.

The PowerRefractor instrument was developed at the University Eye Hospital Tübingen

and is purchasable through PlusOptix (Erlangen, Germany). It operates on this

photorefraction principle and uses infrared illumination (850 nm). The working distance

is 1 meter. Central refraction with the PowerRefractor has shown to have “major

advantages over current autorefractors in that it is faster, measures both eyes at once,

and gives interpupillary distance, pupil size and information on the alignment of the eyes

at the same time”.147 Choi et al.147 measured central refractive errors in children with the

PowerRefractor and a “closed‐field” autorefractor (Nidek AR800) and found the

PowerRefractor detected smaller amounts of myopia, which could also be attributed to

the pseudomyopia caused by the autorefractor.

As indicated in Table 1.8, this technique has also been used for peripheral

photorefraction measurements. Gustafsson et al.54, 117 tested participants with central

visual field loss and attached concentric rings in 5° steps up to 25° to the PowerRefractor

in order to allow the participant to orientate and to find their normal eccentric gaze. The

purpose of their study was to determine and correct the refractive error of the

participant’s preferred retinal locus. Overall, this technique was found to be very useful

and repeatable.


28

Table 1.8: This table lists all authors and their study set‐ups for the measurement of peripheral photorefraction.

Author Year Type of

Photorefractor Pupil

Max.

horizontal

angle (°)

tested

Test

Distance

(metres)

Eye or

Head

Turn

Photorefractor

was compared

to …

Seidemann et al. 23 2002 PowerRefractor

Non‐

cycloplegic 25 1

Eye

Turn

Double‐pass

technique

Gustafsson et al. 117 2002 PowerRefractor

Non‐

cycloplegic 25 1

Eye

Turn ‐

Gustafsson et al. 54 2003 PowerRefractor

Non‐

cycloplegic 25 1

Eye

Turn ‐

Lundström et al. 99 2005 PowerRefractor

Non‐

cycloplegic 30 1

Eye

Turn

Subjective

Refraction

Hartmann‐Shack

Technique

Retinoscopy

Lundström et al. 56 2005 PowerRefractor ‐ 35 1

Eye

Turn

Hartmann‐Shack

Technique

Lundström et al. 55 2007 PowerRefractor

Non‐

cycloplegic 35 1

Eye

Turn

Hartmann‐Shack

Technique

Tabernero and

Schaeffel42 2009

Eccentric

Scanning

Photorefractor

Non‐

cycloplegic 45 ~0.3 ‐ ‐

Tabernero et al.52 2009

Eccentric

Scanning

Photorefractor

Non‐

cycloplegic 45 1

Eye

Turn

to

read

text

‐

Tabernero and

Schaeffel74 2009

Eccentric

Scanning

Photorefractor

Non‐

cycloplegic 45

2.0, 0.5,

0.25 ‐ ‐

Tabernero et al.131 2011

Eccentric

Scanning

Photorefractor

Cycloplegic 45 ‐ ‐ ‐

Seidemann et al.23 also found the PowerRefractor to be a convenient technique. Using

letters as eccentric fixation targets up to 25°, the participant was asked to rotate the eye

retaining straight head position and read the letters. Comparing the PowerRefractor

results of six participants with their double‐pass technique showed significant

correlations in sphere and cylinder values for both techniques.

A different conclusion on this technique was reported in a study by Lundström et al.,99

who compared several techniques. They found difficulties in measuring at large

peripheral angles and indicated an underestimation of high myopic eyes. They attributed

this to the limited power range of the PowerRefractor. In a second study, Lundström et


29

al.55 reported of one case where a very elliptical narrow pupil shape could not be

analysed with the PowerRefractor. Correction of the eccentric peripheral refractive

errors measured with the wavefront sensor showed better improvement of peripheral

visual function in six out of seven participants with central visual field loss, than using

the refractive error corrections measured with the PowerRefractor.

Even though the PowerRefractor was found to be a very useful and easy to use

optometric tool for central refraction, limitations in measuring large peripheral angles

and possible differences with respect to different pupil shapes and analysis may have

some impact on peripheral photorefraction results.

Tabernero and Schaeffel42, 52, 131, 148 have recently introduced the scanning photo‐

refractor, which permits the continuous refraction measurement of the horizontal

meridian up to 45° and thus, allows the faster and more convenient assessment of the

peripheral properties of the eye. With this set‐up, they found that myopic eyes have a

more irregular or “bumpy” retinal shape, than emmetropic eyes. This photoretinoscopic

scanning system is based on a hot mirror, which permits refraction at different angles

through rotational as well as translational movements, while the head and eye remain

stationary. In their first prototype instrument, one main limitation of this continuous

refraction design was the number of required steps (1393 video frames, 19 steps per

mm, 3 steps per video frame) and thus, its long scanning, data acquisition and analysing

duration of approximately 23 seconds. They note that long central fixation could be a

problem when measuring children. They also computed noise of measurement, which

they partly attributed to possible fluctuations of accommodation during fixation, but

mainly due to small fixation errors, which can impact the shift and/or shape of the

peripheral refraction profiles. More measurement noise was found in the nasal side,

which they assume to be due to the partially blocking of the illumination by the

participants nose. Following the first prototype instrument, an upgraded version of the

same instrument was introduced, which reduced measurement time from 23 to 4

seconds. This was achieved with faster mechanics such as a belt‐driven linear translation

stage to speed up the translation of the mirror and a two‐gear belt transmission system

to rapidly rotate the mirror. Although the operation principle of the scanning


30

photorefractor stems from the concept of the PowerRefractor, its main difference and

thus, main disadvantage is that it cannot measure astigmatic errors. Whereas the

PowerRefractor rotates the photoretinoscope to obtain the sphero‐cylindrical refraction

of the eye, the scanning photorefractor only measures the vertical pupil meridian and

thus, provides only spherical errors. The authors mention that a rotational

photoretinoscope principle, such as used in the PowerRefractor, could also been

implemented into the scanning photorefractor, however, this would be complex and

slow down sampling rate and consequently, the peripheral refraction scan would again

require much more time. Instead of using a rotational photoretinoscopic principle, the

authors also suggest to perhaps perform measurements along two pupil meridians, that

is 90 and 180°.131 Despite the many advantages of this peripheral scanning instrument of

having no eye‐ and head‐turn requirements and being a much faster peripheral

refraction technique, being restricted to spherical error measurements limits its use. In

particular, due to the fact that oblique astigmatism is strongly present in the periphery

of the eye and its measurement, assessment and correction has already been shown to

be of relevance to vision scientists.82

1.3.7 Aberrometer

A very simple implementation of the basic principle of aberrometry is the previously

mentioned Scheiner disc. Whereas, the disc of a Scheiner optometer consists of only two

pinholes, Hartmann149 increased the number of pinholes over the entire pupil and traced

the aberrated ray lights accordingly. Shack150 modified this by replacing the disc with an

array of tiny lenses.

Specifically, when using an aberrometer, such as the COAS, a narrow light beam is sent

into the eye projecting a small spot onto the retina. When reflected light from this spot

exits the eye it generates the eye's aberrated wavefront. By use of a set of relay lenses

and the Hartmann‐Shack sensor, which consists of the lenslet array and a detector, the

spots created by the lenslet array are captured by the detector. The relative

displacements of the spots are analysed with respect to their reference spots to provide

the wavefront map of the eye. The wavefront errors or aberration values are provided in

the form of Zernike coefficients, which can then be converted to the conventional

sphero‐cylindrical refraction output.


31

Table 1.9: This table shows all authors and their study set‐ups used for the measurement of aberrometer‐based peripheral refraction.

Author Year Type of

Aberrometer Pupil

Max.

Angle

(°)

tested

Eye or

Head Turn

Aberrometer was

compared to …

Navarro et al. 116 1998 Laser ray‐tracing

method Cycloplegic 40 Eye Turn ‐

Atchison and Scott 31

2002 Hartmann‐Shack Sensor Technique

Cycloplegic 40 Eye Turn ‐

Atchison 29 2003 Hartmann‐Shack Sensor Technique

Cycloplegic 40 Eye Turn Shin‐Nippon SRW5000 Canon Autoref R‐1

Atchison et al. 32 2003 Hartmann‐Shack Sensor Technique


Atchison 118 2004 Hartmann‐Shack Sensor Technique


Lundström et al. 99 2005 Hartmann‐Shack Sensor Technique

Non‐cycloplegic 30 Eye Turn Subjective Refraction

Photorefraction Retinoscopy

Lundström et al.56 2005 Hartmann‐Shack Sensor Technique

‐ 35 Eye Turn Photorefraction

Atchison et al. 120 2006 COAS Cycloplegic 5 Eye Turn Subjective Refraction

Atchison et al. 121 2006 COAS Cycloplegic 40 Eye Turn ‐

Radhakrishnan and Charman 65

2007 Hartmann‐Shack Sensor Technique

Non‐cycloplegic 30 Eye and

Head Turn ‐


Non‐cycloplegic 20 Eye Turn ‐


Non‐cycloplegic 35 Eye Turn Photorefraction

Donovan et al.122 2007 COAS Cycloplegic 30 Eye Turn Shin‐Nippon NVision

K5001 Retinoscopy

Berntsen et al. 33 2008 COAS Cycloplegic 30 Head Turn Shin‐Nippon NVision

K5001

Mathur et al. 123 2008 Hartmann‐Shack Sensor Technique



Non‐cycloplegic 40 Eye and

Head Turn ‐



Mathur and Atchison79

2009 COAS Non‐cycloplegic 21 Eye Turn Shin‐Nippon SRW5000

Mathur et al.127 2009 COAS Non‐cycloplegic 21 Eye Turn ‐



Wei and Thibos128 2010 Hartmann‐Shack Sensor Technique

Non‐cycloplegic 15 ‐ ‐

Atchison et al.77 2010 COAS Non‐cycloplegic 21 Eye Turn ‐

Shen et al.81 2010 COAS Non‐cycloplegic 30 Head Turn ‐

Baskaran et al.130 2010 COAS‐HD VR Non‐cycloplegic 40 Eye Turn ‐

Baskaran et al.62 2011 COAS‐HD VR Non‐cycloplegic 40 Eye Turn ‐


32

Whereas the COAS is a commercially available aberrometer, several research groups

have developed their own Hartmann‐Shack wavefront techniques. Table 1.9 shows all

research groups that reported on peripheral measurements obtained with the

Hartmann‐Shack technique.

One such technique used for peripheral measurements has been explained in detail by

Atchison and Scott.31 A beamsplitter and a system of peripheral fixation targets up to 40°

in 5° steps enable measurement of the desired angles in the periphery. For the analysis

of Zernike coefficients obtained at a peripheral angle, the elliptical pupil shape had to be

taken into account and transformations made.29, 32 Detailed information on analysis for

the measurement of their ocular aberrations in the peripheral visual field has been

published.151

A different set‐up for the measurement of peripheral aberrations using the Hartmann‐

Shack technique has been built and applied by Lundström et al.56 This set‐up was

particularly designed for participants with large central visual field loss. The technique

incorporates concentric ring fixation targets, to allow participants alignment with

respect to their preferred retinal locus position. Moreover, it includes an eye tracker as

well as analysing software with unwrapping algorithms that consider elliptical pupil

shapes.

In 2009 Lundström et al.67 used a Hartmann‐Shack wavefront sensor technique that

allows measuring of the periphery of the eye for different accommodative states. This

was achieved by use of a hot mirror, which allowed for an open field of view and hence

binocular fixation to different off‐axis targets at different distances. A bitebar was used

to stabilise the head during the measurements.

Using the COAS aberrometer, five studies by Mathur and Atchison et al.61, 123, 127, 79, 77

mapped higher order aberrations at horizontal visual field locations up to 21° and

vertical visual field locations up to 16° using a beamsplitter for off‐axis target projection.

For this 38 targets were produced onto a projection screen, which the participants had

to view successively.


33

Whereas, the aberrometry‐based peripheral refractions by Berntsen et al.33 obtained

with the COAS were in good agreement to refraction data of the Shin‐Nippon NVision

K5001, Donovan et al.’s122 measurements revealed peripheral astigmatic values which

were almost half in value using the COAS when compared to the Shin‐Nippon NVision

K5001. Compared to the peripheral refraction data obtained with the Shin‐Nippon

SRW5000, Atchison's Hartmann‐Shack wavefront sensor technique showed good

agreement.29 Lundström et al.’s55, 99 comparisons of different peripheral refraction

techniques showed that the Hartmann‐Shack technique was the most useful technique

compared to subjective refraction, retinoscopy and photorefraction. In comparison to

the PowerRefractor, results showed that the Hartmann‐Shack sensor technique by

Lundström et al.56 measured greater astigmatism in the oblique axis and the total

cylinder value obtained was smaller than with the PowerRefractor. Due to

underestimation of oblique off‐axis astigmatism and limitations for large eccentricities

using the PowerRefractor, the Hartmann‐Shack technique has been assumed to be more

accurate for peripheral refraction.

Baskaran et al.62, 130 have used the COAS‐HD VR aberrometer for the measurement of

peripheral refraction measurements. This COAS instrument has an open‐view optical

relay system attached, which permits measurements of up to 40°.

Although all aberrometer techniques were in good agreement with other methods and

considered very useful, a small overestimation of myopia was found for the aberrometry

refractions compared to all the other instruments used in the comparison studies by

Lundström et al.,99 Berntsen et al.33 and Atchison et al.29. This finding was also observed

in validation studies of aberrometers on central measurements in adults152, 153 as well as

children.154 It was suggested this to be due to differences in calibration (wavelength

differences), set‐up (closed‐view versus open‐view) and/or the operation principles

(pupil diameter) between aberrometers and autorefractors.29, 33 As mentioned for

autorefractors, the same participant‐ and operator‐related intricacies (constant re‐

alignment of eye/head and pupil/instrument) remain, which eventually can lead to

prolonged testing times in particular when numerous peripheral angles have to be

measured.


34

Very recently, Wei and Thibos as well as Jaeken and Artal also introduced new scanning

Hartmann‐Shack aberrometers.128, 155 Just like the technique by Tabernero and

Schaeffel,42, 52, 74 both techniques permit the measurement of peripheral optics of the

eye without the need for off‐axis fixation. Wei and Thibos use double‐pass scanning

lenses and a scanning mirror that enable the measurement of the periphery of the eye.

Currently, this technique is limited to visual field measurements up to a mid peripheral

range of ±15°, which takes up to 7 to 8 seconds. The authors note that by combining

both, peripheral fixation and the scanning Hartmann‐Shack aberrometer the

measurement range can be extended beyond the central 30°. Due to strong backward

reflections from the system and the cornea, the current instrument set‐up does not

permit the measurement of on‐axis aberrations and the measurements along the

horizontal meridian. Currently, there is only limited information published on Jaeken and

Artal’s scanning Hartmann‐Shack aberrometer.155 However, first specifications of this

instrument appear promising, indicating that continuous measurements are possible up

to peripheral angles of ±40° and the complete scan takes approximately 2 seconds.

1.4 Alignment Criteria for Peripheral Refractometry

When using conventional refraction techniques for the measurement of the periphery of

the eye, a form of off‐axis fixation or instrument adjustment is required in order to

permit the alignment of a particular peripheral field angle with respect to the instrument

axis. Commonly, the participant is asked to either turn the eye (Figure 1.3 a) or head

(Figure 1.3 b) towards a peripheral fixation target whilst keeping the refraction

instrument in its fixed position. This involves the participant actively taking part in the

measurement procedure, which often can lead to extensive testing times. A third

alternative is the rotation of the measuring device in front of the eye (Figure 1.3 c). This,

however, is often difficult to achieve when using compact instrument designs such as

ready‐made autorefractors or aberrometers.

Whether eye turn measurements can lead to different peripheral refraction results when

compared to straight ahead gaze has previously been investigated by several authors

(Table 1.10).


35

Figure 1.3: Alignment of the peripheral measurement angle with respect to the instrument axis via a) eye turn, b) head turn and c) instrument rotation.

Table 1.10: Summary of the findings investigating possible refractive changes between eye and head turn as well as instrument rotation.

Author Year Refraction

Technique

Instrument Axis

Alignment was

compared

between...

Max.

Peripheral

Angle

Findings

Ferree et al.68 1931 Zeiss

Hartinger

coincidence

optometer

Eye Turn &

Instrument

Rotation

(60°) Eye turn induced a shift towards myopia

of up to 2.50D

Simensen &

Thorud156

1994 Observation

of

development

of refraction

‐ ‐ 90% of all workers became myopic

whilst carrying out work that required

constant eccentric fixation (eye turn)

and near work

Seidemann et

al.23

2002 Double‐Pass

Technique

Eye Turn &

Head Turn

40° Eye turn induced a shift towards myopia

of an average of 0.70D

Atchison et al.30 2005 Shin‐Nippon

SRW5000

Eye Turn &

Head Turn

35° No evidence of a significant difference

between eye and head turn was found. The

maximum difference was 0.17D.

Radhakrishnan

and Charman65

2007 Hartmann

Shack

Wavefront

Sensor

Eye Turn &

Head Turn

30° They found high levels of inter‐subject

variability and some support for the view

that pressures from external muscles of the

eye may affect the refraction.

Radhakrishnan

and Charman66

2008 Shin‐Nippon

SRW5000

Eye Turn &

Head Turn

30° No evidence of a significant difference

between eye and head turn was found. The

maximum mean difference was 0.195D.

Mathur et al.64 2009 Shin‐Nippon

SRW5000

Eye Turn &

Head Turn

30° No significant changes in axial or peripheral

refraction were found upon oblique

viewing. Nevertheless, 10% and 20% of

participants showed significant

differences in M and J180/J45

Prado et al.157 2009 Hartmann

Shack

Wavefront

Sensor

Eye Turn &

Head Turn

30° Some aberration terms showed changing

trends with gaze. Overall, these changes

were smaller than their variability at each

position.

Lundström et

al.67

2009 Hartmann

Shack

Wavefront

Sensor

Eye Turn &

Head Turn

‐ No significant peripheral refraction

differences found. However, some 3rd and

4th order aberrations (i.e. spherical

aberration) became significantly more

negative with eye turn.


36

The first peripheral refraction study by Ferree et al.68 in 1931 noticed a difference

between refraction results obtained by eye turn or instrument rotation. They observed a

shift towards myopia of up to 2.50D after prolonged peripheral fixation using eye

rotation. Their instrument set‐up permitted peripheral refraction measurements of up to

60°. However, no mention was made for which peripheral angles this 2.50D shift

occurred and for how long the off‐axis fixation had to be maintained in order to achieve

this “phenomenon” of a myopic trend. The authors suggest that prolonged fixation can

temporarily elongate the eye due to pressure of the external muscles and as such can

produce myopia.

More evidence that may support the hypothesis of change in refractive errors with

eccentric fixation was found in a study conducted by Simensen and Thorud156 in a textile

factory in Lillehammer. They monitored refractive error changes in textile workers

(n=11), who were focusing downwards on nearby slowly‐moving textile, in order to find

weaving errors. Whereas, 90% of all textile workers became myopic over the years, all

control participants (n=11) showed no refractive error change towards myopia. However,

it should be noted, that this result may have been affected by the additional factor of

near‐induced myopia, which has been reported to be linked to prolonged near‐work.158

Just like Ferree and co‐workers,68 Seidemann et al.23 found a similar shift towards

myopia when the participants were asked to turn their eyes by 40°. On average the

myopic shift with eye rotation using a double‐pass technique in three participants was

0.70D ± 0.36D.

In contrast, a small difference within normal test‐retest variability between eye and head

turn measurements was found by Atchison et al.,30 who determined peripheral refraction

with the Shin‐Nippon SRW5000 at 35° temporally and nasally.30 Radhakrishnan and

Charman66 conducted a study investigating the contradicting results of Simensen and

Thorud156 to those of Atchison et al.’s.30 The Shin‐Nippon SRW5000 autorefractor was

used for eye and head turns up to 30°. No significant differences (maximum 0.17D)

between eye and head turn data were found. Moreover, to research the effect of

prolonged peripheral fixation they measured peripheral refractions at 25° after a 2.5

minute fixation period and found no significant differences to ≤ 1 minute fixation


37

durations. As retinal eccentricity increased, so did the standard deviations. The authors

explain this to be due to the difficulty for participants to maintain exact eye or head

positions at large eccentricities. In another investigation using the Hartmann‐Shack

technique, the same authors65 found some evidence of eye turn‐induced refractive error

changes of up to 1.00D in hyperopic direction. This finding occurred after 1 to 1.5

minutes viewing at 30° eccentricity. This observation was made in only some individuals

but was not shown for oblique viewing durations of 20 minutes. The same authors65

observed that pupil sizes constricted systematically with increasing oblique viewing

angles. They suggest this pupil constriction to be caused either by stress occurring in the

participant due to the task of maintaining the oblique viewing angle or due to the

mechanical pressures stimulating the ciliary nerves when turning the eye.

Marthur et al.64 measured axial refraction under oblique viewing conditions (30°

temporal and 30° nasal) using the Shin‐Nippon SRW5000 and compared the results to

straight‐ahead viewing. Although they did not find any significant mean effects for the

participant group (n=53), there were at least 10% and 20% of participants that showed

significant differences in the refractive vector components M and J180/J45, respectively. A

similar study was conducted by Prado et al.157 who used a Hartmann Shack wavefront

technique to measure and compare on‐axis aberrations between straight‐ahead and

oblique viewing (30° temporal and 30° nasal). They found that some mean values

showed a trend to change with gaze direction; however these changes were smaller than

the overall variability. Lundström et al.67 showed that some 3rd and 4th order aberrations,

such as spherical aberration, were significantly different between eye and head turn

measurements.

Instead of investigating the impact of eye turn on peripheral refraction results,

Macfadden et al. investigated the impact of eye turn on the peripheral ocular shape and

found a significant shift in retinal profiles when comparing eye rotation and head turn

measurements using the IOLMaster.159

Recently, researchers have also turned their attention to measuring peripheral refraction

when wearing contact lenses81, 160 or spectacle lenses.52, 82 In the latter case, it is

important that the visual axis is perpendicular to the spectacle plane or else peripheral


38

prismatic effects of the spectacle lens can affect the measurement angle. When

measuring peripheral refraction in the contact lens wearing eye, there is a possibility

that eye turn can affect the centration of the contact lens, which potentially can impact

the measured peripheral refractive power. Thus, to avoid peripheral prismatic effects

with spectacle lenses or de‐centration effects of contact lenses, peripheral refraction

measurements should be performed using head turn.

Most of the studies listed in Table 1.10 have shown little or no difference between eye

and head turn measurements. However, these studies have been using somewhat

different study protocols to investigate the impact of eye turn on peripheral refraction

data when compared to head turn or instrument rotation. The use of different

instrumentations, different peripheral angles measured and different durations for

oblique viewing may have had an impact on the different results found. Nevertheless, to

avoid any of the possible effects that may result from eye turn measurements, whether

the eye is measured with or without correction devices, head turn appears to be the

more suitable method for the alignment of the peripheral measurement angle.

1.5 Summary and Conclusion

Clearly, there has been much advancement in refraction instruments over time with

respect to delivering accurate and reliable results for on‐axis measurements but also in

terms of ease of use. These changes in refraction technology are also reflected in their

use for research purposes related to peripheral refractometry. From the current

literature review and Figure 1.4 it is evident that in the last decade, objective techniques

based on autorefraction and aberrometry have become of greatest use for the

measurement of peripheral refraction. The current review suggests that objective

instruments, such as the COAS, the Shin‐Nippon NVision K5001 and the Grand Seiko

WAM‐5500 are the most useful commercially available instruments for peripheral

refraction measurements. Whereas the COAS provides the additional measurement of

higher order aberrations, the Shin‐Nippon NVision K5001 and the Grand Seiko WAM‐

5500 require smallest pupil diameters for autorefractors and they permit binocular

viewing of the external peripheral real‐distance target.


39

Figure 1.4: Number of studies and their peripheral refraction techniques used over the last 40 years (left) and the last decade (right).

Nevertheless, all but three42,128,155 of the mentioned instruments used for peripheral

refractometry, were originally designed for the measurement of central refraction and

had to be modified to achieve the peripheral alignment criteria required for peripheral

refractometry. The need for faster instruments, requiring no off‐axis fixation or

instrument rotation, has been recognised in the last few years and the first research

prototypes, such as the eccentric scanning photoretinoscope of Tabernero and

Schaeffel42 and the scanning Hartmann Shack aberrometers of Wei and Thibos,128 and

Jaeken and Artal155 have been introduced. It should be noted that all of these new

instruments were introduced after the research reported in this thesis had commenced.

One major advantage of the three new instruments is the speed in measuring peripheral

refraction when compared to that of modified techniques. Nevertheless, some

limitations remain. The operation principle of the scanning photorefractor by Tabernero

and Schaeffel, for example, is limited as it permits the measurement of spherical errors

only. Thus, the astigmatic component, which is significant in the periphery of the eye,

can currently not be measured. Moreover, the scanning Hartmann‐Shack sensor by Wei

and Thibos is restricted in measuring only mid‐peripheral angles up to ±15° and at the

current stage measurements are not possible centrally and along the horizontal visual

field meridian. As these peripheral refraction instruments are in the early stages of their

development, it is anticipated that further improvements to current prototype

instruments and/or the introduction of new concepts will follow soon.


40

1.6 Thesis Overview

1.6.1 Rationale for Research

With the discovery that peripheral refractive errors can influence eye growth, their

critical assessment and monitoring has become paramount to current research activities

in the field of myopia. The measurement of rapid and accurate global refraction, that is,

central and peripheral refraction, at individual and population levels has therefore

become of particular demand. Currently, however, time‐consuming sequential re‐

alignments by participants and operators are required when using commercially

available refraction techniques. It has also been shown that when using these

techniques, standard errors commonly increase for larger visual field angles. As there

has been little research conducted to investigate this increase in standard errors,

clarification is still needed to confirm that using these instruments for the measurement

of the peripheral optics of the eye provides accurate results. Preferably, an instrument

dedicated to the rapid and accurate measurement of central and peripheral refraction

would be the ultimate tool for research institutions and clinical practices in the current

quest to understand, monitor and control myopia progression.

Overall, results of this work will help understanding intricacies related to peripheral

refraction measurements when using modified commercially available instruments, will

test new concepts and investigate a new approach of obtaining more rapid and accurate

peripheral refraction measurements.

1.6.2 Hypotheses

The two primary hypotheses of this thesis are:

Refraction measurement accuracy decreases with increasing visual field angle,

due to decreased tolerance to misalignment when using commercially available

refraction instruments for the measurement of peripheral refraction

A new refraction technique, dedicated to measure central and peripheral

refraction rapidly and accurately across the entire visual field, can be developed.


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1.6.3 Aims

Specifically, the aims for the first part of this thesis are to:

Investigate the impact of pupil (mis‐)alignment on peripheral refraction

measurements when using commercially available instruments (Chapter 2)

Develop and introduce a new method for the correction of pupil alignment errors

when measuring peripheral refraction with commercially available instruments

(Chapter 3).

In an effort to overcome current limitations of peripheral refractometry, the second part

of this thesis aims to introduce and develop a new peripheral refraction instrument that

provides fast and accurate measurements across the visual field. The specific aims are

to:

Develop the optical design of a novel peripheral refraction instrument concept,

the EyeMapper, which has the objective to measure refraction rapidly across the

visual field by use of stationary deflecting components and a scanning mirror,

based on the ring autorefraction principle (Chapter 4)

Assess component and safety criteria for this new instrument concept and to test

and cross‐validate the autorefraction principle with a commercially available

autorefractor (Chapter 5)

Integrate the wavefront sensing principle into the optical and mechanical design

of the EM and build, calibrate and test this new instrument. (Chapter 6).

CHAPTER 2: OPERATOR‐RELATED ALIGNMENT INTRICACIES

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CHAPTER 2:

INVESTIGATION OF OPERATOR‐RELATED ALIGNMENT INTRICACIES IN CURRENT PERIPHERAL REFRACTOMETRY§

2.1 Overview

Chapter 1 addressed participant‐related alignment intricacies, such as the requirements

for off‐axis fixation and the time‐consuming measurement procedure involved, when

using conventional instruments for the measurement of peripheral refraction. The

objective of Chapter 2 was to investigate also whether operator‐related tasks, such as

the (mis‐)/alignment of the instrument with the centre of the entrance pupil, could

impact the accuracy of instruments adapted for the measurement of peripheral

refraction.

At first, this chapter aimed to investigate the clinical impact of pupil misalignment on the

peripheral refraction results when using the Shin‐Nippon NVision K5001 autorefractor. In

the second part of this chapter, an entrance pupil model was developed and its

geometrical behaviour as a function of peripheral viewing angle was assessed and its

implications on peripheral refraction measurements were discussed.

2.2 Investigation of Pupil Alignment Tolerance

2.2.1 Introduction

Given the recently inferred association of peripheral refraction with myopia

development,10, 124, 161 the relevance and importance of measuring and monitoring

peripheral refraction profiles as accurately as possible has been recognised and

constitutes the basis of many research efforts.

§ Work from this chapter has previously been presented in part by the author and Arthur Ho at the annual meeting of the American Academy of Optometry, Orlando, 2009.126, 162 Based on these presentations, two papers have been published by the author.163, 164 Whereas, most modelling and analysis of the entrance pupil (Section 2.3) was previously carried out by Arthur Ho, the author's additional contribution was the discussion of its implications and the further processing and analysis of the data.


43

Methodologically, however, the measurement of peripheral refraction with modified

instruments requires compliance with two alignment criteria with respect to the

instrument axis; firstly, the correct rotational alignment to achieve the targeted

peripheral visual field angle and secondly, translational alignment (centration) with the

entrance pupil. For central autorefraction, instruments require good alignment of the

measurement axis with the entrance pupil centre as well as correct longitudinal (axial)

adjustment of the instrument in terms of illumination and calibration. Currently, it is

assumed that both alignment conditions have to be also satisfied when performing

peripheral refraction. This, however, is difficult to achieve in practice due to the

peripheral observation angle of the eye and the resultant elliptical appearance of the

entrance pupil shape. Moreover, the axial alignment, which for autorefractors requires

the focussing of the keratometry ring, is difficult to perform, as the ring shifts

peripherally and distorts in shape.

Although validation studies on modified peripheral refraction techniques have shown

good agreement between instruments, 23, 29, 99 peripheral refraction results often show

an increase in variability as visual field angle increases.23, 25, 34, 40, 64, 66, 71, 73, 130 The source

of such variability could be related to physiological differences within the eye’s central

and peripheral shapes, a degree of measurement noise and/or the increasing magnitude

of the measurement values.

No studies have yet reported on the tolerance of misalignment within the elliptical pupil

when measuring peripheral refractive errors. Cheng and colleagues investigated the

impact of lateral and axial misalignment on aberration data for central measurements

using the COAS aberrometer.165, 166 In consideration of their estimated clinician

misalignment range of ± 0.5 mm, central aberration values were shown to be stable.

Considering that evaluation of peripheral refraction profiles typically require the

measurement of numerous eccentricities and/or numerous repeats at select

eccentricities, a large number of re‐alignments from the participant’s and operator’s

point of view are required. As such, any of these modified peripheral refraction

techniques have considerable potential for alignment errors. Hence, the clinician’s


44

normal operation range for peripheral refraction is likely to be larger than the previously

estimated central normal misalignment range of ± 0.5 mm when using the COAS

instrument.165, 166

Based on the current technical intricacies in peripheral refractometry, the additional

impact of large oblique astigmatism and the elliptical peripheral entrance pupil, it is

reasonable to assume that sensitivity in measurement error for peripheral refraction

increases with increasing eccentricity. Hence, from the methodological point of view and

with its increasing scientific and clinical relevance, the key objective of this first study

was to investigate how sensitive the peripheral refraction results are with respect to

lateral pupil misalignment in comparison to the sensitivity of central refraction results.

2.2.2 Methods

2.2.2.1 Participants

The study protocol was reviewed and approved by the University of New South Wales

Human Research Ethics Advisory Panel and conformed to the tenets of the Declaration of

Helsinki. Ten emmetropic (central M ≤ |0.50|D) and ten myopic (central M ≤ ‐0.75D)

cooperative adult participants were recruited and successfully enrolled into the study.

All participants were screened for good ocular health and had no history of ocular

anomalies, such as manifest strabismus, non‐orthophoric conditions, or any anterior eye

anomalies. Peripheral refraction was measured for the right uncorrected eye in the

horizontal visual field meridian. Pupils were not dilated for the measurements.

2.2.2.2 Instrumentation

Central and peripheral refraction measurements were performed with the open‐view

autorefractor, the Shin‐Nippon NVision‐K5001 (also known as Grand Seiko WR‐5100K,

Shin‐Nippon, Tokyo, Japan). For this study the autorefractor was modified (Figure 2.1,

left) to allow for easier peripheral refraction measurements. The primary modification

includes the addition of an instrument head, which had been mounted on top of the

autorefractor. The instrument head includes several small red laser diodes that are

aligned to project laser fixation targets into the participant’s visual field, one at a time,

at various angles onto a wall, 2.0 to 2.5 m distant. In the present study, the laser fixation


45

targets were presented straight ahead from the centre of the autorefractor and 30° in

the nasal and temporal horizontal visual fields. The use of bright laser targets on the

wall, allows even uncorrected ametropic participants to be able to recognise and fixate

on the targets. As explained in Chapter 1, head turn was the preferred method over eye

turn, and the chin‐rest had been modified to allow easy head turn for off‐axis fixation.

Using the method described by Thibos et al.,167 the sphero‐cylindrical refraction output

S/C × θ was converted to the power vectors, M (spherical equivalent), J180 (with‐ and

against‐the‐rule astigmatism) and J45 (oblique astigmatism) as followed:

Equation 2.1 /

Equation 2.2 /

Equation 2.3 /

All data processing (e.g. averaging) and subsequent analyses were performed in terms of

these power vector components.

2.2.2.3 Participant Alignment

Each participant was instructed to turn his/her head toward the presented fixation

target while keeping both eyes stationary, relative to head position, in forward gaze

(Figure 2.1, right). The participant’s cooperation regarding head alignment and accuracy

of fixation was monitored by the operator throughout the measurement procedure.

Nevertheless, it should be noted that, in practice, an additional small compensatory eye

turn may be difficult to perceive and correct. In three participants head misalignment

was measured (five repeats at 30° nasal and 30° temporal visual field angles), which

ranged from ‐6.85° to +5.15° (mean ‐2.13° ± 2.85°). This small compensatory eye turn is

unlikely to have a real impact on the data, particularly because the differences related to

eye and head turn measurements, were, if at all, only found for large peripheral fixation

angles.23, 65 Fixation targets were viewed with both eyes while maintaining normal

blinking. As no participants had manifest strabismus, accurate binocular fixation was

maintained for all measurements at all eccentricities.


46

Figure 2.1: Modifications to the Shin‐Nippon NVision K5001 autorefractor.

LEFT: Shin‐Nippon NVision‐K5001 with modified chin‐rest and instrument head; RIGHT: Participant’s right eye is aligned for the 30° nasal visual field measurement using head turn.

2.2.2.4 Entrance Pupil Alignment

For each of the three visual field positions, five readings were recorded at each of five

lateral pupil alignment positions, central (0CP), 1 and 2 mm temporal (1TP and 2TP

respectively), and 1 and 2 mm nasal (1NP and 2NP respectively), while ensuring the

instrument was axially in best focus (Figure 2.2 and Figure 2.3).

For subsequent analysis, de‐alignments were considered positive towards the nasal

portion of the pupil and negative towards the temporal portion of the pupil. The data

displayed on the Shin‐Nippon monitor were transferred and retrieved by custom‐

designed software.


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Figure 2.2: Right eye pupil alignment matrix.

The yellow ring and the yellow minimal pupil diameter marking are indicators for the lateral alignment of the instrument axis. The white keratometry ring aids to axially align the instrument and to obtain the central keratometry readings. The images in the figure were captured directly from the Shin‐Nippon NVision‐K5001 composite video output.


48

It should be noted that when performing peripheral refraction measurements using the

Shin‐Nippon, oblique head alignment on the chin‐rest may result in the instrument

incorrectly recognising the measurement position as that of the opposite eye, especially

at large eccentric fixation angles. As such, care needs to be taken that the correct eye

measurements are recorded. In the present study, this potential error was eliminated by

performing real‐time data conformity checks within the data‐acquisition software.

To achieve a sufficiently large natural diameter of the elliptical pupil minor axis for the

performance of de‐aligned measurements through all five lateral pupil positions,

measurements were performed under low (scotopic) room lighting, between 0.3 and 0.5

lux. The measurement beam, as well as the eye illumination for video imaging, operate

in the infrared and thus do not induce pupil constriction. Accurate pupil de‐alignment

was assisted by a pupil alignment scale attached to the alignment monitor as shown in

Figure 2.3. The pupil alignment scale was printed on a transparent sheet and attached to

the monitor. For the given camera magnification, each grid‐square represents a 1 mm2

area in the plane of the entrance pupil.

Figure 2.3: The pupil alignment scale.

Relative to the pupil centre (0CP), the measurement axis of the Shin‐Nippon NVision‐K5001 is aligned with the 2TP, 1TP, 0CP, 1NP or 2NP position. In this image it is aligned with the 1 mm nasal pupil (1NP) position of the right eye with the participants head positioned for the 30° temporal visual field measurement. The pupil alignment scale is a transparent sheet attached to the monitor with 10 mm2 grids. Each grid refers to a 1 mm2 entrance pupil area.


49

2.2.3 Results

2.2.3.1 Central and Peripheral Refraction – Pupil Alignment

Central and peripheral refraction measurements for different pupil alignment positions

were performed in ten myopic and ten emmetropic adults (age 19 to 40). The mean age

(± SD) of the emmetropic group was 30.7 (± 5.6) years, and that of the myopic group was

27.2 (± 3.8) years. The absolute mean refractive values for M, J180 and J45 measured at

the centred entrance pupil position (0CP) are shown in Table 2.1. The emmetropic group

was relatively more myopic in the periphery and the myopic group displayed a small

relative hyperopic shift.

With respect to the five pupil alignment positions, key results are presented graphically

(Figure 2.4) in terms of relative peripheral refractive error (RPRE) from pupil centre. For

this, refractive power vector components of the centred entrance pupil were subtracted

from the corresponding components from the de‐aligned pupil measurements. Results of

the relative refractive power vectors as a function of lateral pupil alignment were

plotted for both participant groups and for both peripheral and the central field angles.

Table 2.1: Absolute M, J180 and J45 (in D) measured at the centred entrance pupil position (0CP) for all three visual field angles. Data are means ± SD.

30° Nasal Visual

Field Central Visual Field

30° Temporal Visual Field

Emmetropes

(n=10)

M ‐1.20 ± 1.00 ‐0.07 ± 0.25 ‐0.50 ± 0.82

J180 ‐1.48 ± 0.34 ‐0.01 ± 0.07 ‐0.79 ± 0.25

J45 0.01 ± 0.14 ‐0.13 ± 0.10 ‐0.24 ± 0.28

Myopes

(n=10)

M ‐3.47 ± 1.86 ‐3.50 ± 2.07 ‐3.06 ± 2.08

J180 ‐1.25 ± 0.52 0.14 ± 0.28 ‐0.63 ± 0.37

J45 0.23 ± 0.37 ‐0.08 ± 0.15 ‐0.24 ± 0.25

The interaction between refractive group and lateral pupil alignment position for each

combination of visual field angle and relative refractive vector component was

investigated using a repeated‐measures analysis of variance (ANOVA).


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Figure 2.4: RPRE of the mean refractive components M, J180 and J45 as a function of pupil alignment for each refractive error group and three different visual fields.

Error bars indicate ± SD. Abscissa‐values have been displaced slightly for clarity. The asterisks show significant differences (p<0.05) of the refractive vector components with 0CP being the reference position.

There was no significant difference between‐groups associated with pupil position for

the nasal visual field for any of the three refractive vector components (M: F=0.397,

p=0.536, J180: F=2.133, p=0.161 and J45: F=1.535, p=0.231). However, there was a

difference between refractive groups in the temporal visual field for M and J180 (M:

F=6.74, p=0.018 and J180: F=13.20, p=0.002), but not for J45 (F=0.014, p=0.906).

Specifically, the curvature as represented by the quadratic term was different between


51

the refractive groups for M and J180 (M: F=5.641, p=0.029, J180: F=7.899, p=0.012). This is

also indicated by the more quadratic pupil alignment functions in the emmetropic group

as compared to the myopic group (Figure 2.4). The central visual field measurements

also showed a difference between groups for M (F=5.853, p=0.026), but not for J180

(F=2.036, p=0.171) or J45 (F=0.027, p=0.870).

Repeated‐measures analysis of variance was carried out on the refractive power vectors

M, J180 and J45, to compare the centred with the de‐aligned entrance pupil positions. For

this, a post hoc test for type‐I probability with Bonferroni correction was used. Figure 2.4

indicates statistically significant differences compared to centred entrance pupil

alignment where the critical type‐I probability (statistical significance) is set at 0.05.

For central visual field measurements, the relative refractive vector components M and

J180 decreased quadratically (r≥0.98, p<0.04) with increasing pupil de‐alignment in both

groups. Compared to centred pupil alignment, M and J180 showed significant differences

for all temporal and nasal pupil de‐alignments of 2 mm. The only exceptions in which no

differences were observed were M and J180 for the 2 mm temporal pupil de‐alignment in

the myopic group. A pupil de‐alignment of 1 mm was only significantly different for J180

in the myopic group, when aligned for the 1 mm nasal pupil position. The maximum M

mean difference to centred pupil alignment was ‐1.03D, found at the 2 mm temporal

pupil alignment in the emmetropic group.

For both peripheral visual fields, lateral pupil de‐alignments of 1 and 2 mm resulted in

significant differences for M and J180 when compared to centred pupil alignment (Figure

2.4). The only exceptions were the 1 mm temporal M and J180 for myopes measured at

the 30° nasal visual field and the 1 mm nasal M and J180 for myopes measured at the 30°

temporal visual field. Entrance pupil de‐alignment at the 30° nasal visual field for the

emmetropic group was found to produce the greatest mean difference from centred

pupil alignment for both 2 mm temporal (ΔM=‐2.77D, ΔJ180=‐1.57D) and 2 mm nasal

(ΔM=+2.23D, ΔJ180=+1.04D) pupil de‐alignments. In both refractive groups, M and J180

showed a significant linear (r≥0.94, p<0.02) correlation as de‐alignment progressed from

temporal to nasal for peripheral refraction measurements. To assess whether there is an


52

asymmetry between the relative pupil alignment slopes of the nasal and temporal visual

fields, the absolute values of the linear slope (D/mm) were determined for M and J180.

Overall, the slopes were greater in the nasal visual field (emmetropic group: slope for

M=1.245, J180=0.618; myopic group: slope for M=0.937, J180=0.455) than in the temporal

visual field (emmetropic group: slope for M=0.684, J180=0.354, myopic group: slope for

M=0.769, J180=0.452). However, paired t‐test analysis showed that this difference in

relative pupil alignment slopes between the nasal and temporal visual field was

significantly different only in the emmetropic (M: p=0.00; J180: p=0.001) and not in the

myopic group (M: p=0.113; J180: p=0.958).

Overall, J45 was least affected by entrance pupil de‐alignment. Compared to centred

pupil alignment, J45 showed only significant differences for central refraction at the 2

mm nasal pupil position in the emmetropic group and for the nasal visual field at the 2

mm temporal pupil position in both groups.

2.2.3.2 Pupil Misalignment Threshold of Clinical Significance

Regression analysis was used to assess the relationship between refractive error

measured for centred and lateral de‐aligned pupil measurements, for the two refractive

groups and the three visual fields.

Data on pupil de‐alignment versus visual fields were fitted with equations to determine

the pupil misalignment threshold of clinical significance (Table 2.2). For this analysis,

first‐order (linear) fits were used for peripheral M and J180, and second‐order (quadratic)

fits were used for on‐axis measurements. A clinically significant difference was defined

as ≥0.25D for M and ≥0.125D for J180 and J45. Positive x refers to nasal pupil misalignment

and negative x refers to temporal pupil misalignment.

For central M and J180 the pupil misalignment threshold of clinical significance ranged

from +0.79 to ‐2.33 mm, while for peripheral M and J180 the range was as small as ±0.20

to ±0.37 mm. Overall, the range was smaller in the emmetropic group when compared to

the myopic group.


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Table 2.2: Pupil misalignment threshold (in mm) of clinical significance (≥0.25D for M and ≥0.125D for J180).

Pupil Misalignment (x) in mm

Emmetropes Myopes

Central Visual Field M ‐0.93 / +1.20 ‐1.70 / +1.19

J180 ‐1.02 / +1.08 ‐2.33 / +0.79

30° Nasal Visual Field M ± 0.20 ± 0.27

J180 ± 0.20 ± 0.27

30° Temporal Visual Field M ± 0.37 ± 0.33

J180 ± 0.35 ± 0.28

2.2.4 Discussion

2.2.4.1 Peripheral Refraction and its Tolerance to Lateral Pupil Misalignment

Measuring the peripheral optics of the eye with modified commercial refraction

instruments has become increasingly relevant, particularly in the area of myopia

research. As no standards exist for calibration and testing of peripheral optics

measurements, and given the presence of asymmetric peripheral aberrations, there is no

certainty that using autorefractors (intrinsically designed for on‐axis refraction) for

peripheral refraction measurements provide accurate results, even though the empirical

comparison of peripheral refraction data using different instruments showed good

agreement29, 33 and repeatability was acceptable.44 Furthermore, research is still

inconclusive regarding modified peripheral refraction techniques, for example, in

relation to whether peripheral refraction data obtained by eye or head‐turn differ.23, 64-68,

157

No report has yet addressed the tolerance of pupil misalignment on central or peripheral

refraction using autorefractors. In two studies, Cheng et al. performed central

aberrometer measurements at different lateral pupil alignment positions in human

eyes166 and in different aspheric model eyes165 using the COAS aberrometer. Their results

showed that the instrument has a high tolerance to the typical lateral misalignment of ±

0.5 mm introduced by the operator when measuring central aberrations. In contrast to

Cheng et al.’s findings, Applegate et al.168, 169 demonstrated that fitting of wavefront

aberrations to Zernike polynomials can introduce the false appearance of significant

artefactual coefficients. These apparently contradictory results may be reconciled if


54

other errors involved in the measurement of wavefront aberrations are taken into

consideration. Indeed, Cheng et al. suggested that variability of measurements in the

human eyes reflects the changes in the eye’s optics, i.e. caused by fixational eye

movements or microfluctuations in accommodation, rather than instrument noise. In

addition, they showed that asymmetric aberrations occur only to a negligible amount for

lateral pupil de‐alignments when measuring central aberrations.

The present study investigated the impact of pupil de‐alignment on central and

peripheral refraction measurements in emmetropic and myopic eyes. Overall, the pupil

alignment slopes between the emmetropic and myopic group appeared to be similar for

all three visual fields. However, with respect to pupil alignment, differences between

both groups were found for the central and 30° temporal visual field measurements as

well as with respect to nasal‐temporal asymmetry across the visual field. Previous

studies have shown that factors such as corneal curvature170 and the shape of the

eyeball171 differ between emmetropic and myopic eyes. In addition, the nasal‐temporal

asymmetry across the visual field has been noted previously and was shown to decrease

as myopia increases.24 Thus, it is possible that these ocular differences between the

refractive groups may have led to some of the differences found in this study.

With respect to pupil misalignment tolerance, the present study has shown that for

central autorefraction, the pupil misalignment threshold of clinical significance was ≥

0.79 mm. As such, assuming a normal misalignment error of ± 0.5 mm in clinical practice,

central autorefraction can be considered highly tolerant with respect to lateral pupil de‐

alignment. This is in accordance with previous empirical validation studies of

autorefraction instruments for central measurements.138, 139 In contrast to the robust

results in central refraction, even small pupil de‐alignments in peripheral refraction led

to significant errors. Independent of the refractive group, results from this investigation

showed that there is a rapid and linear change in the refractive power vectors M and J180,

when de‐aligning the instrument axis even by only a minimal amount from the pupil

centre during the peripheral refraction measurements. Specifically, a small pupil

alignment error of 0.2 mm caused a significant change when the measurements were

performed in the 30° nasal visual field.


55

The pupil misalignment threshold for clinical significance in 30° peripheral refraction

measurements was found to be much smaller than for central refraction and thus, can

have a significant impact on the data. It is reasonable to speculate that this may be a

substantial cause of the higher standard errors in peripheral measurement with

increasing eccentricities as seen in previous studies.23, 25, 34, 40, 64, 66, 71, 73 In fact, the

measurement of one eye at visual field angles of 0°, 20°, 30° and 40° confirmed that with

increasing eccentricity, tolerance to pupil misalignment error decreases even further.

The substantial and significant change in M and J180 found for the peripheral refraction

measurements at different pupil positions can mainly be attributed to the different

entrance angles of the peripheral measurement beam at the curved anterior cornea

surface, caused by the combination of peripheral measurement beam and changing

pupil/cornea position. In addition, it is assumed that the elliptical peripheral entrance

pupil can impact on measurements of the peripheral optics of the eye with respect to

pupil misalignment.

2.2.4.2 Factors Contributing to Misalignment Errors during Peripheral

Refraction Measurements

In practice, it is difficult for the operator to maintain consistent and accurate centration

of the peripheral pupil. Unlike in central refraction, this is particularly so when the

measurement of peripheral refraction profiles requires a large number of re‐alignments

and thus, increased participant cooperation, as well as operator attentiveness.

Alignment error in peripheral refractometry is augmented by inherent additional tasks,

i.e. the need for continuous re‐fixation by the participant, the re‐alignment of the

elliptical pupil with respect to the instrument axis, and the retention of a focused

peripherally shifted keratometry ring. Furthermore, time constraints and multiple

independent measurements can affect the accuracy of these tasks.

The aim of this study was to investigate the impact of lateral pupil misalignment on

peripheral refraction measurements. For future work it may also be of interest to

investigate the impact of vertical pupil misalignment on the tolerance values of the

refraction results. It should be noted that the amount of typical alignment error may be


56

different between the lateral and vertical pupil alignment as lateral pupil alignment, for

example, requires the horizontal movement of the instrument base while the vertical

alignment of the pupil centre is achieved by rotational adjustment using the instrument’s

joy stick.

2.2.4.3 Improving Pupil Alignment

Technology of objective refraction instruments is developing at a rapid pace. The first

autorefractors became commercially available almost four decades ago, and were very

costly.172 Many instruments have been developed since. Especially in terms of

affordability, objective refraction instruments are now a practical consideration for all

practitioners, be they in clinical or research settings. The latest closed‐view

autorefraction models (i.e. CBD/TOMEY RC‐5000, Nidek ARK‐530A) have been equipped

with automated pupil alignment modes, making the instruments even easier to use and

the acquisition of data thereby more reliable and time efficient. In spite of this

advancement, all autorefractors still face limitations with respect to peripheral

refraction, as all are primarily designed for on‐axis refraction while off‐label use and

technical modifications of such instruments potentially compromise some aspects of

their performance.

The results of the present study suggest it would be advantageous to have a fast and

convenient instrument which does not require repeated re‐alignment to the peripheral

entrance pupil for each visual field angle. Until such an instrument becomes generally

available, modifications of current instruments will still be required for peripheral

refractometry. It is suggested that more attention be paid to the issue of pupil alignment

and to provide adequate training for the instrument operator as well as assessment and

validation of intra‐observer and inter‐observer variability prior to the commencement of

any clinical study. A pupil scale attached to the alignment monitor might be a helpful

tool to facilitate more accurate pupil alignment. Finally, given the increased sensitivity in

measurement error it might also be considered to increase the number of repeats for

peripheral refraction measurements, particularly for larger field angles.


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2.2.5 Conclusion

This study has demonstrated that accurate lateral alignment of the entrance pupil with

the instrument axis is critical to obtain reliable results when measuring peripheral

refraction with autorefractors. The error sensitivity to misalignment was shown to

increase linearly towards the periphery. At 30° field angle, lateral pupil misalignment

should be kept well below 0.5 mm to ensure clinically relevant accuracy.

2.3 Three‐Dimensional Model of the Entrance Pupil

2.3.1 Introduction

In Section 2.2 it was shown that the requirement for precise pupil alignment is of greater

importance for the measurement of peripheral refraction when compared to central

refraction. As alignment or centration for measurement of peripheral ocular optics is

also related to the change in the shape of the entrance pupil with peripheral viewing, a

more precise understanding of how the geometry of the entrance pupil behaves as a

function of peripheral viewing angle would be of value in understanding the accuracy of

techniques modified for the measurement of the peripheral optics, such as

autorefractors and aberrometer. Not only would information relating to the peripheral

entrance pupil be useful in the current quest to understand the role of peripheral

refraction in myopia progression, but it would also be of value in many aspects of vision

science, such as those requiring knowledge of retinal irradiation (e.g. calculations of

Stiles‐Crawford effect and ocular radiation safety).

The peripheral entrance pupil has been studied previously.173, 174 However, as these were

in vivo human studies, the size and position of the anatomical pupil (aperture stop) of

the eye is unknown. Hence, information such as pupil magnification and the relationship

between entrance pupil and actual pupil centres could not be ascertained. In addition, in

these studies, the axial position and the consequent three‐dimensional shape of the

entrance pupil were not investigated and only a limited number of pupil sizes were

studied (limited to e.g. large versus normal or dilated versus natural).


58

Thus, the specific aim of this work was to extend the existing work on the peripheral

entrance pupil by modelling and assessing the three‐dimensional entrance pupil

position, shape and centration as a function of viewing angle and pupil size. Moreover,

the implications of this entrance pupil model on current peripheral refraction

measurements are discussed.

2.3.2 Methods

2.3.2.1 Model of the Entrance Pupil for Different Viewing Angles

The anterior segment (i.e. cornea and iris surfaces) of the Navarro schematic model for

the human eye175 was used for the optical modelling of the entrance pupil. The

components of this model were assumed to be circular and co‐axial, and the actual

iris/pupil surface had zero thickness. The entrance pupil of the eye was modelled as a

function of viewing angle and pupil size by ray‐tracing using ZEMAX (ZEMAX

Development Corporation, Bellevue, USA). Nine horizontal viewing angles ranging from

0° to 80° in 10° steps, and six pupil diameters ranging from 1.0 to 6.0 mm in 1.0 mm

steps were analysed.

For the ray‐tracing analysis of one pupil size at one viewing angle, the iris/pupil surface

was set as the object. Viewing angles were modelled as directions in the horizontal

meridian (around a vertical axis). Thus within this model system, the tangential meridian

lies in the horizontal plane while the sagittal meridian lies in a vertical plane. The

iris/pupil diameter was assigned the pupil size to be modelled. Sixteen points on the

iris/pupil surface and lying on the iris/pupil margin were defined, representing points on

sixteen equally spaced semi‐meridians at 22.5° increments. In addition, the point at the

iris/pupil centre was also analysed. Thus a total of seventeen object points were

analysed.

Using the robust, real ray‐aiming options in ZEMAX, from each of these object points, 24

rays consisting of 3 rings by 8 arms of rays (defined using the ZEMAX default merit

function whereby the rings represent ray‐heights of 0.336, 0.707 and 0.942 times the

pupil diameter, and the arms represent ray meridians 0.25π apart starting at 0.125π)

were traced towards the ‘observer’, which is defined as a surface with a 10 mm clear


59

diameter. The orientation of the observer is constrained so the chief ray has an angle

equal to the viewing angle being analysed and the observer surface is perpendicular to

the chief ray. In addition, the position of the observer is constrained so it remains at

100 mm distance from the anterior corneal apex. This distance portrays a typical slit‐

lamp microscope configuration. Within the above constraints, the observer is translated

along the horizontal meridian until the chief ray from the object point passes through

the centre of the observer surface.

For each object point, on emergence from the final surface (anterior cornea) following

ray‐tracing, the position of its virtual image point is determined using a merit function

criteria of minimising RMS radius of the 24 ray‐intercept points from their centroid. In

this way, the sixteen image points defining the margin of the entrance pupil and the

single point defining the image of the centre of aperture stop were computed. This

procedure was repeated for the range of pupil sizes and viewing angles defined. Figure

2.5 illustrates the optical layout for modelling of the entrance pupil at a 40° viewing

angle.

Figure 2.5: Optical layout for modelling the entrance pupil.

The image shows the modelling of the entrance pupil at a 40° viewing angle using ray‐tracing of several pupil margin points. Each individual pupil point (object point) projects 24 rays which are traced to the observer. The corresponding virtual image point was identified by applying a minimum RMS radius criterion to the emergent rays. By joining the locus of image points, as exemplified here (for clarity, only 8 points for the lower pupil margin and the central pupil point are shown), the three‐dimensional entrance pupil (dotted line) is determined.


60

2.3.3 Results

2.3.3.1 Entrance Pupil Relative to the Actual Pupil

Figure 2.6 illustrates the position of the entrance pupil relative to the eye’s actual pupil

for front‐on viewing (0°) and for selected peripheral viewing angles (for clarity, only

select viewing angles are shown; i.e. 20°, 40°, 60° and 80°) and six pupil sizes. The

observer is located in a positive tangential and axial distance from the actual pupil. For

each viewing angle, the composite annuli of all six pupil diameters represent the

entrance pupil surface showing its three‐dimensional shape and its position relative to

the actual pupil. The ‘sidewall’ provides the two‐dimensional projections of the entrance

pupils.

An animated illustration of the entrance pupil’s position for all nine viewing angles can

be found in the published online version of this work.164

Overall, the three‐dimensional position and the side projection of the entrance pupil

reveal that the centre and the distal marginal points of the peripheral entrance pupil

move anteriorly as viewing angle increases. In contrast, the proximal entrance pupil

margin moves posteriorly at low peripheral viewing angles and then anteriorly at higher

viewing angles. Moreover, it can be seen that the peripheral entrance pupil tilts towards

the direction of the viewing angle and curves (primarily concaves along the tangential

meridian) towards the observer as peripheral viewing angle increase.

2.3.3.2 Entrance Pupil Relative to the Viewing Direction

As the entrance pupil exists only from the observer’s perspective, the position changes

of the entrance pupil are best interpreted relative to the direction of the observer. To

evaluate the peripheral entrance pupil as perceived by the observer, the pupil‐

referenced model (Figure 2.6) requires correction via rotation according to the viewing

angles. In this way, the observer‐referenced entrance pupil can be constructed.


61

Figure 2.6: The three‐dimensional entrance pupil for six and nine (Media file online164)

actual pupil sizes (1 mm to 6 mm) at various viewing angles relative to the actual pupil position.

The observer is located in the positive tangential and axial distance quadrant from the actual pupil. Each annulus represents the entrance pupil margin corresponding to one actual pupil diameter. The ‘sidewall’ of the graph shows the two‐dimensional side‐projection of the entrance pupils revealing their increasing tilt and curvature with viewing angle. Note axial distance scale has been magnified for clarity.

The entrance pupil shape and position relative to the viewing direction are shown for

five selected viewing angles in the three‐dimensional graph in Figure 2.7 and for all

viewing angles in succession in the animated media file, which can be found online.164

The observer’s viewing direction is indicated by the blue phantom line. From Figure 2.7

and the online media file, the two‐dimensional back‐projection of the entrance pupil

annuli shows the narrowing and ovoid distortion of the entrance pupil’s shape with

increasing viewing angle. The three‐dimensional entrance pupil shapes and positions, as

well as their corresponding side‐projection, highlight the entrance pupil tilt relative to

the observer’s direction of view.

-4-2

02

4 -4-2

02

40.0

0.5

1.0

1.5

2.0

2.5

Actual

0o

20o

40o

60o

80o

Axi

al D

ista

nce

(m

m)

Sagittal Distance (m

m)Tangential Distance (mm)


62

Figure 2.7: The three‐dimensional entrance pupil for six and nine (online media file164)

actual pupil sizes at various viewing angles as seen by the observer.

The observer’s viewing direction is indicated by the blue phantom line. The apparent rotation of the actual pupil axis relative to viewing direction is towards the positive axial and negative tangential distance quadrant. Each annulus represents the entrance pupil margin corresponding to one actual pupil diameter. The ‘back‐wall’ of the graph shows the two‐dimensional back‐projection of the entrance pupils, which represent the entrance pupil shapes as seen by the observer. The ‘floor’ of the graph gives the side‐projection showing the tilt of the entrance pupils relative to the direction of the observer.

The tangential side‐projection of the entrance pupil is individually plotted for all nine

viewing angles in Figure 2.8. It shows the effect of increasing viewing angle on the axial

positions of points defining the margin of entrance pupils of different sizes. Relative to

front‐on viewing (at 0°) these changes in axial positions across the entrance pupil can

become substantial for large peripheral angles. For example, at 60° viewing angle the

difference in axial position relative to front‐on viewing ranges from ‐1.66 mm for the

proximal pupil margin to +3.20 mm for the distal pupil margin for an actual pupil

diameter of 6 mm. For the viewing angle of 60°, the change in axial position of the

entrance pupil centre may be as large as +0.90 mm.

-3

-2

-1

0

1

2

3

4-4

-20

24

-4

-2

0

2

4

0o

20o

40o

60o

80o

Sagittal D

istance (mm

)

Tangential Distance (mm)

Axial D

istance (mm

)


63

Figure 2.8: The tangential profile (side‐projection) of the peripheral entrance pupil from

the point‐of‐view of the observer for nine viewing angles.

The apparent (i.e. as seen by the observer) tilt of the tangential entrance pupil meridian

plotted as a function of viewing angle (Figure 2.9) demonstrates that the amount of tilt

becomes progressively smaller than the actual viewing angle as the latter increases. For

example, when the eye is observed from a 60° viewing angle, the entrance pupil tilt is

approximately 15° smaller than the viewing angle.

Figure 2.9: Apparent tilt of the tangential entrance pupil meridian as a function of viewing

angle and pupil size.

The broken line of negative 1:1 slope represents the expected apparent tilt. Apparent tilt has negative values as it is opposite in direction to viewing angle.

-3 -2 -1 0 1 2 3

-2

-1

0

1

2

3

4

5

Axi

al D

ista

nce

(mm

)


0o

10o

20o

30o

40o

50o

60o

70o

80o

0 10 20 30 40 50 60 70 80 90

-60

-50

-40

-30

-20

-10

0

App

aren

t P

upil

Tilt

(o)

Viewing Angle (o)

Actual Size 6 mm 5 mm 4 mm 3 mm 2 mm 1 mm

Tangential Meridian


64

This increasing difference between the entrance pupil tilt and the viewing angle,

together with the increasing curvature along the tangential meridian, are the

predominant factors that produce the asymmetric distortion of the peripheral entrance

pupil shape, which becomes more noticeable with increasing viewing angle. Indeed, the

shape of the peripheral entrance pupil does not correspond to an ellipse as often

assumed. Instead, although mathematically different, it resembles the shape of a convex

limaçon of Pascal. Figure 2.10 provides a comparison of the shapes of the actual circular

pupil with the peripheral entrance pupil as viewed from a 60° angle. One consequence of

this asymmetric distortion of the peripheral entrance pupil is that the bisected

(geometric) centre of the peripheral entrance pupil does not correspond to the centre of

the actual pupil.

Figure 2.10: Two‐dimensional (frontal) projection of (a) the actual pupil and (b) the

entrance pupil at 60° observation angle showing the shape as seen by the observer.

Each annulus represents one pupil diameter from 1 mm to 6 mm in 1 mm step. The blue dotted line indicates the geometrical mid‐point of the peripheral entrance pupil for the 6 mm actual pupil diameter. Actual pupil centre is located at the origin (0, 0).

When pupil decentration is considered with respect to viewing angle and actual pupil

size, the general trend demonstrates that with increasing viewing angle or increasing

pupil size the mid‐point (geometrical centre) of the peripheral entrance pupil

increasingly departs from the optical centre of the actual pupil (Figure 2.11). That is, the

geometrical centre of the peripheral entrance pupil does not map to the geometrical

centre of the actual pupil. As a consequence, the light ray corresponding to the line‐of‐

sight passes through different points in the actual pupil at different peripheral viewing

angles. The present model predicts that the systematic error when alignment is made to

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

Sag

ittal

Dis

tanc

e (m

m)


Actual

(a)-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

Sag

ittal

Dis

tanc

e (m

m)


60o

(b)


65

the apparent pupil centre can reach around 0.2 mm for a 6 mm pupil diameter at

approximately 60° viewing angle.

Figure 2.11: Entrance pupil decentration as a function of viewing angle and actual pupil

diameter.

With increasing pupil size or viewing angle, the peripheral entrance pupil gradually

becomes not only more decentred as described above, but also more asymmetric in its

shape (Figure 2.10). To evaluate these pupil size dependent shape changes as a function

of viewing angle, the size (Figure 2.12 a and c) and associated magnification changes

(Figure 2.12 b and d) of the peripheral entrance pupil along the two orthogonal

(tangential and sagittal) meridians, were plotted with respect to actual pupil diameter.

As expected (and illustrated in Figure 2.12), along the tangent meridian the entrance

pupil size decreases with viewing angle. This decreasing effect appears to be more

pronounced for smaller pupils. Geometrically, if there is no optical component between

the pupil and the observer, the tangential entrance pupil magnification would be

expected to follow a cosine function of viewing angle as shown in Figure 2.12 b.

However, due to the entrance pupil tilt and anterior movement towards the observer,

the tangential entrance pupil magnification decreases more slowly than the cosine

function as viewing angle increase.

0 10 20 30 40 50 60 70 80 90

-0.4

-0.3

-0.2

-0.1

0.0

0.1

Pup

il D

ecen

trat

ion

(mm

)

Viewing Angle (o)


Tangential Meridian


66

Figure 2.12: Entrance pupil diameter (a) and (c) and magnification (b) and (d) along the tangential (a) and (b) and sagittal (c) and (d) meridians as a function of viewing angle and actual pupil size.

The broken line in (b) represents the cosine function with viewing angle.

By least‐squares fitting to the results from the ray‐tracing model, a parametric model

that includes pupil diameter and viewing angle for the tangential pupil magnification can

be derived:

Equation 2.4: . . . . .

where p corresponds to the pupil diameter (in mm) and corresponds to the viewing

angle (in °). Equation 2.4 yielded an RMS Error of 0.0015.

It should be noted that the choice of the form of Equation 2.4 was ‘semi‐arbitrary’.

Conventionally, pupil magnification has been assumed to be related to viewing angle by

the cosine function. Since the present model demonstrated that the departure from the

elliptical shape and cosine relationship is due at least to the field curvature, it was

0 10 20 30 40 50 60 70 80 90

0

1

2

3

4

5

6

7

8

Ent

ranc

e P

upil

Siz

e (m

m)

Viewing Angle (o)


Tangential Meridian

(a)0 10 20 30 40 50 60 70 80 90

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Pup

il M

agni

ficat

ion

Viewing Angle (o)


Tangential Meridian

(b)

0 10 20 30 40 50 60 70 80 90

0

1

2

3

4

5

6

7

8

Ent

ranc

e P

upil

Siz

e (m

m)

Viewing Angle (o)


Sagittal Meridian

(c)0 10 20 30 40 50 60 70 80 90

1.10

1.12

1.14

1.16

1.18

1.20

1.22

1.24

Pup

il M

agni

ficat

ion

Viewing Angle (o)


Sagittal Meridian

(d)


67

decided to employ a modification to the cosine function in which the variable (viewing

angle) has been ‘rescaled’ according to a second‐order function. It is possible that other

forms of function can provide a better fit. But given the excellent resultant RMS, no

further attempts were made to search for a more precise form.

While Equation 2.4 quite precisely predicts tangential pupil magnification, it is somewhat

complex in structure. A simplified equation involving only viewing angle ( in °), still

with good precision (RMS Error = 0.0066 mm), may be obtained:

Equation 2.5: . .

Figure 2.12 also shows that the sagittal entrance pupil size and magnification increases

slightly with increasing viewing angle. This small increase in sagittal pupil size is slightly

greater for smaller pupils. In a similar manner as for tangential pupil magnification, a

parametric equation can be derived to predict sagittal pupil magnification with good

precision (RMS Error = 0.0083 mm) from the viewing angle (in °):

Equation 2.6: . . .

2.3.4 Discussion

Much of what is known about the peripheral entrance pupil was established many

decades ago. Spring & Stiles (1948)174 then later Jay (1962)173 measured the peripheral

entrance pupil shape for in vivo human subjects. They established the change in

diameters along the horizontal and vertical meridians with viewing angle and identified

the departure of the peripheral entrance pupil size from a cosine function with viewing

angle. Jay also noted the departure of the peripheral pupil shape from an ellipse.173

However, these early in vivo studies suffered limitations. For example, without

knowledge of the actual pupil size, the pupil magnification could not be estimated. Also,

no attempt was made to evaluate the changes in the entrance pupil in the axial

dimension.


68

The present study attempted to extend knowledge of the peripheral entrance pupil. In

particular, the model predicted the pupil magnification for a range of pupil sizes and

viewing angles. The changing shape and its departure from an ellipse of the peripheral

entrance pupil were evaluated with the consequence that the peripheral entrance pupil

centre was found to not correspond to the actual pupil centre. In addition, by

considering the axial dimension, the forward movement, compensatory tilt and

increasing curvature of the peripheral entrance pupil with viewing angle were revealed.

2.3.4.1 Comparison of the Entrance Pupil Model with in Vivo Pupils

There are a number of differences between the peripheral entrance pupil modelled in

the present study and the direct measurement studies above‐mentioned.173, 174 For

simplicity, the entrance pupil model portrays a thin (zero thickness), circular pupil that is

co‐axial with the corneal surfaces. In addition to the temporal viewing angles, Spring &

Stiles measured a nasal viewing angle and were thus able to identify the presence of

nasal‐temporal asymmetry in the peripheral entrance pupil with respect to viewing

angle. Presumably, this is due to the decentration and tilt of the corneal surfaces relative

to the iris.174 Jay suggested that iris thickness may become relevant and would have the

effect of reducing tangential entrance pupil size at high viewing angles.173 Despite these

differences, the entrance pupil model appears to produce predictions of acceptable

precision with respect to the range of in vivo measurement errors. The ratio of

tangential (horizontal) to sagittal (vertical) entrance pupil diameters as a function of

viewing angle for the entrance pupil model of this study, together with in vivo

measurements previously published173, 174 are shown in Fig. 9. In lieu of Spring & Stiles

who refer to large and small pupil diameters and Jay who refers to dilated and natural

pupil diameters, Figure 2.13 plots the values for the actual pupil diameters of 3 and 6

mm. It can be seen that the predictions lie well within the spread of measured results,

particularly of Jay.173 In addition, as the actual pupil size is known in the presented

entrance pupil model, the pupil magnification was also calculable.

The non‐elliptical shape of the entrance pupil at high peripheral angles has been noted

by Jay. The present entrance pupil model has been able to predict and describe this

shape, which appears to be caused by the increasing curvature (primarily concave

towards the observer along the tangential meridian) with viewing angle. As illustrated in


69

Figure 2.7, this curvature, when combined with the tilt of the entrance pupil, introduces

an increasing ‘fore‐shortening’ effect towards the proximal margin (i.e. the side of the

pupil nearer the observer due to pupil tilt) from the point of view of the observer. This

effect is present for all pupil sizes and viewing angles although it is most readily

observable at higher viewing angles and pupil sizes.

Figure 2.13: Comparison of the ratio of tangential (horizontal) to sagittal (vertical) entrance

pupil diameter as a function of viewing angle determined by in vivo measurements and the current entrance pupil model for 6 mm and 3 mm actual pupil diameters.

2.3.4.2 Implications of the Entrance Pupil Model

One of the major consequences of the asymmetric distortion of the peripheral entrance

pupil is the loss of correspondence between its geometrical centre and the ‘true’ optical

centre of the actual pupil. The light ray that passes through the centre of the peripheral

entrance pupil is not the ray that passes through the centre of the actual pupil. This loss

of correspondence can become relevant to measurements of the peripheral optics of the

eye, especially where measurements, such as performed with autorefractors, rely on

alignment with the centre of the peripheral entrance pupil, or where its analysis requires

knowledge of the centre of the actual pupil (aperture stop).

As shown in Figure 2.10 b, the systematic error of aligning the geometrical centre of the

entrance pupil compared to the centre of the actual pupil, can exceed 0.2 mm for a 6

mm pupil diameter. Despite this systematic error being small in absolute terms and

0 10 20 30 40 50 60 70 80

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Pup

il D

iam

eter

Rat

io

(Tan

gent

ial/S

agitt

al)

Viewing Angle (o)

Model: 6 mm Pupil Model: 3 mm Pupil Jay (1962) Dilated Pupil Jay (1962) Natural Pupil Spring & Stiles (1948) Large Pupil Spring & Stiles (1948) Small Pupil


70

falling within normal measurement variability, for some refraction instruments, this

error could impact measurement accuracy, especially at large peripheral angles. In

Section 2.2 it was shown that tolerance to pupil misalignment is much smaller for

peripheral refraction than for central refraction.126 For example, when measuring

peripheral refraction at the 30° nasal visual field using an open‐view autorefractor, the

refractive power vector components M and J180 reached clinical significance for pupil

misalignments as small as 0.2 mm.

In addition, Applegate et al. have demonstrated that misalignment from the pupil centre

during on‐axis wavefront measurements can introduce spurious coefficients into Zernike

polynomial descriptions of the wavefront. This systematic error is not only Zernike

mode‐dependent but also, the larger the misalignment, the more profound its effect.168

Assuming these findings can be extrapolated to peripheral wavefront measurements, it

is reasonable to suggest that a combination of even small pupil misalignment errors, as

well as the systematic error caused by the loss of correspondence of the peripheral

entrance pupil mid‐point with the actual pupil centre, could adversely affect the

accuracy of peripheral ocular measurements.

In many studies of peripheral optics, comparisons are made to the central optics of the

eye. Consideration of the errors in peripheral refractometry or wavefront measurements

due to systematic misalignment, as well as the loss of correspondence between

peripheral and actual pupil centres, suggest that caution needs to be exercised when

making comparisons of peripheral and central measurements.

The axial alignment of most autorefractor and aberrometer instruments requires that

either the cornea or the pupil plane be in focus. This presents no difficulty for on‐axis

measurements, wherein both the cornea mire and the pupil margin appear completely

and symmetrically in focus. According to the entrance pupil model, the axial position

shifts forward for the peripheral entrance pupil but more significantly, the pupil tilt

produces different axial positions for different points on the entrance pupil. From Figure

2.8, for a 60° viewing angle, the axial position range from the distal to the proximal pupil

margin is around 4 mm for a 6 mm pupil. This is the axial focus range of the aberrometer


71

with the peripheral entrance pupil, when focusing from the proximal to the distal pupil

margin. However, the entrance pupil’s depth of focus range for on‐axis measurements

for the COAS aberrometer lies within ±2 mm.165 Hence, dependent on the specific

instrument’s depth of focus for peripheral measurements, the precise location of the

axial position of the peripheral entrance pupil may be difficult to locate.

An additional issue relevant to the observation of the peripheral entrance pupil as well

as peripheral optical measurements should be considered. In general, the image points

from which the entrance pupil is composed, degrade in quality as viewing angle

increases. This can be seen in Figure 2.14, wherein the tangential and sagittal transverse

ray aberrations were plotted as a function of viewing angle for the vertical superior as

well as the proximal and distal horizontal pupil margins. It can be seen that the image

points at the region of the horizontal pupil, distal to the viewing direction, suffer greater

degradation than those proximal to the viewing direction. The vertical superior (and by

symmetry, vertical inferior) pupil margin was least affected by viewing direction. From

this it can be concluded that with an increase in viewing angle the peripheral entrance

pupil remains better defined along the sagittal than the tangential meridian.

Figure 2.14: Tangential and sagittal spot sizes (in mm) for the horizontal proximal and

distal pupil margins as well as the vertical superior pupil margin as a function of viewing angle.

0 10 20 30 40 50 60 70 80 90

0

2

4

6

8Entrance Pupil Position / Meridional Spot Size

Horizontal Proximal, Tangential Horizontal Proximal, Sagittal Horizontal Distal, Tangential Horizontal Distal, Sagittal Vertical Superior, Tangential Vertical Superior, Sagittal

Viewing Angle (°)

Sp

ot S

ize

, Hor

izo

ntal

Pup

il P

oint

s (m

m)

0.0

0.2

0.4

0.6

0.8

Sp

ot Size

, Ve

rtical Pup

il Po

ints (mm

)


72

2.3.4.3 The Wide‐Field Eye

The eye is exquisitely suited for extreme wide‐field light‐collection. The optical layout of

the human eye resembles the design of a retrofocal, ‘fisheye’ camera lens,176 capable of

collecting light at field angles well beyond the retinal‐neural and facial anatomical limits

of the eye. The entrance pupil model demonstrated that this extreme wide‐field

capability is made possible by the forward movement towards the observer and the

compensatory tilt of the entrance pupil with increasing viewing angle. As a result, the

tangential entrance pupil magnification decreases more slowly than the cosine function

as viewing angle increases. Extrapolation of the results in Figure 2.12 b shows that, even

at 90° field angle, the tangential magnification relative to the front‐on magnification is

around 0.3. Since the sagittal magnification increases with field angle, the outcome is

that even at right‐angle illumination, the entrance pupil is collecting more than 30% of

incident light. This capability represents an obvious advantage in defensive sensing of

the environment but may also present a disadvantage in terms of radiation safety of the

eye. For example, the phenomenon of “peripheral light focusing”,177, 178 particularly the

focusing of scattered light from the peripheral field, has been demonstrated to be a

plausible explanation for the occurrence of radiation‐related cataracts and other light‐

related ocular pathologies (coined the “ophthalmohelioses”178) at post‐iris locations that

are not involved in front‐on light focusing.

2.3.4.4 Recommendations for Future Models

The present model has a number of limitations. The simplification of co‐axial corneal and

iris surfaces has already been mentioned, as have the assumptions of a circular,

concentric pupil and a thin iris. In reality, the iris boundary is not perfectly circular and

varies with age, illumination and pupil size.179 Also, the position of the pupil can shift

during constriction/dilation, which can be as much as 0.6 mm180 and it has been found

that the pupil constricts significantly more during oblique viewing when compared to the

straight ahead gaze.65 An improved model, incorporating non‐circular, eccentric pupils

may provide additional insight into the peripheral entrance pupil.

The measurements of Spring & Stiles suggested that the sagittal pupil magnification

increases to a peak at 80°, decreasing again above that angle. Due to a limitation in the


73

optical layout, the entrance pupil model was not able to compute results for viewing

angles at or above 90°. It would be interesting to model and verify this reversal of

sagittal pupil magnification at very high viewing angles.

Finally, for the study of peripheral retinal image quality or other retinal responses, such

as the Stiles‐Crawford Effect, it might be of more value to analyse the exit pupil shape

and size with viewing angle. Such an analysis would need to take into the account the

complex shape181 and gradient refractive index of the crystalline lens.182 Hopefully,

future work can address these aspects of the peripheral optics of the eye.

2.3.5 Conclusion

As the viewing angle increases, the entrance pupil moves forward, exhibits

compensatory tilt and increases in concavity towards the observer. In consequence the

tangential pupil size does not follow a cosine relationship with viewing angle, the shape

of the entrance pupil undergoes asymmetric (non‐elliptical) distortion, and the

geometrical centre of the entrance pupil does not represent precisely the centre of the

actual pupil. Thus, peripheral ocular measurements may be affected adversely,

particularly where alignment to the pupil centre is required. Given the potential adverse

impact misalignment may have on ocular measurements, such as autorefraction, caution

is warranted when comparing such results between peripheral and central viewing

angles. Overall however, it can be concluded that typically, these departures are small

and may only be of significance for peripheral viewing angles larger than 40°.

2.4 Summary

The clinical study on pupil alignment tolerance demonstrated that, independent of the

central refractive error of the eye, even small lateral pupil alignment errors caused by

the operator can lead to significant measurement errors in peripheral refractometry

when using commercially available autorefractors. In addition, the three‐dimensional

entrance pupil model demonstrated that, due to its geometrical behaviour when viewed

from a peripheral angle, the peripheral entrance pupil is not elliptical as assumed and

the mid‐point of the peripheral pupil does not correspond to the centre of the actual

pupil.


74

From both studies it can be concluded that precise pupil alignment is critical for accurate

measurements of peripheral refraction and that entrance pupil alignment with its mid‐

point, as currently performed in peripheral refractometry, can induce small systematic

lateral errors.

In practice, however, it could be very difficult to circumvent small pupil alignment errors

during peripheral refractometry. Thus, it would be advantageous to have means by

which to correct for such operator‐related errors and to thereby provide more accurate


CHAPTER 3: MEANS TO RECTIFY PUPIL ALIGNMENT ERRORS

75

CHAPTER 3:

MEANS TO RECTIFY PUPIL ALIGNMENT ERRORS IN CURRENT PERIPHERAL REFRACTOMERTY#

3.1 Introduction

Results of Chapter 2 showed that precise pupil alignment is important for accurate

measurements of peripheral refraction. Nevertheless, even for a well‐trained operator,

normal pupil alignment variability is likely to be greater than the precision required for

accurate peripheral refraction measurements. This is due to the fact that measurements

of peripheral refraction profiles require numerous inherent tasks, such as continuous re‐

fixation by the participant and constant re‐alignment of the pupil with respect to the

instrument axis by the operator. The latter is additionally affected by inter‐subject

variability, which is caused by unintended eye or head movements as well as the

anatomy of the eye and eye lid, which can impact the visibility of the pupil area required

to appropriately locate the pupil centre.

The aim of this chapter was to investigate a method that rectifies measurement errors,

which occur during the alignment procedure in peripheral refractometry using modified

commercially available instruments.

In summary, the method requires the following key steps to be taken. Firstly, a

correction algorithm for pupil misalignment is to be established for the instrument to be

used. This can be achieved by using a similar study protocol as explained in Section 2.2,

in which peripheral refraction was measured at pre‐defined pupil positions in order to

determine the functions of pupil alignment.

# Work from this chapter is based on the provisional patent application AU2010901866

(APPENDIX A) and was accepted as poster presentation (ARVO 2011, Fort Lauderdale).


76

Instead of measuring two selected peripheral visual field angles, measurements at

multiple visual field angles may be collected in order to assess and establish the

relevant viewing‐angle‐ and/or pupil‐position‐dependent correction algorithms. In the

second step, the instrument’s pupil alignment monitor is to be interfaced with a

computer for the purpose of simultaneous capturing of the pupil alignment screen. From

each recorded image, the amount of pupil misalignment is to be determined. The

measured parameters, i.e. the refractive error and the amount of pupil misalignment,

are then fed into the pre‐determined correction algorithms to compensate peripheral

refraction data for their alignment errors.

3.2 Methods

3.2.1 Phase 1

3.2.1.1 Participants

Ethics approval for this study was received from the University of New South Wales

Human Research Ethics Advisory Panel. All participants were recruited and pre‐screened

for good ocular health and were not enrolled if they had any history of ocular anomalies.

There was no exclusion restriction with respect to the refractive error of the

participants’ eyes. In order to establish the pupil misalignment correction algorithm,

central and peripheral refraction measurements were performed in the right eyes of 40

adult participants. To confirm instrument binocularity with respect to peripheral

refraction and pupil alignment, in a subset of 10 participants, central and peripheral

refraction was measured in the left eye as well. All eyes were measured under

uncorrected and non‐cycloplegic conditions. To maintain stable fixation and

accommodation at all angles, the participants’ non‐measured eye was occluded during

the entire peripheral refraction procedure.

3.2.1.2 Instrumentation and Alignment Procedure

For this study, the visual field range of the Shin‐Nippon NVision K5001 was modified to

permit the measurements of central and various peripheral visual field angles, i.e. 20°,

30° and 40° into the temporal and nasal visual fields, as well as 20° and 30° into the

inferior visual fields. For this, laser fixation targets were projected onto the wall, one at


77

a time and in randomised order. For the refraction procedure, each participant was

requested to turn his/her head towards the presented fixation target. Correct head

alignment was monitored by the operator throughout the measurement procedure.

For each visual field angle measured, the operator’s task was to align the instrument at

several pupil positions relative to the pupil centre. In addition to the horizontal pupil

alignment meridian as measured in the previous study (Chapter 2), this study also aimed

to investigate the impact of vertical pupil de‐alignment. As the minor elliptical entrance

pupil axis for the 40° visual field angle is narrowed further when compared to the

previously measured 30°, the distance between the five pupil de‐alignment positions was

reduced from 1.00 mm to 0.75 mm. As such, the nine pupil alignment positions were the

centred pupil (0mm) and 0.75 mm, 1.50 mm relative from pupil centre towards the

nasal, temporal, inferior and superior pupil. Positive horizontal de‐alignment was

defined as the movement of the instrument axis towards the nasal portion of the pupil

and negative horizontal pupil de‐alignment was defined as the movement of the

instrument axis towards the temporal portion of the pupil. For vertical pupil de‐

alignments, the definition refers to positive de‐alignment being the movement of the

instrument axis towards the superior portion of the pupil while negative pupil de‐

alignment is the movement of the instrument axis towards the inferior portion of the

pupil. For each pupil position, measurements were repeated five times.

All data retrieval and analyses were performed in terms of refractive power vectors, M

(spherical equivalent), J180 (with‐ and against‐the‐rule astigmatism) and J45 (oblique

astigmatism) as well as with respect to the common sphero‐cylindrical notation, i.e.

sphere, cylinder and axis.

By least‐square fitting to the results obtained from this pupil alignment matrix, three

correction models, i.e. a general linear model to be used for the correction of any

measured visual field angle as well as a linear and a quadratic visual field dependent

model, were established and validated.


78

3.2.2 Phase 2

3.2.2.1 Participants and Instrumentation

In addition to the measurements performed at pre‐defined pupil positions, Phase 2

measurements were taken at random horizontal and vertical positions approximate to

the pupil centre.

Using the same instrument set‐up as in Phase 1, peripheral refraction was sequentially

measured in the right eyes of four participants for seven different visual field angles;

that is for the central visual field 0° and along the horizontal visual field in, 20°, 30° and

40° towards the temporal and nasal direction. This procedure was repeated six times.

3.2.2.2 Entrance Pupil: Image Capture and Analysis

To determine the pupil alignment error during the refraction measurement, the image

from the pupil alignment screen, as seen by the operator, was captured using an image

capture device. Thereupon, customised software (software courtesy Dr. Klaus Ehrmann)

was used to determine the amount of horizontal and vertical pupil misalignment.

By use of the three established correction models from Phase 1, each individual

measurement was corrected. The measurement errors before and after correction were

assessed in terms of the three refractive power vectors M, J180 and J45.

3.3 Results

3.3.1 Phase 1

3.3.1.1 Establish Correction Models

Table 3.1 lists the study demographics of participants who attended Phase 1.

Table 3.1: Study demographics for participants in Phase 1.

Mean Age (± SD) Age range Baseline Mean M (±SD) in D

in years OD OS

n = 40 33.8 ± 9.0 24 to 59 ‐2.44 ± 2.90 ‐

n = 10 29.4 ± 6.0 24 to 44 ‐2.43 ± 2.63 ‐2.44 ± 2.69


79

The refractive vector components M, J180 and J45 as well as the more commonly known

components of the sphero‐cylindrical notation, i.e. sphere, cylinder and axis, were

plotted as a function of pupil alignment position and visual field angle. The data are

provided for central, six horizontal and two inferior visual field angles and for all five

pupil (de‐)alignment positions, i.e. 0 mm. ± 0.75 mm and ± 1.50 mm in the horizontal and

vertical pupil alignment meridian. Key results are presented graphically in terms of

absolute and relative peripheral refractive errors from pupil centre. For all relative

graphs, refractive power vector components of the centred entrance pupil were

subtracted from the corresponding components from the de‐aligned pupil

measurements. In addition to the graphs, regression analysis was performed to indicate

linearity of the individual pupil alignment functions. Parametric equations for the

respective refractive vector components were established by least‐square fitting to

provide the general linear correction algorithm. In addition, for each individual field

angle, linear and quadratic correction models were also determined (APPENDIX B).

3.3.1.1.1 Refractive Vector Component M

Figure 3.1 illustrates the absolute and the relative mean of the refractive vector

component M of the participant group (n = 40) plotted as a function of pupil alignment

and visual field angle.

For measurements of peripheral refraction in the horizontal visual fields, de‐alignment of

the instrument axis in the horizontal pupil meridian showed a good linear correlation in

M across the pupil meridian (r2 > 0.96). This was also found for the measurements of

peripheral refraction in the inferior visual fields, when the pupil was de‐aligned in the

vertical pupil meridian. For both combinations of either horizontal visual field and

horizontal pupil meridian or inferior visual field and vertical pupil meridian, the slope of

the pupil alignment function increased with increasing peripheral visual field angle. The

greatest difference across the pupil meridian was found for the 40° nasal visual field

measurement, where the refractive difference in M was as large as 5.91D between the

1.5 mm nasal and 1.5 mm temporal pupil de‐alignment positions. With reference to the

centred pupil it is shown that with increase in visual field angle, the refractive vector

component M decreased. From this it can be concluded that the participant group had

on average a relative myopic shift in the periphery.


80

Absolute Relative

Horizontal Visual Field

Horizontal Pupil Alignment


Vertical Pupil Alignment

Vertical Visual Field




Figure 3.1 The refractive vector component M (in D) plotted as a function of pupil alignment position (in mm) for the vertical and horizontal pupil meridian (n=40).

Data are plotted for measurements taken in the central visual field, in 6 horizontal visual fields and in two inferior visual fields. Regression analysis was performed to indicate linearity (r2) of the individual pupil alignment functions.


81

The graphs also show that the points of intersection, where the nasal and temporal pupil

alignment functions of the same angle meet, e.g. N40 and T40, are displaced nasally

from the pupil centre. This indicates that the nasal visual field measurements showed a

greater relative shift in M than the measurements of the temporal visual field. Similar

asymmetric findings can be made for the inferior visual field measurements and their

vertical pupil de‐alignment functions. Moreover, the relative graph for the combination

of horizontal peripheral refraction and horizontal pupil de‐alignment indicates that the

differences between nasal and central pupil alignment were larger than the differences

between temporal and central alignment.

The graphs for the combination of either horizontal visual field and vertical pupil

meridian or inferior visual field and horizontal pupil meridian demonstrated that in most

cases M decreases slightly towards either pupil de‐alignment direction. This slight

decrease appeared to be consistent for all nasal visual field angles measured. For the

temporal visual fields there was some linearity found, in particular at 40°, where the

difference to central refraction was greatest, i.e. 0.50D at the 1.50 mm inferior pupil

alignment position. Nevertheless, when compared to the graphs where the visual field

meridian was parallel to the pupil alignment meridian, this refractive difference in M was

relatively small.

In summary, pupil de‐alignments perpendicular to the measured visual field meridian

showed a small or no effect on the refractive vector component M, when performing

peripheral refraction. In contrast, pupil de‐alignments parallel to the visual field

meridian had a substantial impact on the refractive vector component M.

For the correction of M for pupil misalignments, three correction models were

established by least‐square fitting. The first model was selected to be a general linear

model, which can be used for the correction of any measured visual field angle. It

provides a symmetric correction for nasal and temporal visual field measurements. To

also account for the slight asymmetry observed between nasal and temporal visual

fields, the second model chosen corrects for each individual visual field angle by using a

linear correction algorithm. Lastly, a quadratic model was chosen for each individual


82

visual field angle to also correct for the small asymmetry found with respect to nasal and

temporal pupil misalignment.

The linear and quadratic pupil alignment correction algorithms for each individual

peripheral visual field angle can be found in APPENDIX B while the following two

parametric equations provide the general linear correction algorithms for M.

In order to correct the measured refractive vector component Mm (in D) when pupil

misalignment occurs laterally during the measurement of any horizontal visual field

angle (0°<θ<40°), the following equation was derived for calculation of the corrected Mc

(in D):

Equation 3.1: . .

where positive θ is the nasal visual field angle measured (in °), negative θ is the temporal

visual field angle (in °), positive PP is the nasal pupil alignment position (in mm) and

negative PP is the temporal pupil alignment position (in mm).

If vertical pupil misalignment occurs during peripheral refraction measurement in the

inferior visual field (0°<θ<30°), the measured refractive vector component Mm (in D) can

be corrected using the following parametric equation for Mc (in D):

Equation 3.2: . .

where positive θ is the inferior visual field angle measured (in °), positive PP is the

superior pupil alignment position (in mm) and negative PP is the inferior pupil alignment

position (in mm).

Lastly, it should be noted that the standard deviations in Figure 3.1 were omitted for

clarity in order to permit easier comparison of the pupil alignment slopes for each visual

field angle of the group. Standard errors increased with increase in de‐alignment from


83

pupil centre and with increase in peripheral visual field angle. The RMS errors of all

correction models can be found in APPENDIX B.

3.3.1.1.2 Refractive Vector Component J180

With increase in visual field angle, the same linear increasing trends (r2 > 0.96) as found

for M (Figure 3.1) were observed for J180 (Figure 3.2) for the same combinations of either

horizontal visual field and horizontal pupil meridian, or vertical visual field and vertical

pupil meridian.

With reference to centred pupil alignment, the absolute graphs showed that there is a

substantial shift in J180 with increasing viewing angle. This measured shift was greater for

all the nasal visual field angles when compared to the temporal visual field angles. Also,

the relative graphs for lateral pupil de‐alignment in the horizontal visual field

measurements again demonstrate that the differences in J180 (in D) between nasal and

central pupil alignment were larger than the differences between temporal and central

alignment.

With respect to the results obtained for J180 where pupil de‐alignment was perpendicular

to the measured visual field meridian, it was again apparent that for all visual field

angles J180 changed consistently by relatively small amounts with increasing distance

from the pupil centre when compared to pupil de‐alignment measurements parallel to

the visual field meridian.

The following parametric equations provide the general linear pupil alignment correction

algorithms for J180 for the two relevant combinations of visual field and pupil meridian.

If lateral pupil misalignment occurs during peripheral refraction measurement in the

horizontal visual field (0°<θ<40°), the measured refractive vector component J180m can be

corrected using the following parametric equation for J180c (in D):

Equation 3.3 . .


84

Absolute Relative









Figure 3.2 The refractive vector component J180 (in D) plotted as a function of pupil alignment position (in mm) for the vertical and horizontal pupil meridian (n=40).

Data are plotted for measurements taken in the central visual field, in six horizontal visual fields and in two inferior visual fields. Regression analysis was performed to indicate linearity (r2) of the individual pupil alignment functions.


85

where positive θ is the nasal visual field angle measured (in °), negative θ is the temporal

visual field angle (in °), positive PP is the nasal pupil alignment position (in mm) and

negative PP is the temporal pupil alignment position (in mm).

Correction of J180m (in D) for vertical pupil alignment errors when measuring the inferior

visual field (0°<θ<30°) can be achieved using the following parametric equation:

Equation 3.4: .

where positive θ is the inferior visual field angle measured (in °), positive PP is the


position (in mm).

In addition to the general linear parametric equations, the linear and quadratic

correction functions for each individual visual field angle can be found in APPENDIX B.

3.3.1.1.3 Refractive Vector Component J45

Figure 3.3 details the absolute and relative graphs for J45 for all four combinations of

visual field and pupil alignment meridian.

In contrast to the linear correlations found for M and J180 for the combinations where the

visual field meridian was parallel to the pupil alignment meridian, the refractive power

vector J45 did not exhibit any substantial changes with increasing visual field angle.

Instead, J45 showed linear trends for the combinations where the visual field meridians

were perpendicularly directed to the measured pupil alignment meridians (r2 ≥ 0.97). In

these cases, the absolute slope of the pupil alignment function increased with increase

in visual field angle. Again, the greatest refractive difference in J45 across the pupil

meridian was found for the 40° nasal visual field measurement, which in absolute terms

ranged from ‐1.10D to 1.30D. With reference to centred pupil alignment, a small shift in

J45 was observed with increase in peripheral visual field angle. Moreover, the points of

intersection where the pupil alignment functions of the same field angle meet, e.g. N40


86

and T40, were displaced inferiorly from the pupil centre. Similar asymmetric findings

were made for the inferior visual field measurements and their horizontal pupil de‐

alignment functions.

From the J45 data plotted in Figure 3.3 the linear and quadratic correction functions for

each individual visual field angle (APPENDIX B) as well as the following parametric

equations for the general linear model were determined for the calculation of the

corrected J45c (in D).

If pupil de‐alignment occurs in the vertical pupil meridian when measuring peripheral

refraction in the horizontal visual field (0°<θ<40°) the following equation was derived:

Equation 3.5: . .

where J45m is the measured J45 value (in D), positive θ is the nasal visual field angle

measured (in °), negative θ is the temporal visual field angle (in °), positive PP is the


position (in mm).

If pupil de‐alignment occurs in the horizontal pupil meridian when measuring peripheral

refraction in the inferior visual field (0°<θ<30°), the measured J45m can be corrected

using the following parametric equation:

Equation 3.6: . .

where positive θ is the inferior visual field angle measured (in °), positive PP is the nasal

pupil alignment position (in mm) and negative PP is the temporal pupil alignment

position (in mm).

It can be concluded that despite the fact that pupil de‐alignment in the meridian parallel

to the measured visual field affected M and J180, pupil de‐alignment along the meridian

perpendicular to the visual field meridian is also of relevance in obtaining accurate

measurements for J45.


87

Absolute Relative









Figure 3.3 The refractive vector component J45 (in D) plotted as a function of pupil alignment position (in mm) for the vertical and horizontal pupil meridian (n=40).

Data are plotted for measurements taken in the central visual field, in 6 horizontal visual fields and in two inferior visual fields. Regression analysis was performed to indicate linearity (r2) of the individual pupil alignment functions.


88

3.3.1.1.4 Sphero‐Cylindrical Notation

In addition to the refractive vector components M, J180 and J45 the more commonly

known sphero‐cylindrical notation, which is described by the three components sphere,

cylinder and axis, was also plotted as a function of pupil de‐alignment and horizontal

visual field angle (Figure 3.4).

Figure 3.4 shows that for horizontal pupil de‐alignments, the sphere component, which

unlike M has no additional astigmatic portion, showed a symmetrical relationship

between nasal and temporal visual field measurements, when referenced to the centred

pupil. Vertical pupil alignment had no substantial impact on the sphere values for either

horizontal visual field angle.

From the plots of the cylinder and axis components as a function of horizontal visual

field angle, the following is apparent: the cylinder component was only affected by

horizontal but not vertical pupil de‐alignment and the axis component showed a good

correlation for vertical but not for horizontal pupil de‐alignment. The cylinder

component showed greater changes as a function of pupil alignment in the nasal visual

field than in the temporal visual field.

3.3.1.2 Investigation of Instrument Binocularity with Pupil Alignment

The top graphs in Figure 3.5 show the relative mean refractive power vectors M, J180 and

J45 as a function of lateral pupil de‐alignment and visual field angle for the right and left

eyes of the selected participant sub‐group (n = 10). Overall, right and left eye slope data

demonstrated very good agreement for M and J180 (paired samples correlation r > 0.726,

p < 0.017) for all peripheral visual field angles. Paired t‐test analysis showed that there

was no difference in M and J180 between the right and left eye slope data for any of the

peripheral visual fields measured (p > 0.069). The only exception was J180 in the 30° nasal

visual field (p = 0.02). Additionally, for each of the five pupil alignment positions and for

each of the seven visual field angles, the relationship between the right eye and left eye

was plotted with respect to each refractive vector component. These plots are shown in

Figure 3.5 bottom, which show the good agreement for M and J180 between right and left

eye data.

CHAPTER 3 MEANS TO RECTIFY PUPIL ALIGNMENT ERRORS

89

Figure 3.4: The sphere, cylinder and axis components plotted as a function of pupil alignment position (in mm) for the vertical and horizontal pupil meridian (n=40).

Data are plotted for measurements taken in the central visual field and in six horizontal visual fields.

Sphere (in D) Cylinder (in D) Axis (in °)





CHAPTER 3 MEANS TO RECTIFY PUPIL ALIGNMENT ERRORS

90

M (in D) J180 (in D) J45 (in D) Peripheral Refraction Data for

the Right and Left Eye

Relationship betw

een Right

and Left Eye Data

Figure 3.5: Right and left eye refraction data as a function of pupil alignment.

TOP: Relative mean refractive power vectors M, J180 and J45 as a function of lateral pupil alignment and visual field angle for the right and left eyes (n=10). BOTTOM: Relationship between right and left eye data, i.e. M, J180 and J45, plotted for the respective pupil position and field angle measured. The grey dotted line (in graphs M and J180) represents the 1:1 ratio between the right and left eye.


91

As previously shown J45 was not affected by horizontal pupil de‐alignment and

consequently no significant correlation with respect to pupil alignment positions and

peripheral visual field angle was found between right and left eye slope data (paired

samples correlation r < 0.584, p > 0.076) except at the 30° temporal visual field position

(paired samples correlation r = 0.722, p = 0.018).

3.3.1.3 Validation of the Correction Algorithm

For the validation of the three established correction models, each of the individual

measurements obtained in Phase 1 were corrected by the known amount of pupil de‐

alignment. The spread of the remaining errors provides information on the accuracy of

the correction algorithms.

Figure 3.6 compares the models used for the correction of the measured M at the pupil

de‐alignment positions when peripheral refraction was performed along the horizontal

visual field meridian.

Whereas the general linear model, a symmetrical correction model for nasal and

temporal visual field measurements, provided a good overall correction, the algorithm

under‐corrected M for the nasal pupil de‐alignment positions at 40° nasal visual field

measurements. The individual linear model reduced the errors further for most of the

visual field angles (Figure 3.6). However, again, due to the measured asymmetry in the

40° nasal visual field between nasal and temporal pupil de‐alignment positions, the

linear correction remained poorest for this visual field angle. The individual quadratic

model as shown in Figure 3.6 (bottom) provided the best pupil misalignment correction

algorithm for M at all visual field angles.

The standard deviation of the repeated measures of all the measured and the corrected

refractive vector components for all visual field angles and all pupil de‐alignment

positions were determined and plotted in Figure 3.7. All three correction algorithms

reduced the measurement error of each refractive vector component by at least 58%.

Further, the individual quadratic model provided the best correction of pupil

misalignment, which improved the error by more than 80% for each refractive vector

component.


92

Measured M

General Linear Model Corrected M (n=40) using the General Linear Model

Individual Linear Model Corrected M (n=40) using the Individual Linear Model

Individual Quadratic Model Corrected M (n=40) using the Individual Quadratic Model

Figure 3.6: Three pupil alignment correction models.

TOP: RPRE of M as a function of pupil alignment position and horizontal visual field angle for the measured M. LEFT: The three pupil alignment correction models, i.e. the general linear model, the individual linear model and the individual quadratic model. RIGHT: The three corrected RPRE’s of M as a function of pupil alignment position and horizontal visual field angle.

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00

5.00

‐1.5 ‐0.75 0 0.75 1.5

RPRE (in D) ‐Measured Data

Pupil Alignment Position (in mm)

T40

T30

T20

Cen

N20

N30

N40

nasal pupiltemporal pupil

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00

5.00

‐1.5 ‐0.75 0 0.75 1.5

RPRE (in D) ‐General Linear M

odel


T40

T30

T20

Cen

N20

N30

N40

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00

5.00

‐1.5 ‐0.75 0 0.75 1.5

RPRE (in D) ‐Corrected Data


T40

T30

T20

Cen

N20

N30

N40

temporal pupil nasal pupil

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00

5.00

‐1.5 ‐0.75 0 0.75 1.5

RPRE (in D) ‐Individual Linear M

odel


T40

T30

T20

Cen

N20

N30

N40


‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00

5.00

‐1.50 ‐0.75 0.00 0.75 1.50



T40

T30

T20

Cen

N20

N30

N40


‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00

5.00

‐1.5 ‐0.75 0 0.75 1.5

RPRE (in D) ‐Individual Q

uadratic Model


‐40

‐30

‐20

0

20

30

40


‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00

5.00

‐1.50 ‐0.75 0.00 0.75 1.50



T40

T30

T20

Cen

N20

N30

N40



93

Figure 3.7: Standard deviation (in D) for M, J180 and J45 before and after correction.

The three models used for correction were the general linear model, the individual linear model and the individual quadratic model.

3.3.2 Phase 2

3.3.2.1 Implementation of the Correction Algorithms

Figure 3.8 demonstrates the scatter of the pupil alignment positions which were

determined from the images taken during the peripheral refraction measurements of the

four participants. In total, this data set includes six repeats for the central visual field

and the 20°, 30° and 40° nasal and temporal visual field positions. The scatter plot

indicates that there was a slight trend to more nasal and superior pupil misalignment

and that there was a larger spread along the horizontal direction compared to vertical.

From the individually determined pupil alignment positions, the refractive vector

components were corrected for each measurement using the three correction models.

The refractive power vectors M and J180 were corrected for horizontal pupil

misalignments and J45 was corrected for vertical pupil misalignment. Figure 3.9 shows

the mean peripheral refraction profile of the group for all three peripheral refractive

vectors, when measured and corrected using the three correction models.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

M J180 J45

Standard Deviation in D

Measured

General Linear Model

Individual Linear Model

Individual Quadratic Model


94

Figure 3.8: Pupil alignment positions as measured during peripheral refraction.

As the peripheral visual field angle increased, the change between the measured and

corrected M and J180 also increased. This indicates the impact of pupil misalignment on

the mean peripheral refraction profiles. The greatest difference was found for M in the

40° nasal visual field, which was 0.60D for the general linear model, 1.14D for the

individual linear model and 1.02D for the individual quadratic model. Moreover, it

demonstrates that for all three refractive vector components the standard deviations of

the measured data were greater than the standard deviations of the corrected data.

After correction using the best model (quadratic model), the measurement error for M,

J180 and J45 was reduced by 37%, 29% and 25%, respectively.

Figure 3.10 illustrates the spread of the repeated peripheral refraction measurement for

each of the four participants, before and after correction with the individual quadratic

correction model.

Although, in general, the spread of the corrected peripheral refraction measurements

narrowed when compared to the measured data, there are some visual field positions

for some participants where the spread even after correction showed no improvement.

‐1.50

‐1.00

‐0.50

0.00

0.50

1.00

1.50

‐1.50 ‐1.00 ‐0.50 0.00 0.50 1.00 1.50

Vertical Pupil Alignment Position

(in mm)

Horizontal Pupil Alignment Position (in mm)

Pupil Alignment Positions

inferior pupil

superior pupil



95

Figure 3.9: Measured and corrected M, J180 and J45 as a function of horizontal visual field angle.

Error bars indicate standard deviations of the repeats.

‐6.00

‐5.00

‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M in D

Visual Field Angle (in °)

measured

general linear model

individual linear model

individual quadratic model

Nasal FieldTemporal Field

‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

J 180 in D


measured





‐2.00

‐1.50

‐1.00

‐0.50

0.00

0.50

1.00

1.50

2.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

J 45 in D


measured






96

Figure 3.10: Spread of the repeats for the measured and corrected M (in D) as a function of peripheral visual field angle of the four participants.

‐11.00

‐10.00

‐9.00

‐8.00

‐7.00

‐6.00

‐5.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M(D)

Visual Field Angle (°) Nasal FieldTemporal Field

Participant# 1 ‐ Before Correction

‐11.00

‐10.00

‐9.00

‐8.00

‐7.00

‐6.00

‐5.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M(D)


Participant# 1 ‐After Correction

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M(D)



‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M(D)


Participant # 2 ‐After Correction

‐5.00

‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M(D)



‐5.00

‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M(D)


Participant# 3 ‐After Correction

‐5.00

‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M(D)



‐5.00

‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M(D)


Participant # 4 ‐After Correction


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3.4 Discussion

Based on the preliminary findings in Chapter 2, which demonstrated the relevance of

precise pupil alignment in peripheral refractometry, the present study extended this

investigation to establish, validate and test a methodology for the correction of pupil

alignment errors which may arise during peripheral refractometry when using

conventional autorefractors.

3.4.1 Functions of Pupil Alignment

To establish correction models for pupil misalignment, peripheral refraction

measurements were obtained across the horizontal and vertical pupil meridian and along

selected horizontal and vertical visual field angles. From this data set, the relevant

combinations of visual field meridian, pupil alignment meridian and refractive vector

component were identified and three candidate correction algorithms were established.

3.4.1.1 Functions of Pupil Alignment for Different Visual Field Angles

Overall, the functions of pupil alignment obtained in the current study showed that

tolerance to pupil misalignment decreases as visual field angle increases. Specifically, if

pupil misalignment occurred along the same meridian as the measured visual field, the

refractive vector components M and J180 were increasingly affected as visual field angle

increased. Conversely, J45 was affected when pupil de‐alignment was orthogonal to the

measured visual field meridian.

The substantial changes found in the spherical error with increase in pupil misalignment

and visual field angle can be associated to the changing incidence angle of the

measurement beam with respect to the changing cornea positions as the pupil was de‐

aligned relative from its centre. Using a simplified ray‐tracing approach in ZEMAX, the

rotationally symmetric schematic model eye by Escudero‐Sanz and Navarro183 was

selected to show the impact of ray propagation for two visual field angles. For this, rays

were traced into the eye, i.e. central and 40° nasal visual field and at three different

pupil alignment positions, i.e. the entrance pupil was either centrally aligned or laterally

de‐aligned by ±0.75 mm and ± 1.50 mm.


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Figure 3.11 indicates that the rays from the measurement beam entering the eye at

same field angles pass through different locations at the cornea for centred and positive

and negative pupil de‐alignment respectively. For on‐axis rays, pupil de‐alignment

towards the temporal or nasal pupil portion affects the propagation of the rays equally

as the corneal curvature remains symmetrical with respect to the on‐axis rays. This is in

accordance with the empirical results which demonstrated a small quadratic trend in M

with increasing pupil de‐alignment towards the nasal or temporal direction (Section

3.3.1.1.1).

Figure 3.11: Central and peripheral (40°) rays traced into the eye for three different pupil alignment positions, i.e. left: 1.5 mm temporal, middle: central and right: 1.5 mm nasal pupil position.

However, when de‐aligning the pupil temporally for the measurement of the nasal visual

field, the rays enter the cornea at a position at which the cornea is strongly curved with

respect to the incidence beam. Thus, rays refract not only asymmetrically due to the

oblique incidence angle, which is reflected by the large amount of oblique astigmatism

measured (Section 3.3.1.1.2), but also focus in front of the retina, which explains the

more negative peripheral refraction measured (Section 3.3.1.1.1). In contrast, for pupil

alignment towards the nasal pupil, the rays enter the cornea at a much flatter position,

yielding more positive refraction results, when compared to the temporally or centrally

aligned pupil.

In general, when increasing the visual field angle during peripheral refractometry, the

incidence of the measurement beam at the cornea (aligned for pupil centre) becomes

more oblique and astigmatism (J180) increases.23, 24 Where pupil misalignment occurs in

the same meridian as the peripheral visual field to be measured, the amount of

astigmatism (J180) changes additionally across the pupil. Consequently, the combination


99

of increased magnitude of astigmatism in the periphery and the additional astigmatic

changes across the pupil meridian contribute to the decreased tolerance to pupil

misalignment in peripheral refraction measurements.

The current study also demonstrated that vertical pupil de‐alignment affected the

refractive vector component J45. The significant changes found in J45 can be explained by

the linearly changing axis values when aligning the pupil perpendicular to the measured

visual field meridian.

3.4.1.2 Functions of Pupil Alignment for Different Ocular Parameters

In the present study, a method for the correction of pupil misalignment was developed

using refraction data of a general population group. Although, overall linearity of the

pupil alignment functions was good, the RMS error of the functions increased as visual

field angle increased. In order to further improve the correction algorithms, group‐

specific algorithms, such as based those on different ocular parameters, i.e. corneal

asphericity, corneal curvature, vitreous length and retinal curvature, may be considered.

To obtain better understanding of the impact of those ocular parameters on the pupil

alignment function, the same ray tracing approach was used as in Section 3.4.1.1 and the

relative peripheral refractive error (RPRE) of M as a function of pupil de‐alignment was

computed for the central visual field and three nasal visual field angles, i.e. 20°, 30° and

40°.

Using the Zernike coefficients as provided by ZEMAX, M (in D) was calculated using the

equation provided by Atchison et al.,32 for which the pupil diameter was set to the same

fixed circular pupil diameter as used for the Shin‐Nippon NVision K5001 measurement

ring. The pupil stop was de‐centred with respect to the pupil alignment positions which

correspond to the same five measured entrance pupil alignment positions from Phase 1.

The RPRE of M as a function of pupil de‐alignment for the schematic model eye and the

experimental data are shown in Figure 3.12 a) and b), respectively. Although, the overall

trend between the model eye and the experimental data was similar, there were some


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obvious differences in the pupil alignment functions. Whereas, the experimental pupil

alignment data measured with the Shin‐Nippon NVision K5001, showed an overall good

linear trend for peripheral measurements, the pupil alignment functions obtained with

the modelling approach indicate a more quadratic trend.

Figure 3.12: The functions of pupil de‐alignment for the RPRE of M at four visual field angles, i.e. the central visual field and 20°, 30° and 40° nasal visual field, for the Escudero‐Sanz & Navarro model eye (a) and the experimental data (b).

Anatomical differences between the human eyes and the simplified schematic model eye

(rotational symmetric ocular surfaces, homogeneous refractive index of the crystalline

lens), might have contributed to the differences between the model and experimental

data. A further factor could be related to the differences in determining the refractive

error. The experimental data were determined with an instrument based on the

autorefraction principle dedicated to measure central refraction (double‐pass system). In

contrast, Zernike coefficients obtained from ZEMAX were used to calculate the refractive

error of the schematic model eye for into‐the‐eye ray‐trace.

Despite these differences, the aim of using the schematic model eye was primarily to

understand the effect of ocular changes on the RPRE of M as a function of pupil

alignment. Specifically, the model eye was used to investigate the impact on the RPRE of

M when the anterior corneal asphericity (a), anterior corneal radius (b), vitreous length

(c) and retinal radius (d) were modified. Figure 3.13 demonstrates the RPRE of M as a

function of pupil de‐alignment for the schematic model eye by Escudero‐Sanz & Navarro

(solid lines) and when the individual ocular parameters of this model eye were modified

(dashed lines).


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Investigation of the effect of changes in retinal radius did not lead to substantial changes

in the pupil alignment functions. However, vitreous length, corneal asphericity and

corneal curvature were the ocular parameter which showed some impact on pupil de‐

alignment for all visual field angles. It is shown that the flatter or the less aspheric the

cornea, the flatter the pupil alignment function.

In addition to the theoretical ray trace results, the impact of altering corneal curvature

was also investigated in an experimental study using soft contact lenses. Specifically, soft

contact lenses (Acuvue 2, base curve 8.3, Johnson & Johnson) with a power of +6.00D

and ‐6.00D were worn in the right eyes of three participants which steepened and

flattened corneal curvature by approximately 1 mm, respectively. Peripheral refraction

was performed with and without contact lenses for the same pupil alignment positions

as described in Phase 1. For all participants, RPRE results confirmed that the steeper

(flatter) the cornea, the steeper (flatter) was the measured pupil alignment function

when compared to the no contact lens function.

Figure 3.13: Functions of pupil de‐alignment for changing ocular parameters.

The solid lines represent the functions of pupil de‐alignment for the RPRE of M when ray‐tracing was performed at four visual field angles, i.e. the central visual field and 20°, 30° and 40° nasal visual field, using the Escudero‐Sanz & Navarro model eye. The dotted line shows the effects of changes in a) anterior corneal asphericity, b) anterior corneal radius, c) vitreous length and d) retinal radius.


102

From this modelling approach and the experimental study it can be suggested that the

increased RMS error found for the correction algorithms is likely to be related to the

variations in ocular parameters within the general participant group used in the present

study.

3.4.1.3 Functions of Pupil Alignment for Nasal and Temporal Measurements

From previous studies it is known that peripheral refraction profiles often show a typical

nasal‐temporal asymmetry across the visual field with respect to the astigmatic

component. This asymmetry has been related to a lack of coincidence between the visual

and the optical axis,23, 25, 37, 105 but also a lack of rotational symmetry of the retina.58

Results from this study have also shown some asymmetry with respect to the nasal and

temporal visual field pupil alignment functions for M, J180 and cylinder. With reference to

the centred pupil, the pupil alignment functions of the cylinder component showed that

shifts between the central and nasal visual field were much greater than shifts between

the central and the corresponding temporal visual field shifts. This is in agreement with

the nasal‐temporal astigmatic asymmetry found in previous studies.23, 25, 37, 105 Moreover,

the relative graphs for M and J180 have shown that across the pupil meridian for all

horizontal peripheral visual field angles, the difference between central and nasal pupil

de‐alignment was larger than the difference between central and temporal pupil de‐

alignment. From this, it can be concluded that the indicated asymmetry across the pupil

meridian is associated with the combination of increased magnitude of astigmatism in

the nasal visual field and the additional astigmatic changes when performing refraction

across the pupil meridian.

3.4.1.4 Instrumentation used to Establish Pupil Alignment Functions

Due to potential inter‐instrument variability, it is suggested that data for the

establishment of correction algorithms are to be collected using the same instrument

which is to be used for the measurement of peripheral refraction. The autorefraction

instrument used in this study, the Shin‐Nippon NVision K5001, was originally designed to

measure central refraction only. The summary given on current peripheral refraction

techniques (Chapter 1) indicated that many other instruments/methods have been used

and modified for peripheral refraction measurements which are based on different


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operation principles. Unlike the Shin‐Nippon autorefractor, which uses a fixed ring

target, other instruments are based on the principles of aberrometry or photorefraction

to analyse refractive errors across the entire visible pupil, with or without consideration

of the ‘elliptical’ pupil shape. Donovan et al. have compared peripheral refraction

measurements on 28 participants using three instruments which are based on different

operation principles.122 The instruments used were the Shin‐Nippon NVision K5001, the

Complete Ophthalmic Analysis System (COAS aberrometer) and a streak retinoscope.

They found that the output in peripheral J180 of the COAS was almost half the value of

the results obtained with the other two techniques indicating that there may be some

inter‐instrument variability due to different operation principles.

With respect to instrument binocularity, the current study also measured the right as

well as the left eyes of ten participants to confirm the absence of instrument variations

between eye measurements with respect to horizontal pupil de‐alignment in the

horizontal visual field. It was demonstrated that right and left eye data for the pupil

alignment dependent refractive vector components M and J180 correlated very well.

These findings assure that measurements with the Shin‐Nippon NVision K5001 are in

unison for right and left eye measurements, not only with respect to central and

peripheral refraction but also with respect to pupil (mis‐)alignment. Although, it can be

assumed that objective refraction instruments provide consistent binocular central

refraction readings, it is recommended to always verify this assumption for a specific

instrument when measuring peripheral refraction.

3.4.2 Pupil Alignment Correction Models

From the presented data set, three pupil alignment correction models were established

for the correction of the refractive vector components M, J180 and J45 and for the relevant

combinations of visual field meridian and pupil alignment meridian.

Overall there was good linearity, as well as symmetry, between the relative nasal and

temporal pupil alignment functions. Therefore, the first model was selected to be a

general linear model, which has the advantage that it can be applied for the correction

of any measured visual field angle. To also account for the slight asymmetry observed


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between nasal and temporal visual fields the second linear model chosen corrects for

each individual visual field angle. Lastly, a quadratic model additionally corrects for the

small asymmetry found with respect to nasal and temporal pupil misalignment.

Nevertheless, it should be noted that the RMS error of each visual‐field dependent

model increases substantially as visual field angle increases. Thus the use of group‐

specific or even a subject‐individual correction model may improve the accuracy of the

current proposed models even further.

3.4.3 Implementation of Compensation Factor

For the validation of the established correction algorithms, each individual measurement

of Phase 1 was corrected by the known amount of pupil de‐alignment. All three models;

the general linear model, the individual linear model and the individual quadratic model,

improved the measurement error by at least 58% when compared to the measured data.

Greatest improvement was achieved with the individual quadratic model. Nevertheless,

it should be noted that correction was done for large and pre‐defined amounts of pupil

de‐alignment, which cannot be directly compared to the peripheral refraction

measurements performed in practice.

Therefore, in Phase 2 peripheral refraction was performed under normal clinical

conditions, whereby misalignments are random and generally smaller. After correction

of the measured data, the variability reduced by at least 25% for all corrected data.† This

reduction was also indicated by the narrowed spread of the repeats of the individual

corrected participant data. However, for some participants and some visual field

positions the variability remained even after correction, which suggests that other

factors contribute to the remaining error when performing repeated measurements on

the same participant.

† In the absence of measurement data for the correctly aligned pupil positions, the pupil mis‐alignment errors and their improvements cannot be determined with certainty, but the reduction in variability after applying the correction algorithm is a good indicator that measurement results had been improved.


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In fact one technical obstacle was identified with the current image capture procedure in

Phase 2. It was noticed that there is a small delay (i.e. <0.5 seconds) between the

recording of the refraction reading and the capturing of the image from the pupil

alignment monitor. Any instrument or eye movement or blink within that delay period

would have compromised the error compensation. It is expected that a more reliable

error compensation can be achieved once the simultaneous image capture with the

refraction recording has been assured.


The work of this chapter aimed to establish, validate and test a methodology that

rectifies pupil alignment errors that may arise during peripheral refractometry when

using conventional autorefractors.

From the determined pupil alignment matrix in Phase 1, three correction models were

established for the correction of the relevant refractive power vectors. Using the same

data set, the validation of each model exhibited overall improvement in measurement

error of at least 58% for each refractive vector component.

Phase 2 investigated the implementation of the established correction algorithms on

individual data obtained when peripheral refraction was measured with the pupil aligned

approximately to the pupil centre. After correction of pupil misalignment, the variability

for the corrected mean peripheral refraction profile was reduced by at least 25%.

Nevertheless, sample size was small and individual variations remained even after

correction. It is possible that these variations may be related to the observed small delay

in the current image capturing procedure. Moreover, it may be of advantage to increase

precision of the current model by using group‐specific or even subject‐individual

correction models.

Despite the fact that some obstacles and limitations with the current method require

further improvements, the proposed method has shown to reduce the variability caused

by pupil misalignment.

CHAPTER 4: OPTICAL DESIGN OF A NOVEL PERIPHERAL REFRACTION CONCEPT

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CHAPTER 4:

OPTICAL DESIGN OF A NOVEL PERIPHERAL REFRACTION CONCEPT: THE EYEMAPPER

4.1 Introduction

This chapter introduces a novel peripheral refraction concept that aims to eliminate the

limitations of currently available peripheral refraction techniques. The proposed

instrument, which will henceforth be referred to as the EyeMapper (EM), is based on the

patent application: "Characterising Eye‐Related Optical Systems" as published under the

patent cooperation treaty with the International Publication Number WO 2008/116270

A1. The inventors of this patent application are Klaus Ehrmann, Arthur Ho and Brien

Holden (from the Brien Holden Vision Institute, formerly known as the Institute for Eye

Research Ltd.).184

Initially, this chapter provides a brief overview of the proposed EM concept and its

operation principle. This is followed by a detailed description of the optical design work.

4.1.1 Design Concept and Operation Principle

The EM’s design concept aims to measure the clinically relevant 2nd order aberrations

that are spherical and astigmatic refractive errors of the eye, fast and accurately, across

the visual field. The mode of operation selected for the EM is based on the ring‐

autorefraction principle, which has been used in many commercially available

autorefraction instruments, such as the Shin‐Nippon NVision K5001 (Shin Nippon

Commerce Inc., Tokyo, Japan). Unlike the Shin‐Nippon, which uses a ring‐like mask as

target projection, the EM concept aims to use a near infrared SLD (Super Luminescent

Diode) beam which oscillates by use of a small x‐y scanning mirror to create the

illuminating ring target. Once the ring image is projected onto the retina, the aim is to

capture the reflected ring image in the plane of the detector. A lens relay system moves

rapidly back and forth by a linear translation stage which scans through the focal range

to capture the ring‐like patterns. The spherical and astigmatic refractive errors of the eye

can then be determined by comparing the illumination ring with the reflected captured


107

ring. Whereas a change in ring size reflects a spherical error, a shape change from ring to

ellipse signifies the astigmatic error.

Unlike conventional autorefractors, which are designed solely to measure central

refraction, the concept of the EM instrument requires numerous additional optical and

mechanical elements to allow for a refraction scan across the visual field, i.e. ranging

from ‐50° to +50° in 10° steps. The distinctive feature of the EM concept is the use of an

array of ten bending prisms and one scanning mirror to rapidly steer the oscillating

illumination beam across the retina. The basic concept for the propagation of the

illumination and reflection beams is shown in Figure 4.1 (a diagrammatic plan taken from

the patent application). Once the 11 illumination beams are back‐scattered from the

retina, 11 sequential reflection beams are generated, which are captured and analysed

to determine the sphero‐cylindrical refraction output.

To avoid the effects of fluctuating fixation and accommodation during the measurement

of the eye, it is aimed to complete the refraction scan in less than one second.

As with any autorefraction instrument, an optical path has to be incorporated to allow

the participant to fix gaze upon an on‐axis target which is commonly placed at optical

infinity. The EM aims to have this target axially adjustable via a second linear translation

stage to enable the measurement of the peripheral refraction profile as a function of

accommodation. An additional optical path is required for the alignment of the pupil

with the instrument axis. In order to enable measurement of any meridian in the visual

field and thus to be able to generate a refractive power map of the eye, the aim of the

mechanical instrument design is to permit the rotation of the instrument towards

selected meridians.

Prior the building and testing of such an instrument, the first key objective was to

develop and assess the optical design of the EM. Specifically, this chapter aimed to

develop the five optical paths of the EM concept: the deflection system, the illumination

path, the reflection path, the pupil imaging path, and the fixation path. For this the

optical system design software ZEMAX (ZEMAX Development Corporation, Bellevue, USA)

was used in its sequential ray‐tracing mode.


108

Figure 4.1: A basic diagrammatic plan of the optical layout of the EM.

This drawing has been taken from the patent application “Characterising eye‐related optical systems” (WO 2008/116270 A1).


109

4.1.2 Chapter Overview

The development of the optical EM design was achieved in two steps. The first part of

this chapter (Section 4.2) introduces the EM's reference model eye which acts as the

common optical reference system for all optical paths. This schematic model eye was

initially developed in into‐the‐eye ray‐trace (IERT) mode (visible) which provides a good

comparison to the ocular and visual characteristics of published model eyes. According

to the purpose of each of the five optical paths in the EM, into‐the‐eye ray‐trace (IERT)

or out‐of‐the‐eye ray‐trace (OERT) was performed (Figure 4.2) either in the visible (555

nm) or the infrared (IR, 830 nm) wavelength. Thus, the initial reference model eye in

IERT‐visible mode was transposed into IERT‐IR mode for design of the illumination path,

into OERT‐IR mode for the design of the deflection system as well as the reflection and

pupil alignment paths, and lastly, into OERT‐visible mode, for the design of the fixation

path (Figure 4.2).

Figure 4.2: Optical design paths and the respective mode and wavelength used for ray‐trace.

In the second part of this chapter (Section 4.3), the methodology for development of the

five individual optical path designs of the EM is detailed. Although it is possible to

integrate some optical paths within a single design, it was more appropriate to develop

and assess all paths separately, as this reduced computation time, provided design

clarity, and enabled the more efficient and controlled use of the ZEMAX editors with

respect to the optimisation of the individual design criteria of each optical path.


110

However, it is important to note that, these paths are intertwined at some point and

thus, some optical components of optical paths needed to overlap and their design and

position needed to match accordingly.

4.1.3 Introduction into Optical Designing using ZEMAX

Primarily, three ZEMAX editors, the Lens Data Editor (LDE), the Multi Configuration

Editor (MCE) and the Merit Function Editor (MFE), were used for the design of the EM

reference model eye as well as each optical EM path. The following six steps provide a

brief overview for the basic set‐up and scope of each ZEMAX editor in order to

accomplish specified optical design goals:

1. Set‐Up of the ZEMAX Lens Data Editor:

The LDE is the primary editor used to enter surfaces and their lens parameters such

as surface curvature, thickness and diameter. Moreover, the LDE is used to define

the basic surfaces of each optical system; the object, image and stop surfaces.

2. Set‐Up of the ZEMAX Multi Configuration Editor:

The MCE is very similar to the LDE in that it stores information on the surface

parameters. Its advantage is that it allows to create and to work with multiple

configurations, which are distinguished by different values for the same parameters

in the LDE. These parameters are specified using Multi Configuration Operands.

3. Definition of Variable Parameters:

As part of the subsequent optimisation, the LDE and MCE are used to specify all

unknown parameters that require optimisation (variable parameters). With respect

to the EM design, unknown parameters can, for example, include the position of

prism surfaces, or the curvatures of lens surfaces.

4. Set‐Up of the ZEMAX Merit Function Editor:

The MFE is used to define and weigh target values of selected Merit Function

Operands that can achieve the specific optical design criteria (merit function)

according to the defined variable parameters.

5. Optimisation:

The optimisation tool in ZEMAX uses a powerful algorithm that aims to find the

“local” minimum of the merit function and thus enables computation of the variable


111

parameters in the LDE and MCE with respect to the specific design criteria as

defined in the MFE.

6. Review Optical Design Requirements:

The resulting merit function indicates how closely the optimised optical system

meets the specified optical design goals, and thus is used to decide whether the

optical system requires further refinement to achieve the specified optical design

requirements.

4.2 The EyeMapper’s Reference Model Eye

With the advancement of ocular biometric measurements and sophisticated optical

design programs, the modelling of theoretical eyes has become increasingly complex. In

the early development of schematic model eyes, a simple reduced eye consisting of only

a single refracting surface was used. However, gradually, more complex designs, often

rotationally symmetric, with several refracting surfaces, were introduced, such as the

Gullstrand’s No. 1 eye.185 Nowadays, it is possible to work with schematic eye models

having tilted or decentred ocular surfaces and/or having a complex crystalline lens that

consists of different gradient indices.186 Although computerisation makes it possible to

use the most complex and sophisticated eye model, it is not always the most appropriate

schematic model eye with respect to research needs. As such, the aim for the EM’s

reference model eye was not to opt for the most sophisticated of the models previously

published, but to keep it simple, valid and applicable for the design of all the relevant

optical paths of the EM. This section aimed to evaluate the EM reference model eye with

respect to different accommodative and refractive demands and with respect to its

peripheral refraction profile for different ray‐trace modes.

4.2.1 Methods

4.2.1.1 EyeMapper Reference Model Eye

Figure 4.2 shows that the optical paths of the EM instrument require either OERT (visible

and IR) or IERT mode in the IR light. In general, investigations on schematic eye models

are primarily made with respect to eyes in IERT (visible) mode. Having the retina as the


112

image surface permits the assessment of visual performance, such as image quality or

the retinal light distribution of the respective model eye.

To select a suitable reference model eye for the optical design of the EM, previously

published eye models in IERT (visible) mode, were compared. Two of the most current

model eyes were published by David Atchison in 2006,187 and are based on collation of

the most recent ocular biometric data. While the ocular surfaces in Model 1 are co‐axial,

Model 2 considers lens tilt, retina tilt and retina decentration. Both schematic eye

models possess the more complex index coefficients for parabolic gradient index

distribution in the lens as based on the Liou and Brennan model eye.186 The use of the

gradient index enables more precise investigations into the anatomical structure of the

human crystalline lens. However, for this application, a homogeneous lens index, such as

provided by Navarro's model eye175 was adequate. It provides a reasonable substitute

with respect to appropriately retaining the eye’s refractive power across the visual

field.32 With the aim to measure both eyes, one at a time, a rotationally symmetric

model eye is required to retain instrument binocularity and thus, the ocular surface data

for the EM’s reference model eye were based on Atchison’s Model 1 eye.

Lens Data Editor:

Table 4.1 shows the ZEMAX Lens Data Editor, which lists the ocular biometric data used

for the EM's reference model eye in IERT (visible) mode. The shaded layout of this model

eye is shown in Figure 4.3.

Table 4.1: Lens Data Editor tabulating the set‐up for the EM’s reference model eye in IERT (visible) mode.


113

Figure 4.3: Shaded layout of the EM reference model eye in IERT mode for two visual field angles (0° and 50°).

4.2.1.2 Computation of Central and Peripheral Refraction via Ray‐Tracing

In order to design an instrument that measures the refractive error of the eye across the

visual field, the ZEMAX Zernike Standard coefficients were used to compute the central

and peripheral refractive errors of the selected EM reference model eye.

In general, Zernike polynomials are a sequence of polynomials that are orthogonal on

the unit circle, where (azimuthal frequency) and (order) are non‐negative integers

with . Figure 4.4 details the pyramid of Zernike polynomials, where each

polynomial represents a particular mode of ocular aberration.

Figure 4.4: Pyramid of Zernike Polynomials up to the 5th order.


114

Zernike polynomials can be expressed in the form:

Equation 4.1: ,| |

| | | |

0

where is the azimuthal angle, is the radial distance 0 1 and | | corresponds

to a radial polynomial, which is defined as:

Equation 4.2: | | ∑ !

! . | | ! . | | !

| | /

is a normalisation term defined by the following equation:

Equation 4.3: √ , .

The ZEMAX analysis tool provides these coefficients in wavelength units. By multiplying

the values with the measurement wavelength, the coefficients can be converted to

micrometers (μm). Specifically, the coefficients of the 2nd order Z 22, Z 0

2 and Z 2

2 were of

interest to determine the refractive error vector components J180, M and J45,

respectively. To compute the central refractive error of the eye over a circular pupil, the

2nd order coefficients were converted from μm into Dioptres (D) using the following

equations provided by Atchison et al.32

Equation 4.4: √

Equation 4.5: √

Equation 4.6: √

where is the pupil radius.


115

For the computation of peripheral refraction and its subsequent comparison with

published data, Atchison et al.’s32 modified equations were used, which stretch the

‘elliptical’ peripheral pupil shape into a circular one. These equations are:

Equation 4.7: √ √

Equation 4.8: √ √

Equation 4.9: √

.

Finally, the refractive vector components for central and peripheral refraction can be

converted into the more common sphero‐cylindrical notation of S/C × θ, where S

corresponds to the sphere, C corresponds to the cylinder and θ corresponds to the axis

component. The conversion can be made using the following equations:

Equation 4.10:

Equation 4.11:

Equation 4.12:

In the case of J180 being 0, the equation of θ is unresolvable and thus, θ has to be defined

upon the value of J45. If J45 < 0, then θ = 135°, and if J45 ≥ 0, θ = 45°. The following

additional equations have to be applied in order to retain θ within the range of the

conventional cylinder axis, i.e. 0 to 180°.

Equation 4.13: If J180 < 0 → θ = θ + 90°

Equation 4.14: If J180 ≥ 0 and J45 ≤ 0 → θ = θ + 180°

The calculations for the refractive power vectors are not built‐in functions of ZEMAX, but

the ZEMAX programming language (ZPL) was used to write Macro 1 (APPENDIX C) in

order to execute these calculations. Moreover, the "Optreturn" command in Macro 1


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was used for the optimisation of the refractive vector components in the MFE using the

ZPLM Merit Function Operand. The use of this operand is explained in more detail in the

next section (Section 4.2.1.3).

4.2.1.3 Refractive Error‐Dependent Model Eyes

As the aim of the EM instrument is to measure a range of spherical and astigmatic

refractive errors of the eye, the emmetropic EM reference model eye presented in

Section 4.2.1.1 was not sufficient for the modelling of the optical design requirements of

the EM. In order to theoretically assess the instrument’s refractive error range, the EM

reference model eye required modification. The following section demonstrates the

methodological approach for the modification of the refractive state of the EM reference

model eye in ZEMAX.

Lens Data Editor:

As the reflection path of the optical EM design is the determining path for central and

peripheral refraction, the EM reference model eye in IERT (visible) mode was transposed

to the eye in OERT (IR) mode (Table 4.2, top). As a change in central spherical refractive

error can primarily be attributed to changes in axial length,188 the vitreous chamber

depth was selected so that it could be modified to induce a specified spherical refractive

error (M) of the model eye. Moreover, to induce central astigmatism, the assumption

was made that the eye's astigmatism is solely corneal in nature and thus, the surface

type of the anterior cornea was set to biconic with the y‐meridian of the biconic surface

defined to be modifiable. Nevertheless, it should be noted that in human eyes,

astigmatism is commonly composed of a combination of lenticular and corneal

astigmatism. As the change of the two parameters, vitreous chamber depth and corneal

y‐radius, permit a change in the spherical and astigmatic refractive error respectively,

they were tagged with the letter V (variable) in the LDE (Table 4.2, top) as part of the

subsequent optimisation in the MFE (Table 4.2, bottom).

Merit Function Editor:

As mentioned in Section 4.2.1.2, the optimisation was performed using the “Optreturn”

command in ZEMAX Macro 1 (APPENDIX C), which was linked to the ZPML operand in the

MFE (Table 4.2, bottom). The ZPLM operand with its output data 1 and 3 shows that, as


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anticipated, the current reference model eye has no spherical (value for M = 0D) or

astigmatic error (value for J180 = 0D). If, for example, the aim was to induce an error of

the eye in which the refractive vector component M corresponds to +3.00D and J180

corresponds to ‐1.00D, the target values +3.00 (output data 1) and ‐1.00 (output data 3)

were assigned to the respective operand number as shown in Table 4.2, bottom.

BEFORE OPTIMISATION:

Table 4.2: LDE and MFE set‐up prior the optimisation of the eye’s refractive state.

TOP: LDE of the EM reference model eye with defined variable parameters (V), i.e. vitreous chamber depth = thickness Surface 0, anterior cornea radius = y‐radius Surface 6.

BOTTOM: MFE set‐up to tailor the refractive vector components M (Data 1) and J180 (Data 3) to the target values of +3.00D and ‐1.00D, respectively.

Once the MFE was set up, both variable parameters in the LDE were optimised using the

ZEMAX optimisation feature. The resulting model eye is shown in the LDE in Table 4.3,

top. Both variable parameters show the altered thickness of the vitreous chamber and

the altered y‐radius of the anterior cornea surface. In the MFE (Table 4.3, bottom) it can

be seen that the eye's refractive error values now correspond to the target values, and

the merit function value, which is shown on top of the window, is close to zero,

indicating a successful optimisation.


118

AFTER OPTIMISATION:

Table 4.3: LDE and MFE following the optimisation of the eye’s refractive state.

TOP: LDE of the EM reference model eye with optimised parameters (V).

BOTTOM: MFE shows that the ZPLM Merit Function Operand successfully tailored the refractive vector components M (Data 1) to the target value of +3.00D and J180 (Data 3) to the target value ‐1.00D.

Based on the EM reference model eye in OERT (IR) mode, Figure 4.5 (left) shows the

vitreous chamber depth as a function of central spherical refractive error as computed

with Macro 1. In addition, Figure 4.5 (right) shows the anterior cornea y‐radius as a

function of central astigmatic error as computed with Macro 1. These ocular parameters

were used to determine and assess the peripheral refraction profile of the EM reference

model eye as a function of central refractive error. Moreover, with respect to designing

the EM instrument for a required refractive error range (on‐axis), the refractive error‐

dependent model eyes play a prominent role in the subsequent optical design of the EM

illumination and reflection paths (Section 4.3).

Figure 4.5: Vitreous chamber depth as a function of central M (LEFT) and y‐radius of the anterior cornea as a function of central J180 (RIGHT).

10.0

12.0

14.0

16.0

18.0

20.0

22.0

24.0

+10 +5 0 ‐5 ‐10 ‐15

Vitreous Cham

ber Depth (in mm)

Central M (in D)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

‐6 ‐4 ‐2 0 2 4 6

Anterior Cornea Radius (in mm)

Central J180 in (D)


119

4.2.1.4 Accommodation‐Dependent Model Eyes

In addition to the refractive error‐dependent model eyes, the EM’s aim is to also

measure peripheral refraction profiles as a function of accommodation. Thus, for the

subsequent optical design of the on‐axis EM fixation path, an accommodation‐

dependent model eye was required.

Popiolek‐Masajada and Kasprzak have investigated the changes of the crystalline lens as

a function of accommodation189 and have provided accommodation‐dependent functions

for relevant lens parameters. For the accommodation‐dependent EM reference model

eye, the linear functions for the posterior lens surface and the lens thickness were

extrapolated using the following equations:

Equation 4.15: . .

Equation 4.16: . .

Again, it should be noted, that the aim for this model eye was not to investigate the

ocular biometric changes of the accommodating eye in detail, but to have a simplified

model which enables modelling of the optical design of the fixation path with respect to

retaining the different accommodative demands.

Set‐Up of ZEMAX Editors:

The LDE shows the EM reference model eye in OERT (visible) mode (Table 4.4, top). As

indicated by Equation 4.16, as accommodation changes, so too does the thickness of the

lens, and to account for this, an additional surface called "additional lens thickness" was

inserted in the LDE. Moreover, the MCE was used to create an eye for various

accommodative states (Table 4.4, middle). The parameters (Multi Configuration

Operands) differentiating the various accommodative states of the eye are; “additional

lens thickness” (THIC 2), posterior lens curvature (CRVT 1), anterior lens curvature (CRVT

4) and accommodation distance (THIC 8). The accommodation distances were pre‐

defined. Lens thickness and posterior lens curvature are the fixed parameters given by

the functions provided in Equation 4.15 and Equation 4.16. Anterior lens curvature is the


120


Table 4.4: Set‐up of the three ZEMAX editors prior the optimisation of the accommodation‐ dependent parameters.

TOP: The LDE shows the reference model eye in OERT (visible) mode. An additional surface called "additional lens thickness" (surface 2) was inserted.

MIDDLE: The MCE was utilised to create a reference model eye for six different accommodative distances (THIC 8). The parameters (Multi Configuration Operands) differentiating the eye from different accommodative states are lens thickness (THIC 2), posterior lens curvature (CRVT 1), anterior lens curvature (CRVT 4) and accommodation distance (THIC 8). Lens thickness and posterior lens curvature are the parameters given by the functions provided in Equation 4.15 and Equation 4.16. Anterior lens curvature was specified as variable parameter (V).

BOTTOM: Optimisation of the anterior lens curvature was achieved using the MFE operand REAY (real ray y‐coordinate, pupil coordinate Py = 1). This operand aims to tailor the rays to zero for the given accommodation distances (THIC 8).


121

AFTER OPTIMISATION:

Table 4.5: The three ZEMAX editors following the optimisation of the accommodation‐ dependent parameters.

TOP: The radius of the anterior lens surface optimised for an accommodation demand of 1D (Configuration 2).

MIDDLE: The Multi Configuration Operand CRVT 4 (Anterior lens curvature) optimised for all accommodation distances (THIC 8).

BOTTOM: The Merit Function Operand REAY (real ray y‐coordinate, pupil coordinate Py = 1) successfully tailored to zero for all configurations.

yet unknown parameter and was specified as variable (V). The Merit Function Operand

REAY (real ray y‐coordinate, pupil coordinate Py = 1) was used to target the marginal

rays to reach zero for all configurations in the MFE (Table 4.4, bottom).

Table 4.5 shows the resulting editors following the successful optimisation process. As

anticipated, with increasing accommodation, the lens thickness increases and the


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curvatures of both the posterior lens surface, as well as the optimised anterior lens

surface, increase.

This accommodation‐dependent EM reference model eye was then implemented for the

optical design of the EM's fixation path (Section 4.3.3).

4.2.1.5 Computation of Peripheral Refraction for Different Ray‐Trace Modes

With the aim to develop the optical design of the EM, it was of particular importance to

confirm the computation of peripheral refractive errors of the EM reference model eye

with previously published peripheral refraction data of schematic model eyes and to

validate its use for different ray‐trace modes. This validation was performed in three

steps:

Firstly, Macro 1 (APPENDIX C) was used to compute and then compare the peripheral

refraction profiles for the EM reference model eye in IERT mode (visible) with published

model eyes, such as those by Atchison,187 Liou & Brennan,186 Escudero‐Sanz & Navarro183

and Koojiman et al.190 For this, co‐axial ocular surfaces were used for all model eyes. The

refractive power vectors M and J180 were determined for a 3 mm pupil diameter at the

wavelength of 555 nm. Atchison previously compared the peripheral refraction profiles

up to 40° visual field angles of his eye models with the model eyes of other colleagues.

These results were replicated and extended to peripheral refraction profiles up to 50°

and compared with the EM reference model eye (IERT mode, visible).

Secondly, as the reflection path is the refracting path in the subsequent EM design, it is

important to assess whether the peripheral refraction profile obtained in IERT mode is in

agreement with the peripheral refraction profile obtained in OERT mode. In fact,

Atchison and Charman compared on‐axis aberrations of myopic rotational symmetric

model eyes in IERT and OERT mode and found that there are differences, particularly

when refractive error was large.191

Lastly, the difference between ray trace in the visible (555 nm) and IR (830 nm)

wavelengths are compared across the peripheral refraction profile for both, the EM

reference model eye in IERT and in OERT mode.


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Set‐Up of Field Angles:

For the comparison of peripheral refraction profiles in eyes for IERT and OERT mode, it is

important to note that the field angle settings in ZEMAX are always object sided angles

and consequently, these angles differ between IERT and OERT modes. This can be seen in

Figure 4.6, where the object sided peripheral angles in IERT mode (visual field angles) are

greater than the object sided peripheral angles in OERT mode (retinal angles).

Figure 4.6: The object sided peripheral angles in IERT mode correspond to the visual field angles (LEFT) and the object sided peripheral angles in OERT mode correspond to the retinal angles (RIGHT).

When tracing peripheral rays into the eye, the field angles used are simply the selected

visual field angles, e.g. ranging from ‐50° to +50° in 10° steps. In order to trace the same

visual field angles for the eye in OERT mode, some additional ZEMAX computation is

required to determine the corresponding retinal angles. Again, the computation of the

corresponding retinal angles was achieved using the three ZEMAX Editors.

Set‐Up of ZEMAX Editors:

Initially, the EM reference model eye in OERT mode was set up as previously tabulated in

the LDE in Table 4.2, top. Robust real ray‐aiming was turned on. Table 4.6 (top) shows

the set‐up of the MCE with six configurations where the x‐field angle (XFIE Multi

Configuration Operand) corresponds to the yet unknown x‐retinal angles of the eye in

OERT mode. These angles were specified as variable parameter (V) for the subsequent

optimisation. For the computation of the required retinal angles, the MFE was defined as

shown in Table 4.6 (bottom). Using Merit Function operand RAID (real ray angles in

degrees, normalised field coordinate Hx = 1) at Surface 7 permits the computation of the

target angles which are incident at that surface. These angles are the known visual field

angles, which range from 0° to 50° in 10° steps (Configuration 1 to 6). Hence, for each

configuration the target values were defined accordingly.


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Table 4.6: Set‐up of the MCE and MFE prior the optimisation of the retinal angles.

TOP: The six object sided retinal angles were inserted and specified as variable parameter using the Multi Configuration Operand XFIE 1.

BOTTOM: The MFE was set‐up using the operand RAID at Surface 7, which was used to define the respective visual field angle for each configuration.

Once the MFE was set up, the optimisation algorithm computed the retinal field angle of

each configuration. Following a successful optimisation (MFE in Table 4.7, bottom), the

resulting retinal angles are shown in the MCE in Table 4.7, top.

AFTER OPTIMISATION:

Table 4.7: The MCE and MFE following the optimisation of the retinal angles.

TOP: The six computed object sided retinal angles which correspond to the defined visual field angles.

BOTTOM: The visual field angle target values of each configuration were successfully computed.

Table 4.8 lists the object sided ray trace angles which were used for the computation of

peripheral refraction using the EM reference model eye in OERT and IERT mode for

either ray‐trace in the visible or IR wavelength.


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Table 4.8: Field angle settings for ray‐trace in IERT and OERT modes, using either visible (555 nm) or IR (830 nm) wavelengths.

Ray Trace Direction

Wavelength Object sided ray

trace angle Corresponding ZEMAX X‐Field Angles (in °)

IERT Visible (555

nm) Visual Field Angles

(in °) 0 10 20 30 40 50

IERT IR (830 nm) Visual Field Angles

(in °) 0 10 20 30 40 50

OERT Visible (555

nm) Retinal Angles (in °) 0 8.18 16.35 24.47 32.52 40.45

OERT IR (830 nm) Retinal Angles (in °) 0 8.21 16.40 24.55 32.62 40.58

4.2.2 Results

4.2.2.1 Peripheral Refraction Profiles of Schematic Model Eyes

The comparison of the peripheral refraction profiles of the EM reference model eye with

previously published schematic model eyes in IERT mode is shown in Figure 4.7.

It is apparent that the Escudero‐Sanz and Navarro model eye,183 the Koojiman et al.

model eye190 and the EM reference model eye indicate a relatively hyperopic shift (M) in

the periphery. The other two model eyes by Atchison187 and Liou and Brennan,186 which

are based on crystalline lenses with gradient indices, had a more myopic peripheral shift

up to 40°. All model eyes seem to overestimate peripheral astigmatism (J180), when

compared to experimental studies.23-25

All non‐gradient index eyes showed less peripheral astigmatism compared to the

gradient index eyes.

4.2.2.2 Peripheral Refraction Profiles for Different Ray‐Trace Modes

Using Macro 1, the peripheral refraction profiles were calculated for the EM reference

model eye in IERT and OERT mode. The graph in Figure 4.8 shows that on‐axis ray tracing

yielded similar results for both refractive components M and J180 when comparing IERT

and OERT mode. However, peripheral refraction became more inconsistent between

IERT and OERT mode as the peripheral angle increased. The greatest differences of 0.53D


126

and 0.54D, in M and J180 respectively, were found between the OERT and the IERT mode

at the visual field angle of 50°.

Figure 4.7: Comparison of the peripheral refractive vector components M (TOP) and J180 (BOTTOM) as a function of horizontal visual field angle of different schematic model eyes.

The refractive error was computed using ZEMAX Macro 1.

In addition, Figure 4.8 shows that there is a consistent refractive error shift between ray‐

tracing in IR and visible wavelength across the peripheral refraction profile indicating the

expected chromatic shift in M. The chromatic on‐axis difference between ray‐trace in the

visible and IR wavelength was slightly different for the IERT and OERT modes. Whereas

the chromatic on‐axis difference in IERT mode was 0.75D, the difference was 0.89D for

the OERT mode. The mean chromatic difference corresponds closely to the shift

predicted by the Indiana chromatic reduced model eye.192

‐2.00

‐0.50

1.00

2.50

4.00

5.50

0 10 20 30 40 50

M (in Diopters)

Horizontal Visual Field Angle (in °)

Reference Model Eye

Atchison

Liou & Brennan

Escudero‐Sanz & Navarro

Koojiman et al.

‐5.00

‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

0 10 20 30 40 50

J 180(in Diopters)

Horizontal Visual Field Angle (in °)

Reference Model Eye

Atchison

Liou & Brennan

Escudero‐Sanz & Navarro

Koojiman et al.


127

Equation 4.17: .. .

.

Figure 4.8: Comparison of the refractive power vector components M and J180 as a function of horizontal visual field angle between schematic eyes in IERT (visible) and OERT (visible) mode (TOP) and between schematic eyes in IERT (IR) and OERT (IR) mode (BOTTOM).

4.2.3 Discussion/Conclusion

The selected EM reference model eye is based on the ocular biometric surface data

(curvatures, asphericities, thicknesses) of Atchison's schematic Model 1 eye,187 which is

rotationally symmetric and hence retains the binocular use as required for the optical

design of the EM. Moreover, optical media were kept simple and valid by using the

homogeneous refractive indices from the Escudero‐Sanz and Navarro model eye.183

The peripheral refraction profiles computed of previously published model eyes were in

good agreement with Atchison’s comparison data, which were available up to 40°.187

‐10.00

‐8.00

‐6.00

‐4.00

‐2.00

0.00

2.00

4.00

6.00

8.00

0 10 20 30 40 50

Power (in Diopters)


M (IERT)

J180 (IERT)

M (OERT)

J180 (OERT)

Visible Wavelength

‐10.00

‐8.00

‐6.00

‐4.00

‐2.00

0.00

2.00

4.00

6.00

8.00

0 10 20 30 40 50

Power (in Diopters)


M (IERT)

J180 (IERT)

M (OERT)

J180 (OERT)

Infrared Wavelength


128

Neither of the current model eyes, predicted peripheral refraction, in particular J180, well

when compared to in vivo measurements.24 Nevertheless, the aim of this work was not

to study the most accurate wide‐angle schematic model eye with respect to in vivo

peripheral refraction data, but rather to ascertain a model eye that provides a central

and peripheral refraction reference for the subsequent optical design of the EM.

As the optical path designs of the EM instrument require different ray trace modes, it

was important to cross‐validate whether there is a difference in peripheral refraction

profiles between OERT and IERT modes as well as between the visible and IR ray tracing.

Atchison and Charman investigated whether there is a difference between central

aberrations obtained via OERT or IERT mode using Navarro's model eye.191 They showed

that higher levels of ametropia can lead to a considerable change between OERT and

IERT modes. Large refractive errors, as known to be present in the periphery of the eye,

can therefore potentially affect the different ray‐trace modes. The present work has

shown that, as visual field angles increased, the difference between OERT and IERT mode

increased. The difference was as large as 0.54D for J180 at the 50° horizontal visual field

angle. The mean shift for the peripheral refraction profiles obtained at different

wavelengths was in good agreement with the 0.82D shift predicted from the Indiana

chromatic reduced eye model.192

Overall, this model eye was suggested to be an appropriate reference model eye for the

purpose of designing the optical paths of the EM instrument.

4.3 The Optical Design of the EyeMapper

The EM's optical instrument design was developed on the basis of the EM's reference

model eye presented in Section 4.2. In total, the design consists of five optical paths: the

deflection system, the illumination path, the reflection path, the pupil imaging path and

the fixation path. As each path has different optical design requirements, it was

advantageous to develop them as separate designs in ZEMAX. The paths dedicated to

central and peripheral autorefraction are the deflection system, the illumination and

reflection paths. The deflection system comprises the design of the individual prisms and

the determination of the positions of the scanning mirror to allow the ocular scanning of


129

all 11 visual field angles. The illumination and reflection paths are the paths, which

define the intended refractive error range of the EM instrument. In addition to the three

autorefraction paths, the pupil imaging and the fixation path have to be incorporated, to

enable the viewing/alignment of the pupil by the examiner and the fixation of an on‐axis

target by the participant.

The ZEMAX editors were used to set up the optical paths with respect to the pre‐defined

instrument design requirements (Methods ‐ Before optimisation). Subsequently, the

optical paths were optimised to achieve their individual design goals (Results ‐ After

optimisation).

4.3.1 Autorefraction Paths

4.3.1.1 Deflection System

The prime purpose of the deflection system is to enable the scan of the illumination and

reflection beams across the eye without inducing optical distortions or aberrations.

Based on the proposed design concept (Section 4.1.1) it is aimed to guide the beam

across the visual field via a scanning mirror and ten customised prisms.

4.3.1.1.1 Methods

The methodological approach for the optical design of the deflection system is explained

in the set‐up of the three ZEMAX editors.

Lens Data Editor:

1. LDE Pre‐Settings:

As shown in Table 4.9 the previously implemented EM reference model eye in OERT (IR)

mode was used as reference file for the design of the deflection system. The system pre‐

settings of this model eye were as follows: the surface of the pupil was defined as “Stop”

surface, the ray‐trace wavelength was set to 830 nm, the entrance pupil diameter

corresponded to 3 mm and the robust real ray aiming ZEMAX feature was turned on.

2. Insertion and Definition of Prism and Scanning Mirror Surfaces:

The two prism surfaces, the front and back surface were inserted. The prism material

was chosen to be of high refractive index (N‐BK9, nd=1.69). The rectangular shape and


130

size of both prism surfaces were defined using the rectangular aperture type settings.

Moreover, the surface for the scanning mirror was inserted and assigned to the glass

type “Mirror” and was also defined as the "Global Coordinate Reference", which was of

importance for the subsequent optimisation.

3. Definition of Reference Distances for On‐Axis System:

With the aim of constructing a compact instrument design, the on‐axis distance between

the eye and the front prism surface and between the prism and the scanning mirror were

defined as being as small as possible (i.e. 55.5 and 200 mm). The distance between the

scanning mirror and the image surface was set to ‐50 mm, which had a negative sign due

to change of the real propagation direction caused by the previous mirror surface.

4. Insertion of Coordinate Breaks:

Coordinate breaks (CB) are dummy surfaces that allow the change of the global

coordinate system to permit the tracing of non‐axial rays. Consequently, CBs were used

for the design of the prisms of the proposed deflection system, where propagating

beams are to be traced for 11 different field angles. In general, CBs are implemented

before and after ray tracing to the selected non‐axial surface. Parameters accounting for

a change in the coordinate system are CB decentres and CB tilts. The sequential order of

decentring and tilting is crucial with respect to the order of CB decentres and tilts. As

shown in Table 4.9, two CBs were placed in front of each prism surface and one CB was

placed after each prism surface. For each prism surface, the first CB decentres the

surface (Translate 1 & 2) as specified in lens units and the second CB tilts the surface

(Rotate 1 & 2) to a certain degree. In order to return to the coordinate system after ray‐

tracing through either of the prism surfaces, the coordinate return feature was applied

at the third CB of each prism surface, which decentres and tilts the coordinate system

back in the correct sequential order.

The prime aim of the scanning mirror is to direct the beam towards 11 different

directions. Using ZEMAX, this scan requirement can be achieved with a CB y‐tilt. Due to

these tilt requirements one CB was placed before and a second CB was placed after the

scanning mirror surface (Table 4.9). Moreover, a CB x‐tilt was used to position the axis

of the scanning mirror in a pre‐defined 15° angle perpendicular to the measurement

meridian.


131

Multi Configuration Editor:

With the requirement of tracing rays for 11 different field angles, the application of the

MCE was of particular use for the proposed deflection system. The following steps show

the detailed set‐up of the MCE (Table 4.10) including the particular peripheral design

criteria.

1. Definition of Peripheral Angles:

The MCE was utilised to set up the reference model eye, where rays are propagated from

11 different retinal locations (object surface) towards the pupil (STOP surface) by use of

the robust real ray‐aiming feature in ZEMAX. These 11 object sided retinal angles were

defined by the Multi Configuration Operand XFIE 1. The retinal field angles were

specified as previously computed for the schematic model eye in OERT (IR) mode

(Section 0). Negative pick‐up solves (P) were used to mirror the five positive peripheral

retinal angles to the five negative peripheral retinal angles. As pickup solves actively

adjust specific values during the optimisation procedure, they are very useful,

particularly for symmetrical systems with many configurations. Consequently, they were

utilised throughout the MCE set‐up of the deflection system design.

2. Definition of Distances and Aperture Sizes:

To arrange the 10 prisms in an arc shape in front of the eye, the individual distances

between the anterior cornea surface and each of the front prism surfaces (THIC 7) were

pre‐defined for each configuration. Further fixed parameters differentiating the

configurations from each other are related to the different prism sizes which were

defined by prism thickness (THIC 11), minimum rectangular aperture sizes (APMN 10 &

APMN 14) and maximum rectangular aperture sizes (APMX 10 & APMX 14). Due to the

different peripheral ray‐trace angles, the optical path lengths between configurations

differ. Thus, the distance between the second prism surface and the scanning mirror

distance (THIC 15) was as yet, unknown and thus, specified as variable parameter for all

peripheral angles as part of the subsequent optimisation.

3. Definition of CB Parameter:

Parameter 1 of the first CB and Parameter 4 of the second CB, determine respectively,

the different x‐decentrations and y‐tilts of each prism surface relative to the optical axis

in the LDE. The operand PRAM in the MCE is the associated Multi Configuration Operand


132

that defines CB decentrations and tilts for all individual configurations. As these prism‐

defining parameters were to be computed, they were specified as variable (V) for the

subsequent optimisation.

As for the scanning mirror, the PRAM operand 16/3 represents the x‐tilt of the pre‐

defined 15° angle. Moreover, to determine the amount of y‐tilt that is required for each

configuration, the PRAM operand 16/4 was defined as a variable for the further

optimisation in the MFE.


As mentioned previously, the Merit Function Editor was used for the optimisation of the

variable parameters specified in the LDE and MCE. Using either an actively damped least

squares or an orthogonal descent algorithm, ZEMAX optimises a merit function which is

composed of target values (Merit Function Operands). The merit function is defined as:

Equation 4.18: ∑

∑

where the subscript ‘i’ indicates the operand number (row number in the MFE

spreadsheet). With a set of 30 variables in the MCE, this optimisation feature is a

powerful tool to assist with the computation of the optical design of the deflection path.

As shown in Table 4.11 the MFE was set up individually for each configuration in the

deflection system. Merit Function Operands were given target values and weights to

achieve certain design goals with respect to the defined variable parameters in the MCE.

The detailed steps for the set‐up of the MFE were as followed:

Listing of Configurations:

Configurations assigned with pickup solves in the MCE were not listed in the MFE as they

are automatically updated. Thus, only configurations for on‐axis ray‐trace (Configuration

1) and peripheral ray‐trace with positive retinal angles (Configurations 2, 4, 6, 8 and 10)

were specified.


133

Table 4.9: Set‐up of the LDE prior the optimisation of the deflection system.

The LDE for the deflection system was set up using the EM reference model eye in OERT (IR) mode. This is followed by the two prism surfaces which are enclosed by the additional CB surfaces. Whereas the two CBs in front of each prism surface (Translate 1 and Rotate 1) permit their individual decentration and tilt, the CB positioned after each prism surface returns the coordinate system to its global zero location. Similarly, the surface of the scanning mirror was also enclosed by CBs to permit the required x and y‐tilts of the scanning mirror.

R: Return Solves

P: Pickup solves


134

Table 4.10: Set‐up of the MCE prior the optimisation of the deflection system.

The MCE consisting of 11 configurations to propagate rays from 11 different retinal locations towards the pupil (retinal angle XFIE 1, Visual Field Angles MOFF 0). For each of the 11 configurations a prism of different size and position is required. Thus, the variable parameters related to the different prism positions were defined by CB decentres (i.e. PRAM 8/1 & PRAM 12/1) and by CB tilts (i.e. PRAM 9/4 & PRAM 13/4). Fixed parameters are related to the different prism positions and sizes and were defined by the thickness prior to the first prism surface (THIC 7), the prism thickness (THIC 11), minimum rectangular aperture sizes (APMN 10 & APMN 14) and maximum rectangular aperture sizes (APMX 10 & APMX 14). The distance between the second prism surface of each configuration and the scanning mirror (THIC 15) requires readjustment with respect to its global coordinate position and the y‐tilt (PRAM 16/4) requires optimisation to propagate the rays of all configurations towards the centre of the on‐axis image surface. Thus, both Multi Configuration Operands were specified as variable.

V: Variable parameters selected for optimisation

P: Pickup solves


135

Definition of Chief Ray‐Trace for Each Configuration:

The Merit Function Operand REAX (real X‐coordinate, normalised field coordinate Hx = 1)

was opted to trace the chief rays of each configuration to the centre of the prism front

surface (Surface 10), the centre of the prism back surface (Surface 14) and to the pivot of

the scanning mirror (Surface 20). This was done by defining the target value of this

operand at each of the three surfaces to zero.

Definition of Prism Criteria:

For the design of the individual prisms in the deflection system, the following optical

prism criteria were considered. Aberration is at a minimum only when rays of light pass

through a prism at a minimum deviation angle. The minimum deviation in a prism occurs

when the incidence and emergence angles are identical, leading to a symmetrical

configuration. Therefore, the prisms of each configuration in this instrument were

designed to adhere to these criteria, by targeting the difference (DIFF) between the

angles of the chief ray incident at the first prism surface (RAID 10) to be zero to the

angle of the chief ray exiting the second prism surface (RAED 14).

Maintaining Global Coordinates Identical for All Configurations:

Due to the different peripheral angles, the distances between each prism back surface

and the scanning mirror were the unknown parameters. Using ZEMAX, the computation

of these distances was achieved by ensuring that all configurations in the deflection

system are aligned within the same global coordinate system. The global reference

coordinate was used to define the point of overlap for multiple configurations. This

reference surface was previously pre‐defined to be the scanning mirror surface.

Moreover, the total on‐axis distance between the retina and the scanning mirror (GLCZ

0, Configuration 1) was the pre‐defined reference distance of the deflection system.

Thus, for the computation of the peripheral distances, it was the z‐position (GLCZ 0) of

the peripheral configurations that needed to be targeted to be equal to the z‐position of

the on‐axis configuration.

Definition of the Y‐Tilt of the Scanning Mirror for Each Configuration:

The last requirement for the deflection system was to determine how much y‐tilt of the

scanning mirror is required for each configuration. The Merit Function Operand DIFF was

used to target for the zero difference (DIFF) between the on‐axis chief ray coordinates

and the peripheral chief ray coordinates using the operands REAX (real X‐coordinate,


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normalised field coordinate Hx = 1) and REAY (real Y‐coordinate, normalised field

coordinate Hy = 1).

Table 4.11: Set‐up of the MFE prior the optimisation of the deflection system.

For the purpose of clarity, only two configurations are displayed in this Figure, that is Configuration 1 (0° on‐axis, Operands 1 to 18) and Configuration 10 (50° off‐axis, Operands 100 to 119). Note, that configurations assigned with pickup solves were not listed in the MFE as they are automatically updated.

For the computation of the deflection system the MFE was defined using the following Merit Function Operands, which were assigned specific target values. REAX (Surfaces 10, 14 and 20, normalised field coordinates, Hx=1) traces chief rays to the centre of the prism and scanning mirror surfaces. The ray angles defined by the operands RAID (Surface 10) (incident) and RAED 14 (exiting) were aimed to be equal. This was achieved by targeting the difference (DIFF) of the two angles to zero. The angle RAID 8 (Surface 8) was the visual field angle targeted for the computation of the corresponding retinal angles. The difference (DIFF) of the Operand GLCZ 0 (Surface 0, global coordinate z‐position) for Configuration 1 (on‐axis) was targeted to have the same GLCZ 0 position as all the other configurations. Using the DIFF operand, the off‐axis values of REAX and REAY were aimed to have equal intercepts at the image surface as the on‐axis configuration.


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Once the LDE and the MCE with all 30 variable parameters were defined, the

optimisation was performed using the 45 weighted target values in the MFE.

4.3.1.1.2 Results

Optical Design Features of the Deflection System

The side elevation and a three‐dimensional view of the optical design of the deflection

system are presented in Figure 4.9. Overall, the deflection system adheres to the targets

as defined in the editors (Table 4.12, Table 4.13 and Table 4.14).

Figure 4.9: Layout of the optical design of the deflection system.

TOP: A ZEMAX design elevation of a section of the optical EM design containing the EM reference model eye, an array of prisms and the scanning mirror (deflection system). BOTTOM: A three‐dimensional shaded view layout of the optical ZEMAX EM design, indicating the x‐ and y‐tilts of the scanning mirror.

Eye

Prisms

Scanning Mirror

Eye

Prisms

Scanning Mirror


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Table 4.12: LDE following the optimisation of the deflection system.

LDE parameters for the prism and scanning mirror surfaces (deflection path) that correspond to the 30° visual field angle of the eye (Configuration 6).


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Table 4.13: MCE following the optimisation of the deflection system.


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Table 4.14: MFE following the optimisation of the deflection system.

For the purpose of clarity, only two configurations are displayed, that is Configuration 1 (0° on‐axis) and Configuration 10 (50° peripheral). The target values of the optimised Merit Function Operands correspond to the actual system values.

Optical Path Lengths of the Deflection System:

Using the real ray trace data in ZEMAX, the path lengths required for the optical

design of the subsequent illumination and reflection paths were calculated (Table

4.15).

Table 4.15: The total path lengths between the anterior cornea surface and the scanning mirror for all 11 visual field angles in the deflection system.

Visual Field Angles (in °) 0° ± 10° ± 20° ± 30° ± 40° ± 50°

Deflection Path Length (in mm) 258.50 259.85 263.21 269.05 277.83 290.37


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Peripheral Refraction Profiles With and Without Deflecting Components

Macro 1 was used to compute the central and peripheral refractive error of the EM

reference model eye in OERT (IR) mode with and without deflecting components in

place. Figure 4.10 shows the refractive vector components M and J180 as a function of

horizontal visual field angle for both conditions. It can be seen that the peripheral

refractive error measured with the deflecting components does affect the peripheral

refraction profile slightly for the larger peripheral angles, i.e. the greatest difference

was 0.15D in M at 50°. Thus, the prisms as designed with the minimum deviation

criteria do not introduce any clinically significant artefactual aberrations that could

influence the peripheral refractive error measured. In practice, using this model,

these small deviations for the far peripheral measurements can be accounted for via

calibration.

Figure 4.10: The RPRE of M and J180 as a function of horizontal visual field angle for the eye with and without deflecting components in place.

4.3.1.2 Illumination Autorefraction Path

The prime aim of the optical design of the illumination path is to project a ring target

onto the retina, which provides a source image for the reflection path. As the retinal

ring size varies as a function of refractive error, the optical design of the illumination

path has to consider the intended refractive error range of the EM. Using the

refractive error‐dependent model eye, the illumination path was designed in IERT (IR)

‐10.00

‐8.00

‐6.00

‐4.00

‐2.00

0.00

2.00

4.00

6.00

8.00

0 10 20 30 40 50

RPRE (in Diopters)


M (eye only)

J180 (eye only)

M (eye and deflection system)

J180 (eye and deflection system)


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on‐axis mode. Specific aperture and location boundaries from the deflection system

had to be taken into account for the illumination path design.

4.3.1.2.1 Methods

The methodological approach of the optical design of the illumination path under

consideration of the components from the deflection system is shown in the set‐up

of the three ZEMAX editors (Table 4.16 and Table 4.17).

Lens Data Editor:

LDE Pre‐Settings:

For the illumination path design the LDE was set up using the EM reference model

eye in IERT (IR) mode (Table 4.16, top).

Insertion of Additional Surfaces and Pre‐Definition of Distances:

The surfaces of Lens 1 (L1) were entered in the LDE. In order to achieve large and

refractive error sensitive retinal images within the pre‐defined desired refractive

error range (Sphere: +10.0 to ‐15.0D) of the instrument, the position of L1 was

chosen to be as close as possible to the front of the eye (51 mm). The “Stop” surface

was defined at the distance of the prism front surface (as computed in the deflection

system) and was set to 4.5 mm. This diameter subsequently corresponds to the size

of the illuminating ring target at this position. The positions of a pellicle beam splitter

and the x‐y scanning mirror were also pre‐defined.

Definition of Variable Parameter:

The yet unknown parameter of the illumination path design is the power of L1 (i.e.

the front and back surface radii of L1). Assuming L1 is a biconvex lens, the back

surface radius was preset using a negative pick‐up solve linked to the front surface

radius (Table 4.16, top). The front surface radius of L1 was specified as variable

parameter for the subsequent optimisation.


Range Definition for Refractive Error Eyes:

In order to assess and define the retinal image sizes for a range of different refractive

error eyes (central M: +10.0 to ‐15.0D) the MCE was opted to create a selection of


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refractive error‐dependent eyes (Table 4.16, bottom). The eye’s vitreous chamber

depth (Multi Configuration Operand THIC 11) was altered as described previously

(Section 4.2.1.3) using Macro 1 (APPENDIX C).

Table 4.16: LDE and MCE prior the optimisation of the illumination path.

TOP: The LDE set‐up in IERT (IR) mode with an additional lens (L1) placed 51 mm in front of the eye.

BOTTOM: The MCE was used to assess the retinal image sizes in the illumination path for a range of central refractive errors. Vitreous chamber depth (THIC, Surface 11) was computed as described in Section 4.2.1.3.


Definition of the Criteria for the Illumination Path

The Merit Function Operand REAY (real Y‐coordinate, pupil coordinate Py = 1) was

used to compute the radius of the retinal ring images for all refractive error eyes

(Configuration 1 to 6) (Table 4.17).

As the hyperopic eye (Configuration 1) is the most restrictive with respect to retinal

image size, the estimated retinal ring diameter of 0.70 mm was defined as smallest

target value. In an experimental set up using a physical reduced model eye it was

confirmed that this is the minimum ring size required to enable its capture in the

reflection path.


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Table 4.17: MFE prior the optimisation of the illumination path.

The MFE was used to target the smallest possible retinal image radius of 0.35 mm for the hyperopic eye (Configuration 1). The marginal pupil rays, which correspond to the radii of the retinal images of all configurations were computed using the REAY (Surface 12, pupil coordinate, Py = 1) Merit Function Operand.

4.3.1.2.2 Results

Table 4.18 shows the editors with its updated values following the optimisation. The

LDE shows that the radii of the biconvex lens surfaces are ± 61.73 mm, which

produces retinal ring image radii from 0.35 mm to 1.21 mm (Configuration 1 and 6),

from the most hyperopic to the most myopic eye, respectively. With respect to the

required refractive error range of the EM instrument, this computed lens fulfils the

pre‐defined criteria for the illumination path design.

The SCHOTT glass catalogue in ZEMAX is a great tool to search for ready‐made lenses

that meet the focal length and diameter requirements which are closest to the

optimised lens parameter. Taken into account the aperture restrictions of the

deflection system, the optimum lens (L1) opted for the illumination path is a

biconvex lens with a focal length of 60 mm (Melles Griot: N‐BK7, BICX‐8.0‐61.8‐C‐

830).


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Table 4.18: All three editors following the optimisation of the illumination path.

TOP: The LDE with optimised surface radii of L1.

MIDDLE: The optimisation did not alter any MCE data.

BOTTOM: The hyperopic retinal image radius (REAY, Surface 12, pupil coordinate, Py = 1, Configuration 1) optimised to the target value.

Figure 4.11 illustrates the change in retinal image size as a function of refractive

error for the designed illumination path with the final L1 in place. The smallest retinal

image diameter is 0.82 mm corresponding to the most hyperopic eye.

Finally, Figure 4.12 provides the summarised layout for the combined optical design

of the deflection system (the prisms and the scanning mirror) and the illumination

path design (SLD light source, x‐y scanning mirror and L1). For clarity, only six angles

are illustrated.


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Figure 4.11: The side layout of the different retinal positions for a range of refractive error eyes.

The blue marginal rays represent the outer diameter of the illumination ring, which provides the smallest retinal ring size for the most hyperopic eye.

Figure 4.12: Graphical illustration of the design of the deflection system (the prisms and the scanning mirror) and the illumination path (SLD, x‐y scanning mirror and L1).

For clarity, only six angles are shown.

4.3.1.3 Reflection Autorefraction Path

The prime aim of the reflection path design is to capture and analyse the reflected

ring images that were projected onto the retina during the illumination scan. Its

concept is based on a CCD camera positioned on a movable translation stage, which

aims to scan through the pre‐defined focus range to locate the best focus position.

The ring images are recorded and the size and shape, which contain the required


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information of the spherical and astigmatic refractive error, can be analysed with

respect to the corresponding field angle positions.

4.3.1.3.1 Methods

The set‐up of the following three ZEMAX editors shows the methodological approach

for the optical design of the reflection path under consideration of the optical

components in the deflection system and the illumination path.

Lens Data Editor:

LDE Pre‐Settings:

The LDE was set‐up as shown in Table 4.19 top using the reference model eye in

OERT (IR) mode.

Insertion of Pre‐Determined Lenses, Surfaces and Distances:

L1, the scanning mirror and the beam splitter were entered at the same location

relative from the EM reference model eye as in the illumination path. As the optical

path lengths of the deflection system differ between the central and peripheral

configurations (Section 0), the relative focal plane positions for the image capture are

different. Consequently, at least two reflection path systems, one with the shortest

optical path length (205.5 mm 0° on‐axis) and one with the longest optical path

length (237.37 mm 50° peripheral) were required to be designed to ensure the entire

refractive error range of the EM instrument can be covered.


Both front surface radii (L2 and L3) as well as the distances between L2 and L3, and

between L3 and the movable CCD (image surface), were set to zero and defined as

variable (V) for the subsequent optimisation.


Definition of Retinal Ring Image Sizes for Each Configuration:

The range of retinal ring image sizes which were determined in the illumination path

was transposed into the MCE using the YFIE (object height) Multi Configuration

Operand (Table 4.19, bottom).


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Table 4.19: LDE and MCE prior the optimisation of the reflection path.

TOP: The LDE set‐up of an eye in OERT (IR) mode. Lens 1 was placed 51 mm in front of the eye. The distance between the anterior cornea and the scanning mirror corresponds to the on‐axis distance obtained from the deflection system (258.5 mm). Surfaces for L2 and L3 were also inserted. The movable CCD was defined as the image surface.

BOTTOM: The configurations in the MCE represent eyes with different refractive errors (vitreous chamber depth, THIC 0). The radius of the retinal ring (YFIE in mm) was defined using the corresponding refractive error dependent values from the illumination path. The distance between L3 and the CCD (THIC 19) was specified as a variable parameter.


With the aim to image the reflected retinal ring image onto the CCD camera, the

distance between L3 back surface and the movable CCD varies as a function of

refractive error and thus, this distance (THIC 19) was specified as the variable

parameter for all configurations.


Definition of Reflection Path Criteria

In order to produce images of the same size regardless of the distance between the

CCD and the focussing lens (L3), the reflection path was designed to be telecentric in

image space. This was achieved, using the Merit Function Operand DIFF to tailor the


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difference in the normalised y‐ray coordinate between the back surface of L3 (REAY

19, Hy = 1) and the image surface (REAY 20, Hy = 1) to zero (Table 4.20). To

determine the focal planes, the marginal pupil y‐ray coordinate (REAY 20, Py = 1) was

set to zero. This set‐up was repeated for all configurations.

Definition of Lens Data Constraints

When there are many variable LDE parameters to be computed it is advantageous for

the subsequent optimisation algorithm to pre‐define some general constraints on

lens data with respect to the instrument needs. For the reflection path design, these

lens data constraints were given by the Merit Function Operands TTGT (thickness

greater than) of Surfaces 15 and 19, and CVLT (curvature less than) of Surface 17.

Moreover, the aperture of the detector surface (image surface) is restricted with

respect to the actual CCD size of the selected camera that is 3.6 mm. Thus, the Merit

Function Operand OPLT 51 of Configuration 6 was targeted to a detector image size

radius (REAY 20, Hy = 1) of less than 1.8 mm. This constraint was solely specified for

Configuration 6, which is the most myopic eye and thus, produces the largest ring

image to be captured.

Insertion of Additional Surfaces and Distances:

Following the beam splitter, the surfaces of Lens 2 (L2) were inserted. An initial

approach of using only one additional focussing lens (L2) for the reflection path

design failed, as optimisation did not provide valid results with respect to the

required reflection path requirements. Hence, the additional surfaces of a third lens

(L3) were inserted. The back surface radii of L2 and L3 were preset by negative pick‐

up solves (P) to aim for biconvex lens designs.

Definition of Translation Stage Range With Respect to Refractive Error Range

A further aim of the reflection path was that the pre‐defined focus range of the EM

instrument had to be covered within the 25 mm distance of the selected translation

stage. As this distance corresponds to the difference between the focal position of

the CCD (TTHI 19) for the most hyperopic eye (Configuration 1) and the most myopic

eye (Configuration 6), this constraint was targeted using the DIFF operand.


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Table 4.20: MFE prior the optimisation of the reflection path.

For simplicity, only two configurations are displayed, that is Configuration 1 (+10 Hyperope) and Configuration 6 (‐15 Myope).

For each configuration the value for the normalised field ray coordinate (REAY 20, Hx = 1) was targeted to be zero to render the retina conjugate to the CCD surface. Moreover, to achieve telecentricity in image space, the pupil ray coordinates (Surface 19, REAY, pupil coordinate Px = 1) were targeted to be equal to the pupil coordinates at the detector surface (Surface 20, REAY, pupil coordinate Px = 1). The difference between the focal position of the CCD (Surface 19, TTHI) for the most hyperopic eye (Configuration 1) and the most myopic eye (Configuration 6) was targeted to be zero.

4.3.1.3.2 Results

Under consideration of the previously designed EM deflection system (Section

4.3.1.1) and illumination path (Section 4.3.1.2), the resulting reflection path design

(after optimisation) can be seen in Table 4.21 and Table 4.22.

The LDE shows the computed surface radii of L2 and L3 and their positions for the

emmetropic eye. The MCE shows the change in CCD position (THIC 19) as a function

of refractive error. Due to the longer optical path length at the 50° position, the

positions for the focal planes of the same refractive error eye's shift closer towards

L3. The closest CCD position is 10.59 mm for the most myopic eye at 50°, and the

furthest CCD position is 32.33 mm for the most hyperopic eye at 0°. Thus, this

difference of 21mm covers the refractive error range of the EM instrument with


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respect to the given translation stage distance. Moreover, the largest detecor ring

image size (2.54 mm) was covered by the selected CCD size (3.6 mm).

Table 4.21: LDE and MCE following the optimisation of the reflection path.

TOP: The LDE with the optimised surface radii and positions of L2 and L3.

MIDDLE: The MCE with the computed CCD positions (THIC 19) for each configuration of the on‐axis system.

BOTTOM: The MCE with the computed CCD positions (THIC 19) for each configuration of the 50° off‐axis system.

Again, the ZEMAX Schott Glass catalogue was opted to find available lenses that are

close to the computed values (L2: Newport: KPX596 and L3: Melles Griot BXB‐12.7‐

40.7).


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Table 4.22: MFE following the optimisation of the reflection path.

The weighted target values for the reflection path design were successfully optimised in the MFE.

In summary, in conjunction with the components of the deflection system and the

illumination path, Figure 4.13 and Figure 4.14 show the additional optical

components of the reflection path. This includes L2, L3, an aperture and the movable

CCD. Whereas the layout in Figure 4.13 indicates the focal planes of the reflection

path design, Figure 4.14 illustrates the image spaced telecentricity of the system.

Figure 4.13: Graphical illustration of the design of deflection system (prisms and scanning mirror) and the reflection path (L2, L3, A1, movable CCD). The movement of the CCD camera permits the focussing of the retinal ring images.


153

Figure 4.14: Graphical illustration of the design of deflection system (prisms and scanning mirror) and the reflection path (L2, L3, A1, movable CCD) indicating the system’s image spaced telecentricity.

4.3.2 Pupil Imaging Path

The purpose of the pupil imaging path is to permit the alignment of the eye with the

instrument. The pupil alignment path was designed to integrate with the already

determined optical components from the autorefraction paths.

4.3.2.1 Methods

Again, the methodological approach for the optical design of the pupil imaging path,

under consideration of the components from the autorefraction paths, is shown in

the set‐up of the ZEMAX editors.

Lens Data Editor:

LDE Pre‐Settings:

The LDE was set‐up as shown in Table 4.23 (top) using the OERT (IR) model eye. The

aperture of the stop was set to 10 mm. L1 was entered at the same location relative

from the EM reference model eye as in the illumination path.

Insertion of Surfaces of Lens 4 and Pre‐Definition of Distance:

A surface for a beam splitter was inserted, which separates the on‐axis

illumination/reflection paths from the pupil alignment path. Moreover, the surfaces

of the biconvex Lens 4 (L4) were inserted with a negative pick‐up solve assigned to


154

the back surface radius, and the front surface radius specified as variable for the

subsequent optimisation.


Definition of Pupil Imaging Path Criteria:

The Merit Function Operand REAY (Surface 15, normalised ray field coordinate, Hy =

1) was targeted to zero to image the pupil area onto the CCD image surface (Table

4.24, bottom). In addition, the use of the merit function operand REAY (Surface 15,

pupil coordinate, Py = 1) permits the computation and optimisation of the image

radius size. Thus, this operand was targeted to be 2 mm, which corresponds to the

size of the selected CCD radius.

Table 4.23: LDE and MFE prior the optimisation of the pupil imaging path.

TOP: The LDE with the reference model eye and L1 in OERT (IR) mode. The surfaces of the beam splitter and the biconvex L4 (P) were added. The front surface radius of L4 as well as the distance to the CCD were specified as variable (V).

BOTTOM: The Merit Function Operand REAY (normalised ray field coordinate, Hy = 1) was used to focus the pupil area onto the pupil camera CCD and REAY (pupil coordinate, Py = 1) was selected to target the pupil camera CCD radius to 2 mm.

4.3.2.2 Results

The resulting pupil alignment path design (after optimisation) can be seen in Table

4.24. The LDE shows the computed surface radii of L4 and the position of the pupil

camera CCD. The MFE shows the correct image radius of 2 mm which corresponds to


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the CCD radius size. A lens that is available from the Schott glass catalogue with a

focal length of 20 mm (47663, Edmunds Optics) was selected as final L4.

Table 4.24: LDE and MFE following the optimisation of the pupil imaging path.

TOP: The LDE with the computed front surface radius of Lens 4 and the position of the pupil camera CCD.

BOTTOM: The weighted target values successfully optimised.

Together with the previous autorefraction path designs, Figure 4.15 shows the pupil

imaging path incorporated into the on‐axis instrument path. The additional

components of the pupil imaging path are two beamsplitters, L4 and the selected

pupil camera CCD, which is conjugate to the eye’s pupil.

Figure 4.15: Graphical illustration of the pupil imaging path (dotted lines) and the autorefraction paths.

The pupil plane is conjugate to the position of the pupil camera CCD.


156

4.3.3 Fixation Path

The prime aim of this path is to enable the fixation of an on‐axis target which is

placed at optical infinity. Moreover, the target is aimed to be movable via a

translation stage to also permit the measurement of the accommodation response

curve as a function of visual field angle. As the fixation path requires the participant

to fix gaze on a visible target, this was the only path designed in the visible spectrum.

4.3.3.1 Methods

Lens Data Editor:

LDE Pre‐Settings:

The LDE was set‐up as shown in Table 4.25 (top) using the eye in OERT (visible) mode.

L1 and L4 were entered at the same location relative to the EM reference model eye

as pre‐determined in the pupil imaging path.

Insertion of Surfaces of Lens 5 and Pre‐Definition of Distance:

The surfaces of a fifth lens (L5) were inserted. The back surface radius of L5 was

defined by negative pick‐up solve (P) to aim for a biconvex lens design. The front

surface radius as well as the distances between L5 and the movable fixation target

(image surface) were specified as variable (V) for the subsequent optimisation.


Definition of Fixation Target Positions:

The MCE was set‐up for accommodation dependent model eyes as explained

previously in Section 4.2.1.4. In addition, the Multi Configuration Operand TTHI 17

was inserted (Table 4.25, bottom) and defined as variable for each of the six

accommodation states to permit the computation of the corresponding fixation

target position in the subsequent optimisation.


Definition of Fixation Path Criteria:

For each configuration the Merit Function Operand REAY 18 (pupil ray coordinate, Py

= 1) was targeted to zero to determine the fixation target position (Table 4.26) of the


157

Table 4.25: LDE and MCE prior the optimisation of the fixation path.

TOP: The LDE was set‐up using the eye in OERT (visible) mode. Settings of L1 and L4 were pre‐defined from the illumination and pupil imaging path. Biconvex L5 surfaces were inserted. Front surface radius of L5 was specified as variable.

BOTTOM: The MCE was set up as explained in Section 4.2.1.4. In addition the position of the fixation target (THIC 17) was defined as the variable parameter for all configurations.

Table 4.26: MFE prior the optimisation of the fixation path.

The MFE was set up for all 6 configurations using the operand REAY (Surface 18, pupil coordinate, Py = 1) which determines the respective fixation target positions. The difference (DIFF, Operand 4 ‐ Operand 20) between the position of the fixation target in Configuration 1 (TTHI 17) and the position of the fixation target in Configuration 6 (TTHI 17) was targeted to 20 mm.


158

respective accommodation status. Moreover, the difference (DIFF) between the

position of the fixation target at 0D accommodation (Configuration 1) and the

position of the fixation target at 5D accommodation (Configuration 6) was tailored to

20 mm, which corresponds to the distance of the translation stage.

4.3.3.2 Results

The resulting editors for the fixation path design (after optimisation) can be seen in

Table 4.27.

Table 4.27: All three editors following the optimisation of the fixation path.

TOP: The LDE for Configuration 1 with the optimised surface radii of L5 and the optimised position of the fixation target.

MIDDLE: The MCE with the optimised six fixation target positions. The difference between the fixation target position (THIC 17) for Configuration 1 and Configuration 6 successfully tailored to 20mm.

BOTTOM: The weighted target values successfully optimised in the MFE.


159

The LDE shows the computed surface radii for L5. The MCE shows the change in the

fixation target position as a function of accommodation. The difference of the

fixation target positions between Configuration 1 and 6 was successfully targeted to

20 mm by the MFE optimisation algorithm.

The ZEMAX Schott Glass catalogue was selected to find an available lens that is close

to the computed values of L5 (Edmund Optics: 45‐087, focal length = 30 mm, surface

radii = 30.36 mm).

Figure 4.16 shows the two‐dimensional layout of the final optical fixation path design

with all six fixation target positions.

Figure 4.16: The two‐dimensional layout showing the fixation path design with all six fixation target positions for the accommodating eye.

Lastly, Figure 4.17 shows the integration of the components of the fixation path, i.e.

L5 and the movable fixation target, with all the other optical EM paths.

Figure 4.17: Graphical illustration of the fixation path, which has been incorporated into the autorefraction paths and pupil alignment path.


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4.4 Summary

On the basis of the proposed peripheral refraction concept (patent application WO

2008/116270 A1), the EM reference model eye presented in Section 4.2 was used to

design the five optical paths of the EM instrument with respect to the individual path

criteria (Section 4.3). Table 4.28 shows the summary of all key design requirements

and the respective optical components of each optical path. Moreover, Figure 4.18

provides a summary of all the paths. The prime objectives of each path were

highlighted by the corresponding chief or marginal rays.

4.5 Conclusion

The significance of measuring the peripheral optics of the eye and the current

limitations related to its measurement with commercially available refraction

instruments were addressed in the previous chapters.

The EM concept (patent application WO 2008/116270 A1) proposed in this chapter

aims to overcome peripheral refraction measurement limitations related to both, the

time‐consuming re‐alignment (off‐axis fixation) requirements by participants and the

strict requirements for precise pupil alignment by the operator. The distinctive

feature of this concept is based on a deflection system, which consists of prisms and

a scanning mirror, in order to achieve a fast refraction scan across the visual field.

The ring‐autorefraction principle was the proposed operation principle for the

determination of the eye’s sphero‐cylindrical refraction.

Based on this concept, the optical design work of the EM was developed in this

chapter. For this, a model eye was selected, first, which was used as a reference

point for the subsequent design of the 5 optical paths of the EM; the deflection

system, the illumination path, the reflection path, the pupil imaging path and the

fixation path. Due to the complexity of the optical EM design, particularly the

deflection system, the five paths were designed and assessed individually. For each

optical path, the pre‐defined optical instrument criteria were successfully achieved

with the help of the optical system design software ZEMAX.


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Table 4.28: Summary of the ray‐trace mode, ray‐trace wavelength, optical components and individual design criteria of each optical path.

Autorefraction Paths Fixation Path Pupil Alignment Path

Deflection System Illumination Path Reflection Path

Ray Trace Mode

OERT

IERT

OERT

OERT

OERT

Wavelength IR (830 nm) IR (830 nm) IR (830 nm) Visible (555 nm) IR (800 nm)

Optical Components

‐ Scanning Mirror‐ Prisms

‐ SLD Light Source‐ X‐Y Scanning Mirror ‐ Scanning Mirror ‐ Beamsplitter ‐ Prisms ‐ Lens 1

‐ Lens 1‐ Prisms ‐ Scanning Mirror ‐ Beamsplitter ‐ Lens 2 ‐ Lens 3 ‐ Movable CCD

‐ Lens 1‐Beamsplitter ‐ Lens 4 ‐ Beam splitter ‐ Lens 5 ‐Movable Fixation Target

‐ Lens 1‐ Beamsplitter ‐ Lens 4 ‐ CCD

Design Criteria ‐ Compact Instrument Design

‐ Prism Criteria: arc‐shaped prism

alignment minimum prism

deviation angle equal aperture sizes

‐ Imaging Requirements: large image entrance

angle minimum retinal

ring image diameter is 0.7 mm

‐ Imaging Requirements: range of refractive error

eyes for on‐ and off‐axis path lengths using the available CCD (image sizes) and translation stage (focal plane locations) is covered

image‐space telecentricity (maintain constant image magnification)

‐Imaging Requirements: retina: conjugate to movable fixation target position accommodation demands from 0 to 5D are covered on a 25 mm movable translation stage

‐Imaging Requirements: pupil: conjugate to CCD

location


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Deflection System:The arrangement of the prisms and the scanning mirror was designed to permit the propagation of the beam towards the selected visual field angles. Illumination Path (black solid ray lines): A collimated SLD light beam is oscillated by the x‐y scanning mirror to generate a ring target. The ring target is scanned via the scanning mirror towards the individual prisms. L1 was designed to project a ring target of pre‐defined size onto the retina.

Reflection Path (black solid ray lines): The reflection path was designed to focus the reflected retinal ring images onto the CCD camera. The movement (∆ = 25mm) of the CCD camera compensates for any refractive errors within the pre‐defined refractive error range of the EM instrument, and for different path lengths. Fixation Path: A movable fixation target allows for the measurement of pre‐defined accommodation distances.

Reflection Path (black solid ray lines): To maintain constant image magnification, the position and powers of L2 and L3 were designed to have a reflection path system which is telecentric in image space. Pupil Alignment Path (black dotted rays): The pupil area is imaged onto the selected pupil camera CCD via L1 and L4.

Figure 4.18: Summary of the layout of each optical path designs.

Following this optical design work, the next chapter addresses the further steps,

including the assessment of specific component criteria and safety aspects, and the

cross‐validation of the ring‐autorefraction principle with a conventional autorefractor.

CHAPTER 5: RING‐SCAN‐AUTOREFRACTION PRINCIPLE

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CHAPTER 5:

RING‐SCAN‐AUTOREFRACTION PRINCIPLE: COMPONENT CRITERIA, SAFETY ASSESSMENT AND EXPERIMENTAL VALIDATION

5.1 Introduction

In Chapter 4 the optical design of a novel peripheral refraction concept, the EM, was

developed. For this, optical components such as prisms and lenses were selected to

achieve particular optical design goals that permit the measurement of the eye's

refraction profile across the retina, ranging from ‐50° to +50° in 10° steps.

In order to implement and test this optical design, a number of additional functions and

components are required. Moreover, issues such as optical radiation safety limits of the

ring‐ scan illumination, and the speed and precision of the image detection, require

closer examination to ensure the safe and effective operation of the EM.

Thus, the following chapter aimed to:

Evaluate and source the components required to achieve the operational goals of

the proposed EM autorefraction instrument,

Assess the safety requirements of the new illumination principle, that is, ocular

ring scanning and peripheral retinal illumination when using the selected EM

light source,

Set‐up an optical bench experiment, based on the EM’s specific illumination

feature and the critical optical components required to verify the on‐axis ring‐

autorefraction principle and

Cross‐validate the experimental ring images obtained on the optical bench with

the images computed with ZEMAX and those measured with the Shin‐ Nippon

NVision K5001 autorefractor.


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5.2 On‐ and Off‐Axis Ring Scan Illumination

5.2.1 Component Criteria

In contrast to common autorefractors, such as the Shin‐Nippon NVision K5001, where a

light source and a ring‐like mask are used for the projection of a retinal ring target, for

the EM, one narrow light beam and two scanning mirrors were chosen to rapidly project

and scan a ring target onto 11 retinal locations. The aim of the scanning principle is to

provide a sharply focused ring and, if required, to permit the adjustment of the ring

size/shape for peripheral measurements.

5.2.1.1 Infrared Light Source – Super Luminescent Diode

Light sources such as lasers, light emitting diodes (LEDs), super luminescent diodes

(SLDs) and incandescent light sources (i.e. tungsten halogen lamps) have been employed

in many different on‐axis ophthalmic applications.193 Some applications use ultraviolet

(UV) sources, short‐wavelength light or infrared (IR) radiation. As is the case for most

fundus imaging applications, a near infrared light source was also chosen for the EM.137,

194, 195 The advantage of infrared light is the higher fundus reflectivity compared to

shorter wavelength light, allowing a reduction in illuminating power.196 Given that near‐

infrared light has no significant visible component, the participant does not produce the

natural aversion response as is the case for visible light sources. Hence, no pupil dilation

is required and the participant does not get distracted by intense light during the

measurement, as happens when visible light is used for the fundus illumination. As such,

the use of near infrared light enables better alignment, focusing and image detection

during the measurement procedure.

Specifically, the optical light source selected for the EM instrument was a fibre coupled,

near‐infrared super luminescent diode (SLD, SuperlumTM Ireland, SLD‐38‐MP, Class IIIB

Laser products, output power = 1.5 to 3.0 mW) with an operating wavelength of 830 nm.

In general, the use of the SLD is advantageous due to its high brightness and short

coherence length (∆λ = 20 nm). The SLD output is coupled into a single mode fibre (SMF)

with small core size (numerical aperture (NA) of 0.14) that propagates only a single ray

or mode of light parallel to the length of the fibre. The use of a single mode fibre enables

superior beam quality and fine collimation. Collimation of the output beam at the FC


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(fibre channel) terminated patch cable was achieved by connecting a fibre collimator

(Thorlabs Inc., CFC‐5‐B).

5.2.1.2 Dual Axis Galvanometer Scanner

The proposed autorefraction principle for the EM requires a ring image to be imaged

onto the retina. To generate the ring, it is aimed to steer the collimated beam of the SLD

with the help of an x‐y high speed galvanometer scanner. The selected x‐y scanner (Dual

Axis Galvanometer Scanner, Model 6200 H, Cambridge Technology Inc., Cambridge,

U.S.A, Figure 5.1 left) consists of two mirrors mounted onto two galvanometers.

Together, the mirrors permit deflection of the beam to any point on a square raster and,

for the purpose of the EM’s operation principle; the beam is scanned to generate the

intended ring target. The scanning mirror has an optical aperture of 3 mm and the inbuilt

moving magnet motor permits short step response times, which allow the rapid scanning

of the beam in 0.1° steps (130 μs settling time).

5.2.1.3 Single Axis Galvanometer Scanner

To measure the eye’s peripheral refraction profile quasi simultaneously, the oscillating

illumination beam has to be scanned rapidly across the 11 visual field positions. For this,

a single axis galvanometer scanner was selected (Single Axis Galvanometer Scanner,

Model 6240 H, Cambridge Technology Inc., Cambridge, U.S.A, Figure 5.1 right).

Figure 5.1: LEFT: Dual Axis (x‐y) Galvanometer Scanner, RIGHT: Single Axis Galvanometer Scanner


166

Unlike the small x‐y scanner, which is positioned closely to the SLD light source for the

oscillation of the beam, this scanner features a large (25 mm) aperture with a ±25°

excursion, to permit on‐ and off‐axis ring scanning of up to ±50°. Due to the larger size of

the mirror, settling time is slower (350 μs) but adequate to meet the EM’s peripheral

refraction scan speed requirements, i.e. to scan 11 positions in less than one second.

5.2.2 Safety Assessment

5.2.2.1 Introduction

Over the last decades, several laser safety standards have carefully been developed to

ensure safe use of lasers.197, 198 With the objective of safe use of both lasers, as well as

optical fibre communication systems utilising laser diodes and light emitting diodes

(LED), the American National Standards Institute (ANSI) standards Z136.1‐2007199 and

Z136.2‐1997200 were introduced for the protection of the human eye from hazardous

light exposures. These standards consider not only accidental ocular exposures to lasers

(i.e. medical or industrial lasers), but also intentional single or repetitive pulse

exposures, as implemented in many ophthalmic applications.201

The EM light source operates in the retinal hazard region, defined as the region including

exposure to wavelengths between 400 and 1400 nm.199 It is therefore critical to consider

the risk of thermal retinal damage that may result following prolonged light exposure

due to resulting protein denaturation of the retinal pigment epithelium.202 However, it

should be noted that near‐infrared light is absorbed much less by the retinal pigment203

than visible wavelengths and thus, the ocular damage threshold is much higher.195

Although the ANSI standards are the most current standards available for the EM light

source application, no consideration is taken with respect to peripheral or ocular

scanning exposures as proposed for the EM instrument. Therefore, the safety standards

of this specific EM light source application were assessed as recommended by de Wit204

and Delori et al.205 For this, the complex scanning system was broken down into a variety

of simulated sub‐exposures, which were assessed on the basis of the ANSI single and

repetitive pulse rules as well as the analysis on ocular scanning by Delori et al.205


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5.2.2.2 Methods

5.2.2.2.1 Single and Repetitive Pulse Exposures

In general, the ANSI standards are very rule‐orientated and are based on four separate

types of ocular exposures in their formulations, i.e. single or repetitive pulse exposures

for either small or extended sources (Table 5.1).

Table 5.1: ANSI ocular exposure definitions (α=visual angle subtended by the retinal image to the centre of pupil (mrad))

Single Pulse Exposure

(=continuous wave CW)

Small Source (αmin=1.5 mrad)

a collimated single pulse beam is incident on the cornea and a small, nearly diffraction limited image (≤ 25 μm diameter) is focused on the retina

Extended Source (α>1.5 mrad)

an area larger than αmin is continuously imaged on the retina

Repetitive Pulse

Exposure

Small Source (αmin=1.5 mrad)

an optical laser emitting multiple intrabeam pulses that occur in a certain sequence

Extended Source (α>1.5 mrad)

an extended source exposure is pulsed within a certain frequency

Whereas the ANSI standards express all exposure limits as maximum permissible radiant

exposure MPHC (in J/cm2) at the cornea, Delori et al.205 implemented the more common

expression of exposure limits in intrapupillary radiant power MPФ (in watts). Figure 5.2

(single pulse SP) and Figure 5.3 (repetitive pulses RP) show all the formulations required

for the calculation of the MPФ as provided by Delori et al.205 With the objective to

calculate the MPФ laser safety values for the EM instrument, the equations used are

limited to exposure durations ranging from 18 μs to 10 Ks and operating wavelengths λ

ranging between 400 and 1400 nm.

The correction factor CT in equation SP (Figure 5.2) is wavelength‐dependent, and was

set to 1.82 for all following EM calculations. The parameter CE changes with the visual

angle α of the exposed retinal area. The MPФ for an extended angular source (retinal

image diameter >25 μm (α > 1.5 mrad)) equals the MPФ of a small source (retinal image

diameter ≤25 μm (αmin ≤ 1.5 mrad)) multiplied by CE. In general, the EM represents a case

of intrabeam illumination, which is also known as Maxwellian view illumination, whereby

a narrow collimated light beam is sent into the eye. Through oscillation of the narrow

collimated SLD beam (approx. 0.8 mm in diameter), a ring is projected onto the retina,

which size depends on the refractive error of the eye.


168

Figure 5.2: ANSI Single Pulse Rule as described by Delori et al.205

Figure 5.3: Three ANSI Repetitive Pulse Rules as described by Delori et al.205

Safe exposure of repetitive pulses can be determined using the three ANSI rules as

shown in Figure 5.3. From the three rules, the appropriate exposure limit is the one that

provides greatest protection. In general, the first repetitive pulse rule, RP1, provides

limits for which each single pulse t1 of the pulse train T is safe. If the pulses are not


169

evenly spaced, the brightest pulse within T has to be safe. In the view of the proposed

EM instrument, where the ring target is generated through oscillation, the pulses are

aimed to be evenly spaced within one measurement. Equation RP2 assesses the average

power limit for exposure durations of the pulse train T. The third rule RP3 determines

whether an exposure duration of n*t1 is safe. The rule yielding the lowest MPФav value

indicates greatest hazards for one measurement. The permitted peak power before

beam oscillation is calculated by dividing the MPФav of the most conservative rule by the

duty factor δ. The MP energy per pulse is MPФav /F.

Using the SP and RP equations of Delori et al.,205 the MPФ laser safety values for the EM

instrument were determined. Although these ANSI equations provide safety values for

single and repetitive pulse exposures at one retinal location, they do not consider the

additional factor of ocular scanning.

5.2.2.2.2 Ocular Scanning

Due to the ANSI ambiguity with respect to ocular scanning, a re‐evaluation of safety

analysis was required with the introduction of the first ocular scanning instruments.

Webb & Hughes developed the first scanning laser ophthalmoscope (SLO) and set the

power to be ten times safer for ocular scanning than the ANSI permissible power for

continuous viewing.206 Klingbeil,207 de Wit204 and Delori et al.205 addressed the scanning

limitation with respect to the ANSI standards. Klingbeil’s objective was to study the

thermal model of temperature rise during intraocular scanning and compare it with

calculated ANSI values. He concluded that the pulsed extended source exposure is very

similar to retinal scanning features and advocates this for permissible light level

exposures. De Wit investigated Maxwellian view scanning devices, such as the SLO, and

also showed that the pulsed extended source exposure is the most conservative

exposure when based on the ANSI standards. Most recently, Delori et al.205 performed a

revised SLO exposure analysis with respect to ANSI rules. They approached the safety

calculations of a SLO by comparing the single pulse exposure of the entire field with a

pulsed line segment (PLS) exposure. Dependent on wavelength, field size and scan frame

rate F, it is either the single pulse or the PLS exposure that provides the most limiting

factor for the SLO’s use.


170

Since the EM application differs to that of the SLO, not only in spectral distribution but

also in retinal image form, size, location and scan exposure, a detailed safety analysis of

the instrument comprising those different illuminating characteristics was performed. To

assess the factor of ocular scanning for the EM light source application, the PLS

exposure, which more closely reflects the scanning situation, was calculated on the basis

of the SLO safety analysis by Delori et al.205

The PLS, which is the slit‐shaped retinal area with the angular length that is covered

within tmin (18 μs – “thermal confinement duration”), and its exposure were calculated

using the ANSI repetitive pulse exposure rules. Whereas the operation of the SLO

requires the scanning of numerous raster lines in order to illuminate a commonly square‐

shaped retinal area, the EM light source application oscillates the beam to generate a

ring image onto the retina. Both scanning features are similar by virtue of the narrow

beam that is moved across the retina. In contrast to SLO analysis, where the length and

frame rate of the raster lines is used to determine the PLS, the EM’s ring illumination

was described by the ring circumference (line) and the scan frame rate F. The scan frame

rate was anticipated to be around 1 kHz. To compare safety values, lower and higher

scan frame rates were also assessed. To determine the safe ocular scanning MPФ, the

PLS exposure was compared with the single pulse line (ring circumference) exposure, and

the more conservative MPФ was identified as safe ocular scanning MPФ.

5.2.2.3 Results

5.2.2.3.1 Retinal Image Size – Visual Angle

In Chapter 4, into‐the‐eye ray‐trace was performed to calculate retinal ring image sizes

under various refractive conditions (Section 4.3.1.2.2). According to the EM’s

illumination path design and the defined refractive error range, the ring size can vary

approximately between 0.75 mm for the most hyperopic eye and 2.0 mm for the most

myopic eye. To cover all retinal ring image sizes for the subsequent safety calculations,

the most hyperopic ring image was chosen as it is the smallest ring image and therefore

has the highest focussing density on the retina.

As recommended by ANSI199 and Delori et al.,205 single pulse non‐circular exposures, such

as a ring, should be assessed with respect to possible sub‐exposures, which subtend an


171

equivalent circular area. Figure 5.4 illustrates all retinal image exposures and their

corresponding visual angles that could possibly describe the EM’s ring illumination for

single exposures. The three retinal images are the spot, the circle and the line

(circumference of the ring). Whereas the spot was entirely chosen to be added as worst

case exposure (i.e. scanner failure), it is the line exposure that best describes the retinal

ring illumination with respect to the size of the exposed area.

Figure 5.4: Retinal images and corresponding visual angle for single exposure MPФ calculations

Prior to the calculation of the single exposure MPФs using equation SP (Figure 5.2), the

correction factor CE (function of visual angle) was determined for each of the three

retinal images.

As the collimated SLD beam can focus a retinal image which is so small to be nearly

diffraction limited, the ANSI standards define the effective retinal image of 25μm

(αmin=1.5mrad subtended apparent source angle) as the minimal “thermal” retinal

dimension. Thus, the correction factor CE of equation SP was set to 1 for the spot MPФ

calculation. For non‐uniform or non‐circular sources the standard defines the angle of

the apparent source as the maximum effective diameter or dimension. Given that the

exposed retinal ring source is an extended non‐uniform source, the maximum effective

diameter of the retinal ring corresponds to a 0.75 mm circle or beam diameter. From

Figure 5.2 it was calculated that this circle corresponds to a subtended apparent source

angle of 44 mrad and thus, the correction factor CE is 29.3.

In addition, Delori et al.205 also provided the effective CE’ for non‐circular sources, such

as rectangles, slits and squares. Since the angular width of the line (circumference of the

ring) equals the beam diameter (αmin, small source) the equation for the slit was used to

describe the line exposure (Figure 5.2).

Retinal Images:

Visual Angle α:

1.5 mrad 44 mradLength: 138 mrad

Height: 1.5 mrad

Spot Circle Ring

=Line = circumference of the ring

Retinal Images:

Visual Angle α:

1.5 mrad 44 mradLength: 138 mrad

Height: 1.5 mrad

SpotSpot CircleCircle Ring

=Line = circumference of the ring


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To account also for the factor of ocular scanning, the definition from Delori et al.’s205

pulsed line segment (PLS, Figure 5.5) exposure was used. For this, the correction factor

CE’ was determined using the same equation as for the line exposure. The length of the

pulse segment now varies as a function of scan frame rate F.

Figure 5.5: Pulsed Line Segment (PLS) definition

Table 5.2 (top) provides an overview of all four exposures and their retinal image shape

characteristics and the respective formulations, which were used to calculate the visual

angle dependent correction factor CE.

5.2.2.3.2 Maximum Permissible Exposure as a Function of Exposure Duration

Using the correction factor CE or CE’, the MPФ was calculated for all four sub‐exposures,

i.e. spot, circle, line, and PLS. Table 5.2 provides the detailed MPФ calculations for an

exposure duration of 0.05 seconds. This is the approximate intended scan duration to

illuminate each of the 11 retinal locations during the EM peripheral refraction scan. In

addition, Figure 5.6 provides the MPФ as a function of exposure duration for each of the

four retinal image exposures.

Overall, the MPФ analysis showed that the spot exposure was the most limiting sub‐

exposure and the circle exposure was the least restricted. However, with respect to the

exposed area, it is the line and the PLS exposure that come closest to the real retinal ring

scan illumination. When comparing repetitive PLS exposures for different frame rates,

RP3 always provided the most conservative MPФ value out of the three repetitive pulse

exposure rules. When comparing the MPФ values for the single pulse line exposure with

the PLS exposure (RP3 rule), the latter was the limiting factor only if the frame rate was

very high (Table 5.2 and Figure 5.6). For slower frame rates, it was the single pulse line

exposure that provided the more conservative exposure limit. Dependent on the EM’s

final scan frame rate for the ring scan illumination, Figure 5.6 provides an overview and

comparison of the MPФ for all four sub‐exposures as a function of exposure duration.

Ring

=

PLS (Pulsed Line Segment -depends on Frame Frequency F)

Line = circumference of the ring

PLS

tmin=18μs

RingRing

=





PLS

tmin=18μs

PLS

tmin=18μs


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Table 5.2: MPФ calculation for all single pulse simulations (spot, circle and line) as well as PLS exposure when the measurement of one of the 11 retinal positions takes 0.05 seconds.

*For the application of the exposure rules see equations of Figure 5.2 and Figure 5.3.

Frame Rate -

Fframe

Length Width

= Circumference

= π* Retinal Image Diameter

αmin αC αL αW=αmin

1.5 mrad 44 mrad 138 mrad 1.5 mrad0.1° 2.52° 7.91° 0.1°

0.025 0.75 2.35 0.025

Circle Circle

CE

Formula- α/αmin

CE 1 29.33

Single Pulse (SP)

Single Pulse (SP)

Repetitive Rule 1 (RP1)









t1 (sec) - Single

pulse durationT (sec) - Pulse train duration

tline (sec)

Number of lines in PLS

2.67 78.19 24.64 942 13.86 38.05 144.85 11.97 47.83 18.3 8.51

5.0×10-5

2

1.8×10-5

0.05

5.0×10-4

2

>tmin

Ring = LineLine Scan

Duration (sec)5.0×10-3 5.0×10-4 5.0×10-5

10000 Hz100 Hz 1000 Hz

Length Width

1.5 mrad

Length Width

1/(Frame Rate*Number of lines in PLS)

5 mrad

Length

Slit

CE

=Frame Rate *T*number of segment lines

1000

αW=αmin

1.5 mrad

= Beam Diameter = Beam Diameter = Beam Diameter =t min*a/t line

t line=1/(2*F frame)Retinal Image Characteristics

Pulsed Line Segment = PLS

1/(Frame Rate*Number of lines in PLS) 1/(Frame Rate*Number of lines in PLS)

αPLS

49.7 mrad

= Retinal Image

Diameter

1.8×10-5

0.05

Retinal Image

Source Shape

Visual Angle α

Spot Circle

= Beam Diameter

ANSI Rules

Exposure Rules*

2.85°0.1°0.1°0.1° 0.29°

0.025 0.025

1.27

Exposure Duration t (sec)

MPbeam (mW)

2.47

Number of pulses

0.05 0.05

100=Frame Rate *T*number of

segment lines

(8*αPLS)/(π*(a max+a min)

=t min*a/t line

t line=1/(2*F frame)

αPLS

1.5 mrad

αW=αmin

Slit

=(8*αPLS)/(π*(a max +a min)

Slit

=(8*αPLS)/(π*(a max +a min)

0.1°

0.085 0.025 0.845 0.025

1.5 mrad

αPLS αW=αmin

Single Pulse (SP)

0.05

Slit

(8*α L)/(π*(a max+a min)

3.46

Width

=t min*a/t line

t line=1/(2*F frame)

1.97

= Beam Diameter

9.23

=Frame Rate *T*number of segment lines

10

1.8×10-5

0.05

5.0×10-3

2


174

Figure 5.6: Maximum permissible MPФbeam in mW for all sub‐exposures, i.e. spot (red), circle (pink), line (green), PLS – F 100 Hz (blue – dashed), PLS – F 1000 Hz (turquoise – dashed) and PLS – F 10000 Hz (light blue – dotted).


175

5.2.2.3.3 Repeated Refraction Measurements

In general, it is common practice to perform several repeats not only for peripheral but

also for central refraction measurements. To ensure safe use for repeated

measurements over a certain period of time when using the proposed EM instrument,

the ANSI repetitive pulse rules (Figure 5.3) were applied. For this analysis, the line

exposure was chosen as it best describes the exposed retinal area with respect to the

single pulse exposure analysis.

Table 5.3: Maximum permissible exposure in mW.

Calculations are based on a wavelength of 830 nm and the duration of the single pulse retinal ring (line = ring circumference) projection is 0.05 seconds.

Number of measurements

per day 1 2 3 5 10 20 50 100

Maximum Permissible Exposure in

mW

9.23 7.76 7.01 6.17 5.19 4.36 3.47 2.92

The results are shown in Table 5.3, indicating that even in the unlikely event of 50

peripheral refraction measurements per day (50 x 11 individual retinal rings), the EM

light source with a maximum output power of 3.0 mW (Section 5.2.1.1) operates below

the maximum permissible exposure.

5.2.2.4 Discussion

The EM’s operation is based on the same ring‐autorefraction principle as the Shin‐

Nippon NVision K5001 autorefractor. The proposed imaging procedure for the EM,

however, differs in that it requires ocular ring scanning and off‐axis illumination.

Therefore, it was important to source and assess the additional components required to

achieve this illumination technique, while also ensuring that optical radiation safety

limits are not exceeded for clinical use.

5.2.2.4.1 ANSI Exposure Limits and Ocular Scanning

In general, the ANSI limits are based on literature reports of eye damage after laser

exposure of different wavelengths and they are “set to be at least 10 times lower than


176

the damage threshold, expressed as a 50% probability of a minimum visible lesion”.205

These standards cover either single or repetitive pulse source exposures to the eye, but

they do not consider the specific cases of ocular scanning or off‐axis illumination, as

proposed for the EM instrument. During the ring scanning process, the small spot images

are partially overlapping on the retina and the temperature gradient changes during the

movement within two neighbouring points. With respect to this special ocular ring scan

illumination, a thorough analysis was conducted to assess all possible exposures that

cover this new illumination feature.

Firstly, single pulse exposures were assessed using the ANSI standards and the definition

of Delori et al. on non‐circular exposed retinal areas, which are defined by a visual angle

subtending an equivalent circular area. On the basis of the EM’s ring illumination, the

visual angles for the circle and the line exposure (ring circumference) as well as the spot

exposure (worst case scenario) were therefore assessed with respect to single pulse

exposure. For the same exposure duration of 0.05 s, it was the spot exposure which

proved the most hazardous (MPФ is 2.67 mW), followed by the line exposure (MPФ is

9.23 mW) and lastly, the circle exposure (MPФ is 78.19 mW). To compare similar single

pulse exposures to that of the EM light source application, one example for threshold

determination after a near‐infrared Maxwellian‐view exposure is given by the study by

Roach et al.,208 who compared the effects of 10 s near‐infrared laser irradiation (860 nm,

60 μm retinal spot) on four primate eyes with an implemented standard thermodynamic

model. Experimentally, they performed threshold measurements for the occurrence of

minimum visible lesions on primate retinas, by varying power levels and number of

exposures. They found the minimum visible lesion threshold power to be 27.0 mW after

one hour post‐exposure assessment, which is in very good agreement with their thermal

model damage threshold calculation of 24.12 mW. Their threshold results are 12 times

greater than the MPФ obtained by ANSI exposure limits.

Safety for ocular scanning first became relevant with the introduction of the first SLOs.

Due to the limitations of safety standards in terms of scanned light exposure, Klingbeil207

performed an extensive analysis on retinal temperature rise during intra‐ocular scanning

using a theoretical thermal model in order to find a safe measure. Specifically, he aimed


177

to predict more accurate light‐level limits for intrabeam ophthalmic scanning devices

(i.e. SLO) by comparing several ANSI retinal exposure limits to predicted retinal

temperature increase. He found best similarity when comparing thermal effects of

retinal scanning with extended pulsed source illumination. He also concluded that the

calculated ANSI power levels for SLOs at that time were 100‐5000 times less hazardous

than his recommendations based on his theoretical model. De Wit204 also described

safety norms for a laser scanning Maxwellian view system with respect to the SLO

device. By comparing pulsed intrabeam exposure with pulsed extended source exposure,

he also concluded that the latter illumination provided the greatest degree of protection

for SLOs.

The most recent approach on safety assessment for ocular scanning was done by Delori

et al.,205 who suggested a different method to the one used by De Wit204 and Klingbeil.207

Instead of assessing the pulsed extended source exposure with respect to ocular

scanning, Delori et al.205 used the PLS exposure and compared it to the subtended area

single pulse exposure. For their SLO analysis they assessed the MPФ with respect to the

SLO’s operating wavelength range 400‐800 nm and concluded that although a single

pulse exposure over the entire field is the most conservative model for small fields at

short‐wavelengths, for larger wavelengths greater than 700 nm the PLS exposure is to be

selected as safest. The analysis presented here of the EM’s ocular ring scan illumination

showed that when comparing the line and PLS MPФs in Figure 5.6, the PLS calculation

provides the more restrictive exposure when the ring is scanned at a very fast scan frame

rate. For slower scanning the single pulse line exposure provides the more conservative

MPФ.

5.2.2.4.2 Illumination of Peripheral Retinal Locations

The ANSI standards are not only deficient with respect to ocular scanning but also with

respect to the assessment of peripheral retinal imaging as aimed with the proposed EM.

The only ANSI statement made with respect to off‐axis illumination is that “combinations

of sources whose centres are separated by an angle greater than αmax (100 mrad) are

considered as independent”. According to that, the minimum distance where each

retinal spot can be considered as an individual exposure is 1.70 mm (visual angle αmax =


178

100 mrad). Using a ray‐tracing approach, the distance between the ring centres of each

of the adjacent illuminated retinal locations was calculated to be approximately 2.9 mm.

Having, no specific off‐axis illumination standards available, studies on the peripheral

retina may provide greater clarification on the impact of exposures on different retinal

locations. As mentioned earlier, thermal retinal damage occurs at threshold levels due to

strong light absorption by melanin of the retinal pigment epithelium.196, 202, 205 Although

attempts were made to measure melanin concentration as a function of retina location,

different results were reported, making a prediction of off‐axis light absorption

inconclusive.196, 209, 210 Polhamus et al.211 developed a model to estimate laser‐induced

threshold damage in the peripheral retina. Their predictions show that with increasing

distance from the macula into the periphery, the threshold for retinal injury rises.

Variation in fundus reflectance with retinal location is of particular interest when the

reflected light requires it to be detected efficiently, for example, for refraction purposes.

Delori and Pflibsen196 compared fundus reflectance on three different retina locations

within a wavelength range of 445 ‐ 805 nm. They showed that fundus reflectance is

affected by the degree of pigment distribution in relation to the retina location

measured. They found that the longer the wavelength and the further into the periphery

it extended, the higher the fundus reflectance.

A review by Berenschot et al.212 lists several studies and modelling investigations into

central and peripheral fundus reflectance. These studies considered not only reflectance

with respect to pigment distribution but investigated the different layers describing the

fundus. One concise fundus reflection model by van de Kraatz et al.213 incorporates the

impact of the Stiles‐Crawford Effect, by including a retinal angle parameter that

describes the directionality of the photoreceptors. This model provides an understanding

of the degree of captured light and the degree of receptor disc reflectance. For the EM,

this may be of relevance considering that the illumination beam for on‐axis

measurements is perpendicular to the retina, but for off‐axis measurements, the

incidence of the illumination beam is oblique on the retina. This impact of oblique light

reflection on the off‐axis fundus was modelled and experimentally determined in a study


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by Bedell and Enoch.214 They investigated the directionality of the retina for central and

eccentric retina locations up to 35° and found that independent of retinal location, all

photoreceptors on the retina align approximately with the centre of the pupil of the eye.

As such, the Stiles‐Crawford Effect exhibits no impediment to the EM application with

respect to amount of fundus reflectance needed.

In summary, with respect to the illumination of peripheral retinal locations as proposed

for the EM instrument, it can be concluded that under consideration of the statement

made within ANSI standards, the retinal damage thresholds found across the retina and

the increased fundus reflectance in the periphery, the above calculation for the ring scan

illumination will provide exposure limits that safely cover both, on‐ as well as off‐axis

ring scan exposures.

5.2.2.4.3 Scanner Safety

In the current safety analysis, a single spot or beam exposure was included. This worst

case scenario can only occur if the scanner were to fail in a position where light is still

directed towards the eye. However, the selected galvanometer scanners are equipped

with the intrinsic safety feature to steer the beam away from the eye as soon as there is

a system shutdown or malfunction and thereby preventing accidental exposure to a non‐

scanned beam. In addition, to the scanners’ in‐built safety features, the ANSI standards

recommend that any “Class 3B laser or laser system should be provided with a

permanently attached beam stop or attenuator.” Hence, a spring loaded mechanical

shutter has been selected to normally block the light beam. A solenoid pulls the shutter

open briefly while the refraction scan can be performed.

5.3 Component Criteria for Image Detection

In addition to the safety and design considerations for the illumination path, the

reflection path also required special optical configuration and component selection,

primarily with respect to minimising interfering reflections and permitting the rapid and

precise capture of the reflected ring images.


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5.3.1 Reduction of Interfering Reflections

Reflections that occur from optical surfaces such as the optical EM components, i.e.

lenses, mirrors and prisms, or the anterior ocular surfaces are disadvantageous, as they

can adversely affect the detection and thus, analysis of the captured retinal ring images.

Possible provisions to overcome the obstacles of unwanted reflections when detecting

EM retinal images have been considered as follows.

Coatings on ocular surfaces control light reflection and transmission through the

mechanisms of optical interference. Particularly, wavelength‐specific anti‐reflection

coatings can reduce reflections to less than 1% on optical surfaces and thus, are widely

used in many optical applications and instruments. Nevertheless, for the EM purposes,

elimination of reflections on optical surfaces alone is not sufficient, as unwanted ocular

reflections from cornea and the crystalline lens surfaces remain.

Figure 5.7 illustrates how the use of linear polarisers and beam splitters can be used to

reduce reflections from the cornea and crystalline lens surfaces and permit detection of

reflections from the retina. Firstly, the non‐polarised beam of the light source (SLD) is

linearly polarised in order to generate s‐polarised light. This light propagates to the

polarising cube beam splitter, which is the optical component that separates the

illumination from the reflection paths. Its polarising properties permit the reflection of

the s‐polarised light, which is directed towards the eye. Whereas, the crystalline lens and

the cornea are highly reflective ocular surfaces which maintain polarisation of the

reflected light, the retina acts as a highly diffuse reflector, reflecting de‐polarised light.

At the polarising beam splitter, only the p‐component of the reflected retinal image can

pass through to the detector and the s‐polarised light from the cornea and crystalline

lens is deflected. The p‐polarised light, as reflected from the retina, can be captured and

analysed.

When using polarising optics, it should be noted that although the state of polarisation

does not affect the measurement output,215 polarising filters and beam splitters result in

loss of light, which may need to be compensated.


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Figure 5.7: Graphical illustration on the use of linearly polarised light for the reduction of interfering reflections.

5.3.2 Translation Stage and CCD Sensor

For detection of the retinal ring image, the Sony CCD sensor ICX445 was selected (Basler

Scout, Basler Vision Technologies, mono) with high resolution (1296 × 966 pixels), small

pixel size (3.75 μm) and high frame rate (32 Hz). A fast and precise linear translation

stage (Physik Instrumente (PI) GmbH & Co. KG, M‐122.2DD Precision Micro Translation

Stage) with a travel range of 25 mm and a maximum velocity of 20 mm/s was selected to

permit the movement of the camera, in order to compensate for large spherical

refractive errors. By combining camera position with automated image analysis to

extract the ring size and distortion information, the sphero‐cylindrical refraction output

of the eye can be determined.

5.4 Experimental Validation of the Ring‐Autorefraction

Principle

5.4.1 Methods

5.4.1.1 Experimental Set‐Up and Procedure

As a preliminary validation step for the optical design, image capture and image analysis,

the critical components required for the on‐axis autorefraction principle of the EM were

assembled and tested on the optical bench. The components required for the on‐axis


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ring‐scan illumination, i.e. x‐y galvanometer scanner and light source, were connected,

installed and configured using customised software. This software permitted the change

in settings of the x‐y scanner with respect to scan frame rate, centration and ring image

size/shape. For ease of alignment, the light source used for this experimental set‐up was

a fibre coupled red laser (Melles Griot 57 PNL 062/P4/S) which operates in the visible

spectrum (λ = 635 nm) with 7 mW output power. The critical optical on‐axis components,

such as lenses, polariser and polarising cube beam splitter, were positioned and aligned

on the optical bench. Figure 5.8 provides the layout of the experimental set‐up with the

relevant components. Optical components were assembled according to the optical

illumination and reflection path designs as developed in Section 4.1.3. The camera was

installed and settings with respect to brightness, contrast and exposure were adjusted to

provide sufficient signal levels for the image capture.

For the initial testing, a calibration model eye (Shin‐Nippon NVision K5001 calibration

model eye) was measured. The CCD of the camera was positioned on an adjustable rail,

which permitted the manual movement through the focussing range. A number of

different trial lenses were placed in front of the model eye to induce a known amount of

refractive error. The CCD was axially adjusted until best focus of the ring image was

achieved. The image was then captured and the respective detector position was

recorded. With the help of the Brien Holden Vision Institute Technology Group, a further

software program was developed which assesses the luminance threshold of the ring

image and applies a circle/ellipse fitting algorithm in order to determine the size and

shape factor of the reflected captured ring images. From this, the sphero‐cylindrical

refraction output was determined.

In order to assess the feasibility of capturing and analysing small changes in refractive

error, low powered trial lenses were placed in front of the calibration model eye. This

was done in five sequentially 0.25D steps, measuring refraction from 0.00 to ‐1.00D.

After manual adjustment of the CCD position to achieve best focus for each induced

small refractive error change, the detector images were recorded and analysed using the

circle/ellipse fitting algorithm. The procedure of aligning the five positions was repeated

three times.


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Figure 5.8: Layout of the optical bench set‐up.

a) the illumination path which generates the ring image that is projected onto the retina and b) the reflection path which captures the reflected retinal image. Focal lengths of lenses and distances between lenses were assembled in accordance with the optical path designs from Section 4.3.1.

5.4.1.2 Investigation of Shin‐Nippon Detector and Retinal Images

Despite the restricted information pertaining to the optical system of the Shin Nippon

NVision K5001, determination of detector and retinal image size and image size

sensitivity as a function of refractive error can provide some cross‐validation of the

autorefraction principle between the Shin‐Nippon NVision K5001 and the proposed EM.

As the detector image is of little interest to practising clinicians, it is solely the sphero‐

cylindrical refraction output which is the commonly displayed parameter on the monitor

of the Shin‐Nippon instrument. Nevertheless, the image capturing feature within the

instrument also permits the assessment of the detector images. Access to these images

was obtained by altering the menu in the “Maintenance Mode”. To select this menu, the

measurement button had to be held down whilst the autorefractor was turned on. After

approximately 10 seconds a buzzer sounded twice and the measurement button could

been released. From the menu the option “Freeze Image” was selected, which displayed

SLD

X‐y scanner

Polarizing Cube Beam Splitter (30/70%)

Polarizer

Lens 1Calibration Model Eye

Lens 1Calibration Model Eye

Lens 2

Lens 3

Movable CCD

a)

b)

Aperture


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the detector image on the monitor once a measurement has been taken. Retrieval of the

displayed detector image was done by using the instruments in‐built low resolution

printer as well as by interfacing the display monitor to an external computer. For this a

USB video capture device and a video capturing and processing software (VisioForge

Video Capture SDK) were used to permit the capture of the detector images. Again, using

a calibration model eye and a set of trial lenses, these detector images were assessed

with respect to image size sensitivity as a function of refractive error.

Moreover, a calibration model eye with a plane retinal surface was used to assess retinal

ring image size and image size sensitivity of the Shin‐Nippon NVision K5001. The infrared

ring image which was projected onto its retina was captured with an infrared digital

camera during the measurement. The procedure of capturing the retinal ring is indicated

in Figure 5.9. A known amount of refractive error was induced with a set of different trial

lenses, which were placed as close as possible in front of the model eye. In addition, a

rule placed at the plane of the retina was captured together with the retinal ring to

provide a reference scale for the subsequent determination of the retinal ring image size

as a function of refractive error.

Figure 5.9: A calibration model eye with a known induced refractive error (trial lens) was measured with the Shin‐Nippon NVision K5001.

An image of the reflected infrared retinal ring and a reference scale (rule) was captured using a digital infrared camera.


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5.4.2 Results

5.4.2.1 Cross‐Validation of the Autorefraction Principle with optical ZEMAX

design

Figure 5.10 illustrates the detector images as computed for a range of refractive error

eyes when using the optical design in ZEMAX as well as when the images were recorded

at the position of best focus using the optical bench experiment.

Figure 5.10 shows that the image sizes of the computed and captured images are

comparable. Moreover, it was confirmed that the approximate distance between the

most hyperopic and the most myopic focussed detector position was about 22 mm,

which is in good agreement with the computed distance of the optical reflection path

design.

Figure 5.10: Detector images for a range of refractive error eyes as computed with ZEMAX (TOP) and as captured on the optical bench set‐up (BOTTOM).

Using the circle/ellipse fitting algorithm and pixel‐by‐pixel analysis, small changes in

refractive error were assessed with respect to the captured ring images. Figure 5.11

shows the number of pixels that define the radius of the captured ring image as a

function of change in refractive error. Due to manual focus adjustment on the optical

bench rail, the standard errors for the three repeats were large; however, the mean

slope of three measurements correlated very well (Figure 5.11).


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Figure 5.11: The number of pixels (± SD) that define the radius of the captured ring image as a function of change in refractive error.

5.4.2.2 Cross‐Validation of the Autorefraction Principle with the Shin‐Nippon

Autorefractor

Using the same calibration model eye and a set of trial lenses, the detector images of the

Shin Nippon NVision K5001 autorefractor were printed (Figure 5.12). The detector

images of the Shin‐Nippon instrument corresponded well to the images captured on the

optical bench with respect to image size and their relative changes with refraction.

Figure 5.12: Printed detector images of the Shin‐Nippon NVision K5001 for an emmetropic eye and a +15D hyperopic and ‐15D myopic eye.

As there is no information about the optical autorefraction path design of the instrument

or the CCD features or the image analysis algorithm, the retinal image sizes obtained

with the Shin‐Nippon NVision K5001 and the illumination path design of the EM were

also investigated. Figure 5.13 details the comparison of the retinal ring image diameters


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(in mm) as a function of refractive error change (in D) between the Shin‐Nippon NVision

K5001 and the illumination path design of the EM.

Figure 5.13: The comparison of the retinal ring image diameters (in mm) as a function of refractive error change (in D) between the Shin‐Nippon NVision K5001 and the illumination path design of the EM.

It shows that the Shin‐Nippon instrument projects much larger ring images onto the

retina, when compared to the optical design of the EM, which is more restricted with

respect to its numerical aperture (NA). As expected ring image sensitivity, that is the

slopes of retinal image size as a function of change in refractive error, compared well for

both methods.

5.4.3 Discussion

5.4.3.1 On‐Axis Optical Bench Experiment

To validate the on‐axis autorefraction principle of the EM, the ring scan illumination and

the reflection paths were set up on the optical bench. In an initial experiment, the

measurement range of different refractive errors, from most hyperopic to most myopic

eye, was tested using a calibration model eye and high powered trial lenses. For this, the

CCD camera was manually aligned in the position of best focus. The experiment showed

that for the range of refractive errors measured, the ring images captured on the CCD

agreed well with the image sizes computed from the illumination and reflection path

design in Chapter 4. The translation distance of the CCD was also in accordance with the

y = ‐23.17x + 43.15

r² = 0.99

y = ‐20.61x + 22.71

r² = 0.98

‐20

‐15

‐10

‐5

0

5

10

15

0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60

Change

in Refractive

Error (in D)

Retinal Ring Image Diameter (in mm)

Shin‐Nippon Nvision K5001

EM Illumination Path


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theoretical calculations, confirming the suitability of the selected translation stage. The

second experiment aimed to assess whether smaller refractive error changes can reliably

be detected using the circle/ellipse fitting algorithm and the selected CCD camera. The

same calibration model eye and a series of spherical trial lenses increasing in power in

0.25D steps were chosen to induce these small refractive error changes. Despite some

inaccuracies with the manual adjustment of the CCD for best focus position, the average

circle diameter that was fitted to the detected ring images correlated well with the small

changes in refractive error. From this it can be concluded that using such a set‐up with

the optical components chosen, it is possible to measure the desired refractive error

range with a 0.25D resolution when images are adjusted for best focus.

One key difference in the optical design between the Shin Nippon instrument and the

EM is the NA on the object side. With an objective lens diameter of ~30 mm and a focus

distance to the eyeball of ~150 mm, the NA of 0.20 of the Shin‐Nippon NVision K5001 is

much larger than what can be achieved with the EM. With the selected scan interval of

10° field angle, the EM’s maximum achievable NA is 0.16. Given some engineering

constraints, the EM has a NA of only 0.12.

Despite the fact that information of the Shin‐Nippon NVision K5001’s CCD detector is not

available, assessment of image size sensitivity on the detector was possible and was

shown to be in good agreement with that of the optical bench experiment. Similarly, the

slopes of retinal ring image size as a function of refractive error compared well for both

methods.

5.4.3.2 Major Obstacles Encountered During Experimental Testing

5.4.3.2.1 Image Analysis for Off‐Axis Ring Images

The experiments performed on the optical bench assessed the measurement range and

measurement sensitivity of the EM’s on‐axis illumination and reflection paths. For this,

the images were aligned and captured in best focus position. However, as the refractive

error of the eye changes with increasing visual field angle, the best focus position for the

image on the CCD detector also changes. Aiming to have an instrument that measures

peripheral refraction in less than one second, the CCD camera would either have to be


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moved very quickly in between the 11 scan positions, or be in a stationary position at the

best averaged focal position and capture images, some of which will be out of focus.

Despite the fact that most of the components permit the fast scanning and translation, it

was found that the camera itself limits the operational goals with respect to

measurement speed if each of the 11 positions had to be aligned for best focus before

being captured. In order to achieve images of high resolution at low light levels, a certain

camera integration time is required per image, which would eventually prolong the

intended peripheral refraction scan duration. With rapid scanning of the peripheral

refraction profile being a key feature and requirement of the EM, the only alternative is

the capturing of all 11 images at one single translation stage position. The best average

CCD position may be determined from an initial alignment scan that computes an

average focal position from three visual field positions, i.e. 0° and ±50°. At this stage,

first attempts to analyse ring images that are well‐out‐of focus were not successful when

using the current circle/ellipse fitting program.

5.4.3.2.2 Impact of Higher‐Order Aberrations on Peripheral Ring Images

As the initial optical bench experiment was not set up for testing in humans, a simple

calibration model eye with plane retinal surface was measured. In addition, experimental

autorefraction measurements with the Shin‐Nippon NVision K5001 were done on both

the calibration model eye and human eyes. When capturing the detector images with the

Shin‐Nippon NVision K5001, a few eyes were also measured during off‐axis fixation. It

was observed that some detector images measured during peripheral refraction

appeared to be slightly asymmetric or distorted in shape and sometimes also in

luminosity. Due to the restrictions in assessment of these low resolution detector images

and due to the unknown image analysis algorithm of the Shin Nippon NVision K5001, an

attempt was made to model the retinal ring image shape as a function of visual field

angle, in order to further investigate these observed distortions of the ring images.

Into‐the eye‐ray trace was performed using the EM reference model eye (Section 4.2.1.1)

and the illumination path design (Section 4.3.1.2). To assess the ring shape in the

periphery, a coordinate break was inserted prior to the surface of the anterior cornea in

the ZEMAX Lens Data Editor. Parameter 3 (PRAM 3, tilt) of this coordinate break was

altered to induce eye turn with respect to the illumination beam of up to 50° in 10°


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steps. Previously (Section 4.3.1.2), the illumination path was simplified, by propagating

the on‐axis circular beam through the pupil. However, in order to understand the change

of the retinal ring image size and shape as a function of visual field angle, two additional

surfaces of zero thickness were inserted prior to Lens 1 which permits the generation of

a ring shaped beam. Specifically, this was done by defining the first surface as an angular

aperture, whose size defines the outer ring diameter and the second surface is an

obscuring aperture, whose size defines the inner ring diameter. Together, the surfaces

generate an illumination ring of defined width. The generated retinal ring image can be

assessed either by using the ZEMAX spot diagram feature or by computation of the

marginal positions of the ring retinal points using ZEMAX ray‐trace analysis. Due to the

different sizes of ring images projected onto the retina when using the EM and the Shin

Nippon NVision K5001 (Section 5.4.2.2) concept, changes of the retinal ring image size as

a function of visual field angle for different NA’s were also investigated. Figure 5.14

illustrates the modelling approach of the peripheral ring illumination in ZEMAX for three

different NA’s, i.e. 0.09 (small NA), 0.12 (medium NA) and 0.15 (large NA). Moreover, it

shows the plot of the ratio between the tangential retinal ring radii which are distal (–x)

and proximal (+x) to the fovea as a function of visual field angle and NA. It should be

noted that the sagittal retinal ring radii, which are superior and inferior to the fovea

respectively, have not been plotted as they were not affected by the horizontal visual

field angle.

The plot in Figure 5.14 shows that with increasing visual field angle and with increasing

NA, the ratio between the ring radius distal and the ring radius proximal to the fovea

gradually decreases.

From Figure 5.14 it is apparent that the two tangential radii of the retinal ring image

obtained with the schematic model eye differ by up to 30% and 44% at 50° for small and

large NA’s, respectively. As a consequence, the peripheral retinal ring corresponds

neither to an annular nor an elliptical shape. Instead it is a non‐elliptical, asymmetric

ring‐like shape. This modelling approach confirms the previously observed slight

asymmetry in the peripheral Shin Nippon NVision K5001 detector images. It also shows

that the effect of this asymmetry increases with increasing NA. Thus, the asymmetric

effect would be smaller with the EM illumination path design, than that with the Shin


191

Nippon NVision K5001. However, it is not only the NA of the optical instrument design

which is associated to this asymmetry, but also the change in the refractive error of the

eye (the retinal ring image size).

Figure 5.14: Modelling of the retinal ring image as a function of visual field angle.

The EM reference model eye (Section 4.2.1.1) and the illumination path design (Section 4.3.1.2) were used to model a system with a) small, b) medium and c) larger NA’s. The marginal retinal ray coordinates were computed to determine the ratio between the tangential retinal ring radii that are distal (‐x) and proximal (+x) to the fovea as a function of visual field angle and NA.

Figure 5.15 illustrates the ratio between the tangential retinal ring radii distal and

proximal to the fovea as a function of visual field angle and refractive error. As visual

field angle increases the myopic eye, which produces the larger retinal ring image, has

the greatest asymmetry along the tangential retinal ring meridian and the hyperopic eye,

which produces the smaller retinal ring image, is least asymmetric.

Dependent on the image analysis algorithm of the ring images with respect to the

sphero‐cylindrical refractive error, this finding could adversely affect the accuracy of

peripheral refraction measurement results obtained with the Shin‐Nippon NVision

K5001. As the Shin‐Nippon NVision K5001 was designed to measure on‐axis refraction, it


192

is reasonable to assume that the image analysis algorithm fits a best‐fitting ellipse to the

non‐elliptical retinal ring shapes to extract the sphero‐cylindrical refraction result. As

this was also the intended method for the EM image analysis, this asymmetric effect may

also affect the EM refraction results, although to a slightly lesser degree, as the NA is

smaller, reducing the ring image asymmetry.

Figure 5.15: The ratio between the tangential retinal ring radii which are distal and proximal to the fovea as a function of visual field angle and refractive error.

This finding suggests that the asymmetric higher order aberrations found previously in

the periphery of the eye can affect the ring‐autorefraction operation principle as

commonly used for peripheral refraction measurements (Section 1.3.5). Instruments

based on the ring‐autorefraction principle do not differentiate between higher order

aberrations such as coma and the lower order aberrations (defocus and astigmatism).

Previously (Chapter 3) it was shown pupil misalignment leads to increased sensitivity in

peripheral refractive error measurements with the Shin‐Nippon NVision K5001. It is

reasonable to suggest that the asymmetry found in the peripheral ring images may also

have some impact on the misalignment sensitivity. In fact, it may explain some of the

differences identified between the schematic model eye and the measured data in the

pupil alignment function slopes. Nevertheless, as the schematic model eye is based on

certain assumptions and as there is no information available on the image analysis

algorithm of the Shin Nippon instrument, this remains to be verified.

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

0 10 20 30 40 50

Ratio betw

een the ‐x radius and the

+x radius of the retinal ring


emmetropic eye

‐5 D myopic eye

+5 D hyperopic eye


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5.5 Future Work

Despite the fact that the EM’s proposed autorefraction principle was successfully

confirmed in its operation and safety, some of the experimental work discussed in the

present chapter raised considerable concerns with respect to achieving the EM’s

performance goals.

One of the issues is related to the intended rapid measurement of the peripheral

refraction profile. In order to achieve a peripheral refraction scan in less than one

second, the 11 images have to be captured at one CCD position, even if they are out of

focus. Due to the reduced luminosity profile for the captured out of focus ring images,

the current experimental set‐up, as well as the circle/ellipse fitting algorithm, require

further improvement to permit the better capture and analysis of these images.

Of major concern is the identified distortion of the peripheral ring images. With

increasing visual field angle and retinal image size (e.g. myopic eyes), the ring image

becomes increasingly more asymmetric. Previously it was assumed that if alignment with

the pupil centre was ensured, the ring‐autorefraction principle would provide valid

sphero‐cylindrical peripheral refraction measurements. However, it appears that these

peripheral ring images are affected by higher order aberrations, in particular coma, as

they increase with peripheral visual field angle. Even if the sole purpose of the

instrument is to measure the sphero‐cylindrical refraction output, the outcome may

differ depending on the ring image analysis algorithm. The best approach for the

computation of the sphero‐cylindrical refraction output may be to find the average

ellipse that best describes the ring‐like shape and thereby ignores the asymmetric

peripheral ring shape. Nevertheless, if one aims for accurate peripheral refraction

measurements, it would be of value to also account for this asymmetry in the peripheral

ring image. This may be done by fitting a function that best describes this asymmetric

ring shape, perhaps a double‐ellipse function. From this it may be possible to compute

the size and shape by providing not only sphere, cylinder and axis values, but also coma.

Commonly the term coma, however, is provided in unit µm, measured with a wavefront

sensing technique. Thus, extraction of the coma term from the ring image may not be

the most expedient approach.


194

The measurement of peripheral higher order aberrations has gained attention most

recently. A study published by Mathur et al.127 measured peripheral aberrations in a

group of emmetropic and myopic young adults. It was found that coma across the visual

field varied significantly between both groups. In fact, coma slopes were two‐fold

greater in the myopic group than in the emmetropic group. The mean slope for coma in

myopic eyes was ‐0.014 μm/degree, whilst in emmetropic eyes the mean slope was ‐

0.006 μm/degree. Using a ray‐tracing approach it was suggested that this difference in

the coma slopes between both groups can be explained by the differences in anterior

corneal radius of curvature, corneal asphericity as well as axial length. Moreover, in a

further study, the impact of age on peripheral aberrations in emmetropic eyes was also

assessed. In older eyes coma increased with visual field angle at a significantly higher

rate (‐0.018 μm/degree) than in younger eyes (‐0.006 μm/degree).61 These findings were

also confirmed in a larger sample sized study by Baskaran et al.62

With the demonstrated differences in peripheral higher order aberrations, such as coma,

between different population groups, it may be of increasing importance for future

research activities to neither ignore nor average these higher order aberration effects

when measuring peripheral refraction. Thus, based on this increased interest and the

other limitations encountered with the ring‐autorefraction principle, a wavefront sensing

technique appears to be the more appropriate operation principle for a dedicated

peripheral refraction instruments.


This chapter assessed the safety requirements with respect to the proposed EM’s new

peripheral and ocular ring scan illumination. For this, several exposure cases were

simulated and assessed and the MPФ with the greatest degree of protection was

determined. Under the assumption that a single beam (non‐scanned) exposure is

prevented, the greatest protection was obtained with either the single pulsed line

exposure for slow to medium scan frame rates or the PLS exposure for fast scan frame

rates. Other specific EM characteristics, such as exposure of the peripheral retina and

possible malfunction of the scanners were also addressed with respect to safety

assessment of the proposed EM instrument.


195

In addition to the safety requirements, this chapter also assessed the technical

implementation and feasibility of the autorefraction principle for central and peripheral

refractometry. Based on both, the safety and component criteria, the EM on‐axis

autorefraction principle was experimentally verified on the optical bench, and was also

successfully cross‐validated with the Shin Nippon on‐axis autorefraction paths. However,

an obstacle relating to the ring‐image analysis was identified, which would impair one of

the main goals of the EM; the performance of a peripheral refraction scan in less than

one second. Moreover, for the peripheral refraction measurements it was discovered

that higher order aberrations have the potential to interfere with the sphero‐cylindrical

refraction readings. As ray‐tracing and experimental testing have demonstrated,

asymmetric higher order aberrations can distort the symmetry and elliptical shape of the

retinal ring.

This ring asymmetry for peripheral measurements may not only affect the sphero‐

cylindrical peripheral refraction output of current autorefraction instruments but also

that of the proposed EM instrument. With the aim to develop an instrument dedicated

to measure peripheral refraction accurately, it is of importance to account for these

asymmetric changes. The most expedient approach of segregating higher and lower

order aberrations is by measuring the eye’s peripheral wavefront rather than analysing

the asymmetric peripheral ring when using the autorefraction principle. The change of

the EM’s operation principle from the autorefraction ring principle to the wavefront

sensing technique also seems reasonable with respect to the recent and future research

interests in measuring peripheral higher order aberrations. The following chapter

describes the technical implementation of the peripheral wavefront sensing principle in

detail.

CHAPTER 6: THE EYEMAPPER: A REAL‐TIME GLOBAL ABERROMETER

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CHAPTER 6:

THE EYEMAPPER ‐ A REAL‐TIME GLOBAL ABERROMETER

6.1 Introduction

Initially, the aim of the newly proposed peripheral refraction instrument, the EyeMapper

(EM), was to measure the clinically relevant sphero‐cylindrical refractive errors of the

eye by use of the well‐known ring‐autorefraction operation principle. Findings from

Chapter 5, however, revealed that peripheral higher order aberrations have the potential

to interfere with the autorefraction results. The use of an operation principle based on

the Hartmann‐Shack wavefront sensing principle, which segregates higher and lower

order aberrations, was therefore deemed to be more suitable for an instrument

dedicated to measuring peripheral refraction.

Based on the knowledge gained from the previous chapters, the aims of this chapter

were to:

‐ Update the optical design of the EM to integrate the wavefront sensing principle

(Hartmann‐Shack sensor),

‐ Develop the mechanical design of the clinical EM instrument,∏

‐ Build∏ the EM instrument, and therefore:

o Perform a tolerance analysis,

o Source the additional components required,

o Re‐assess safety requirements on the basis of the new operation

principle,

o Manufacture the instrument parts according to the mechanical design,∏

o Develop the instrument software required,∏

‐ Validate the EM instrument by performing measurements on a model eye and on

ten human eyes.

∏ Aims and tasks labelled with this symbol were achieved with the help of the Brien

Holden Vision Institute Technology Team.


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6.2 Instrument Design

6.2.1 Optical Design‡

To permit the measurement of central and peripheral aberrations of the eye by use of

the Hartmann‐Shack wavefront sensing technique, the optical design of the EM required

updating. Stationary optical components and a scanning mirror are the optical main

components chosen to permit the fast measurement of the eye's refraction profile,

ranging from ‐50° to +50° in 10° steps. The optical sub‐systems of the EM are again the

deflection system, the illumination path, the reflection path, the pupil imaging path and

the fixation path. Figure 6.1 shows the layout of the updated EM instrument design

indicating the five optical paths. The individual design goals of each optical sub‐system

are explained in more detail in the next sections.

Figure 6.1: Layout of the EM instrument design.

It shows the EM’s five optical paths: 1. deflection system, 2. illumination path, 3. reflection path, 4. pupil imaging path and 5. fixation path.

For clarity, only the central path and 5 peripheral paths are shown.

‡ ZEMAX was used to update the optical design of the EM, for which the EM reference model eye (Section 4.2) was used. As described in detail previously (Section 4.3), the design of the individual paths was done using the three ZEMAX editors in sequential ray‐trace mode.

2.

3.

5.

4.

0°

(33 mirrors)

5

Hot Mirror

PBS

1.


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6.2.1.1 Wavefront Sensing Paths

6.2.1.1.1 Deflection System

Instead of using prisms as deflecting components, the updated deflection system of the

EM comprises a set of three mirrors per field angle (per configuration). Hence, a total of

33 mirrors and one scanning mirror are used to first direct the illumination beam across

the retina and to then re‐direct the reflection beam towards the wavefront sensor.

A three‐dimensional view of the deflection system indicating the propagation of the

illumination beam is shown in Figure 6.2.

Figure 6.2: Three‐dimensional layout of the deflection system.

It shows the propagation of the scanned illumination beam for 0° (red line) and all peripheral beams (orange lines).


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A key feature of the modified deflection system is the equal optical path length for all 11

scanning positions. This is achieved by deflecting the beam upwards, out of the scanning

plane and back, by mirrors positioned at different heights. Mirror heights for the

peripheral angles are successively reduced to compensate for the longer optical path

distances in the scanning plane. Mirror pairs M1 and M3, as well as lens pairs L1 and L2,

are arranged symmetrically with respect to the vertical mirror plane of M2.

6.2.1.1.2 Illumination Path

Unlike for the design of the previous EM autorefraction concept, where the aim of the

illumination path was to image the oscillating ring‐target onto the retina, the

illumination path of the Hartmann‐Shack technique simply requires a narrow

illumination beam from the SLD (super luminescent diode) to be sent into the eye. With

this mirror arrangement, together with the scanning mirror, 11 discrete spots on the

retina can be illuminated in rapid succession (Figure 6.2).

6.2.1.1.3 Reflection Path

Back scattered light from the 11 sequentially illuminated retinal spots form the

reflection beams, which contain the wavefront information of the eye for each of the

individual angular visual field positions. The reflected beams follow the same optical

paths as the illumination beams until they are separated by the beam splitter and

directed towards the wavefront sensor. The Hartmann‐Shack wavefront sensor consists

of an array of identical lenslets and a CCD camera positioned in the lenslet array’s focal

plane. For an aberration‐free wavefront, the light spots on the CCD camera generated by

the lenslet array would be distributed regularly. The wavefront emanating from eyes

may contain higher and/or lower order aberrations that can be quantified by evaluating

the irregularities of the detected spot positions. Supporting optical sub‐systems, such as

relay systems of specific magnification, are used to transfer the wavefront onto the

Hartmann‐Shack sensor.

For the wavefront sensing EM design, two relay‐lens pairs [Lens 1‐Lens 2 (L1‐L2) and

Lens 3‐Lens 4 (L3‐L4)] were used to image the exiting wavefront onto the Hartmann‐

Shack sensor. From Figure 6.1 it can be seen that for each of the 11 configurations, the

first relay lens pair (L1‐L2, f'=100 mm, Edmunds Optics A49‐333‐INK) is located within


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the deflection system. Together with the particular arrangement of mirrors in the

deflection system, the optical design goals of the relay‐lens pairs (L1‐L2) were to ensure

that for all 11 scan angles, the pivot of the scanning mirror is conjugate with the centre

of the eye's pupil and that equal magnification and defocus is maintained to provide

consistent capture, analysis and comparability of the wavefront for each scan angle. The

second relay lens pair (L3‐L4, f'= 100 mm, Edmunds Optics A49‐333‐INK and f'=50 mm,

Edmunds Optics A45‐882‐INK) with a magnification factor of × 0.5 was used to relay and

resize the wavefront so that it can be captured in full with the selected Hartmann‐Shack

sensor. The sensor was positioned at the plane conjugate to the pivot of the scanning

mirror.

6.2.1.2 Pupil Imaging Path

A pellicle beam splitter (PBS) (Edmunds Optics, NT 39‐478, 8R/92T) was inserted into the

reflection path between Lens 3 (L3) and Lens 4 (L4) for imaging and observation of the

pupil. Positioning it behind the scanning mirror provided the option of observing the

pupil from any of the 11 scanning angles. The pupil observation angles chosen for the

EM were: central, 30° nasal and 30° temporal, assisting with the symmetrical alignment

of the pupil across the visual field. Six infrared LEDs illuminate the anterior eye segment

while the operator adjusts for the correct pupil alignment.

6.2.1.3 Fixation Path

Similarly to the previous EM design (Section 4.3.3), the aim of the fixation path was to

not only have the participant fixate towards a target placed at optical infinity, but to also

enable measurement of the accommodation stimulus‐response curve as a function of

peripheral visual field angle. Using ZEMAX, the fixation path was designed to stimulate

an infinite to 5.00D accommodation range while moving the fixation target with a

motorised linear translation stage (25mm).

Figure 6.1 shows the first mirror after L1 (relative from the eye) in the central deflection

path is a hot mirror (M1, Edmunds Optics, NT43‐955). This hot mirror permits infrared

light to be reflected for the illumination and reflection paths, and visible light to be

transmitted to enable the participant to observe the fixation target provided.


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6.2.2 Mechanical Design

To develop the intricate three‐dimensional arrangement of numerous components, i.e.

mirrors and lenses, the CAD (Computer‐Aided Design) Software SolidWorks (Dassault

Systèmes SolidWorks Corp.) was used for the EM's mechanical design. This software

proved particularly useful for development of the instrument, as parametric, three‐

dimensional design constraints can be defined to determine the component positioning

and assess and simulate the design prior to building the instrument.

Figure 6.3, Figure 6.4 and Figure 6.5 illustrate the three‐dimensional view of the EM

SolidWorks drawings from three different perspectives. The mechanical instrument

design was developed by Darrin Falk from the Brien Holden Vision Institute Technology

Group.

Figure 6.3: SolidWorks EM design from above.

The red dotted line indicates propagation of the on‐axis reflection beam, from the eye towards the HASO wavefront sensor. The mechanical instrument design was developed by Darrin Falk.

Mirror holding bridge with M2 x 11

Base plate

Eye

L1 x 11

L2 x 11

Mirror mounts with M1 x 11

Shutter PCBS

PBS

HASO

Hot Mirror


L3

L4

Mirror Light Source

Polariser

Pupil Imaging CCD

Scanning Mirror


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Figure 6.3 shows the SolidWorks EM design from above, with all the main components

for the deflection system, the illumination and reflection paths positioned above the

base plate. The red dotted line indicates propagation of the on‐axis reflection beam,

from the eye towards the HASO wavefront sensor. The design of the mirror mounts (M1

and M3) was particularly complex, as they had to be spaced tightly and arranged along

an arc shape to fulfil the optical design requirements of the deflection system. All front

surface mirrors were bonded to metal base plates and then attached to the mirror

mounts with four small screws and semi‐flexible O‐rings, which permitted the mirrors to

be finely adjusted for proper alignment. The mirror (M2) holding bridge is the

component that engenders the three‐dimensional structure. Other optical and

mechanical components illustrated in Figure 6.3 are, for example, the mounts for the

lenses, the polarising cube beam splitter (PCBS), the pellicle beam splitter (PBS), and the

light source, as well as the scanning mirror, the shutter and the wavefront sensor

(HASO).

Figure 6.4: SolidWorks EM design from the side and below.

The orange dotted line partially indicates the propagation of the fixation path and the yellow dotted line partially indicates the pupil imaging path. The mechanical instrument design was developed by Darrin Falk.

Base plate

HASO Mirror

MirrorL7

L6

Translation Stage

Galvano Meter

Eye

Bearing Rail for Rotation


Mirror

Pupil Imaging CCD


203

Figure 6.4 illustrates the three‐dimensional SolidWorks EM design from the side and

below, showing most of the components positioned underneath the base plate. These

components are required for the fixation and pupil imaging paths as well as the

instrument rotation. The fixation and pupil imaging paths are partially indicated by the

orange and yellow dotted lines, respectively. Note that L5 from the fixation path cannot

be seen as it is located within the base plate. The bearing rails are used to rotate the

instrument’s base plate from 0° to 90° in 15° steps in order to permit the measurement

of seven different visual field meridians.

Figure 6.5: SolidWorks EM design from the front and above.

The green dotted line indicates the propagation of the on‐axis illumination beam, from the light source towards the eye. The mechanical instrument design was developed by Darrin Falk.

Figure 6.5 illustrates the three‐dimensional SolidWorks EM design from the front and

above, indicating most of the components for the deflection system, the illumination and

reflection paths, as well as sections of the fixation path. The propagation of the

illumination beam is indicated by the green dotted line.

HASO

Polariser

PCBS

L4

Eye

Base plate


L1 x 11

L2 x 11



Scanning Mirror

MirrorL6

Hot Mirror

Light Source

L3


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6.3 Instrument Construction

Following completion of the optical and mechanical design work, a tolerance analysis

was carried out to determine the required accuracy level of the sourced components and

manufactured mechanical parts. The safety requirements had to be re‐assessed to

comply with the wavefront sensing principle. All mechanical parts were manufactured in

accordance with the required accuracy, after which the instrument was assembled and

aligned. Several calibration tools and methods were developed to ensure that the

instrument performed to the necessary degree of accuracy. Comprehensive software

tools were developed to operate the instrument and to acquire and analyse the data.

6.3.1 Tolerance Analysis

6.3.1.1 Aims

Prior to any instrument manufacture, a tolerance analysis is a helpful method that can

be used to account for the effects of manufacturing and alignment errors. It permits not

only the identification of the individual critical components/elements of the optical

system (sensitivity analysis), but it also assesses the system’s overall performance for a

combination of alignment/manufacturing errors (Monte Carlo simulation).

With the reflection path being the critical optical path for the EM, the aim was to

investigate the impact of manufacturing deficiencies, such as axial position, decentration

and tilts on the individual lenses/elements of the reflection path.

6.3.1.2 Methods

6.3.1.2.1 Sensitivity Analysis and Monte Carlo Simulation

The ZEMAX sensitivity analysis and the Monte Carlo simulation were used for the

computation and analysis of tolerances for the EM. The flow chart in Figure 6.6 provides

an overview of the tolerancing procedure.


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Figure 6.6: Flow chart used for the tolerance analysis of the EM using ZEMAX.

6.3.1.2.2 Tolerance Analysis for the Reflection Path

To evaluate the required assembly accuracy for the EM’s reflection path, the following

tolerance analysis steps were performed using ZEMAX:

1. Set‐up of the Lens Data Editor (LDE)

The EM reference model eye (Section 4.2.1.1) and the components in the reflection path

(Section 6.2.1.3) were set up in the ZEMAX LDE. A paraxial surface, which acts as an ideal

thin lens and which has the same focal length as each of the lenslets (f’=2.3 mm) of the

selected Hartmann‐Shack sensor, was inserted at the lenslet array position in the

reflection path.

Figure 6.7 shows the diagrammatic layout of this set‐up. For computation of the

aberrations, the ZEMAX Zernike coefficients were determined at the image surface (the

Hartmann‐Shack CCD), which is the surface conjugate to the retina.

Definition of Initial Tolerance Criteria

Establish the “worst offenders”in the system

Sensitivity Analysis (Analyses of each perturbation for each optical element in

the system)

Assessment of the impact of each

tolerance criterion on the performance

Tighten criteria for “worst

offenders”, if required

Monte Carlo Simulation (Simultaneous analysis of all

perturbations for all optical elements in the system)

Evaluation of Tolerance Analysis

Assessment of estimated change in overall performance


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Figure 6.7: Reflection path set‐up used for the tolerance analysis.

The simplified Hartmann‐Shack sensor consists of an ideal thin lens, which acts as the Hartmann‐Shack’s micro‐lens and an image surface, which corresponds to the CCD of the Hartmann‐Shack sensor.

2. Set‐up of the Tolerance Data Editor (TDE)

Using the ZEMAX Tolerance Data Editor, all assembly relevant tolerances were

defined for the following tolerance operands, i.e. TTHI (tolerance on thickness or

position), TEDX/TEDY (tolerance on element x/y‐ decentration) and TETX/TETY

(tolerance on element x/y‐tilt). All tilt and decentration tolerance operands were

assigned to the four lenses and the thickness tolerance operand was assigned to the

relevant surfaces in the reflection path. In total, 21 perturbations were listed in the

TDE.

3. Performance of the Sensitivity Analysis

For each perturbation, the initial tolerance criterion was defined. This was an

estimation based on the feasibility and complexity for the building of the EM. Criteria

values were ± 0.5 mm for decentration tolerances, ± 0.5 mm for thickness tolerances

and ± 1° for tilt tolerances. Using the Merit Function Editor and its ZERN operand, as

well as the Merit Function criterion in the ZEMAX tolerancing tool, the parameters

that represent the performance of the EM (e.g. term of defocus, astigmatism, coma

or spherical aberration) were specified individually.

4. Performance of the Monte Carlo Simulation

This simulation creates a series of Monte Carlo files, for which all of the parameters

as pre‐defined in the sensitivity analysis, are randomly modified using a statistical

model of the distribution of that parameter. Five hundred Monte Carlo files were

generated on the basis of the tolerances specified in the sensitivity analysis. The

statistical model follows the normal distribution with a total width of four standard

deviations between the extreme minimum and maximum permitted values. The

Lens 1 Lens 2 Lens 3 Lens 4Simplified HS‐sensor


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model estimates the performance changes (change in criterion) based on the root‐

sum‐square method. From the sensitivity analysis, worst offending tolerances were

re‐evaluated where required.

6.3.1.3 Results

6.3.1.3.1 Sensitivity Analysis

Tolerance analysis results are presented for each optical component (L1, L2, L3 and L4)

and each perturbation (axial misalignment, decentration and tilt) as a function of change

in performance (the change in merit function measurement error). For decentred and

tilted lenses, the change in performance was assessed with respect to the terms defocus,

astigmatism, coma and spherical aberration. Axial misalignment of lenses was assessed

for the terms defocus and spherical aberration only, as astigmatism and coma remain

unaffected by this perturbation.

Axial Misalignment of Optical Components:

Figure 6.8 shows the absolute change in performance for the terms defocus and

spherical aberration, if the axial distance between the individual optical components

would deviate by ± 0.5 mm from its optimum position. It can be seen that the distance

between L1 and L2, as well as the distance between L3 and L4, are the “worst offending

tolerances” with respect to axial misalignment.

Figure 6.8: Absolute change in performance with respect to the terms defocus and spherical aberration, for axial lens misalignment of ± 0.5 mm.

0.000

0.010

0.020

0.030

0.040

0.050

0.060

Eye ‐ L1 L1 ‐ L2 L2 ‐ L3 L3 ‐ L4 L4 ‐ HASO

Change in

microns

Axial Change (in mm)

Defocus Spherical Aberration


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Decentred Optical Components:

Figure 6.9 shows the effects of individual lens decentration on the performance of the

system. Specifically, it shows the change in defocus, astigmatism, coma and spherical

aberration for each individual lens that was decentred by 0.5 mm. Coma showed the

greatest change as a function of decentration, in particular for L4 (0.036 µm), followed

by spherical aberration. Defocus and astigmatism showed changes that were less than

0.007 µm for individually decentred lenses.

Figure 6.9: Absolute change in performance for the terms defocus, astigmatism, coma and spherical aberration, when the individual lenses were decentred by ±0.5 mm.

Tilted Optical Components:

Figure 6.10 shows the impact of 1° lens tilt on the performance of the system.

Figure 6.10: Absolute change in performance for the terms of defocus, astigmatism, coma and spherical aberration, when the individual lenses were tilted by 1°.

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

L1 L2 L3 L4

Change in

microns

Decentration (in mm)

Defocus Astigmatism Coma Spherical Aberration

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

L1 L2 L3 L4

Change in microns

Tilt (in °)



209

Overall, it shows that lens tilt has the smallest impact on the optical performance of the

system (<0.0074 µm). The greatest change in performance occurred for the term coma

for L2, L3 and L4.

6.3.1.3.2 Monte‐Carlo Simulation

By means of the Monte Carlo simulation, the occurrence of all perturbations was

simulated simultaneously and the estimated change on the performance of the optical

system was assessed. Table 6.1 shows the change in performance for the individual

terms, i.e. defocus, astigmatism, coma and spherical aberration, if all perturbations were

to occur simultaneously within the specified tolerance range of ± 0.5 mm for axial lens

misalignment, ± 0.5 mm for decentred lenses and ± 1° for tilted lenses.

For the defocus term, the estimated change in performance was 0.077 µm (~0.06D). If

the tolerance criterion for the axial misalignment of L1‐L2 and L3‐L4 was tightened by a

factor of two, that is ± 0.25 mm, the estimated change in performance (defocus) would

improve by 0.02 µm.

Table 6.1: Results of the ZEMAX Monte Carlo simulation shown as a change in merit function degradation.

Tolerance values were set to ±0.5 mm for axial misalignment, ±0.5 mm for decentred optical components and ±1° for tilted optical components. In total, 500 Monte Carlo Files (MCF) were generated.


(in µm)

Estimated Change in performance based upon RSS 0.07697 0.01596 0.04561 0.00831

Change in performance for the best performing MCF 0.00003 0.00000 0.00005 0.00000

Change in performance for the worst performing MCF 0.09474 0.02596 0.06621 0.00000

Mean change in performance of all 500 MCFs 0.02806 0.00382 0.01672 0.05127

StDev of the change in performance of all 500 MCFs 0.01952 0.00346 0.01205 0.01224

98% < Performance 0.07578 0.01339 0.00461 0.01067

90% < Performance 0.05514 0.00803 0.03285 0.03975

80% < Performance 0.04419 0.00597 0.02665 0.02879

50% < Performance 0.02532 0.00305 0.01485 0.02077

20% < Performance 0.00946 0.00098 0.00577 0.00911


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6.3.1.4 Discussion

Prior to manufacture of the instrument, the tolerance analysis presented here was

performed for the EM’s reflection path. The tolerance analysis showed that the distances

between L1 and L2, as well as between L3 and L4, are the most sensitive parameters with

respect to the change in performance (defocus). This result was anticipated, as the

change of these distances reflects the typical set‐up of a Badal system, which has been

used in many optical systems for the compensation of defocus (the participant’s

spherical refractive error). Whereas, Atchison et al.,31 for example, compensated for the

refractive error by moving the eye together with L1 (changing the distance between L1

and L2), other systems, such as the one by Llorente et al.216 use focussing blocks to

increase or decrease this distance and hence to compensate for defocus. For the EM,

stationary components are used (no defocus compensation) and thus, axial lens

misalignment is the most sensitive perturbation. The perturbation with the next greatest

impact on the performance of the system is lens decentration. Specifically, the term

coma was affected most by decentration, in particular for L4. Lens tilt caused the

smallest impact on the system’s performance, with coma showing again the greatest

change.

The Monte Carlo simulation showed that on the basis of the initial tolerance criteria, the

defocus term was most affected by the aggregated effect of all tolerances, followed by

coma, then astigmatism and lastly spherical aberration. It also showed that the

estimated overall performance of defocus was 0.077 µm. A further improvement of 0.02

µm can be achieved when tightening the most critical tolerances by a factor of two.

Monte Carlo files such as those generated during the Monte Carlo simulation, were also

used for the subsequent assessment of change in performance during the manufacturing

process, when specific combinations of perturbations had to be assessed individually.

The tolerance analysis presented here assessed the assembly accuracy required for the

individual optical components in the EM’s reflection path. It should be noted that this

analysis was performed under the assumption that there are no manufacturing errors in

lenses or the Hartmann‐Shack sensor itself. Nevertheless, even after good calibration of


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the Hartmann‐Shack sensor, measurement accuracy can be affected by its manufacturing

and alignment tolerances.217, 218

6.3.2 Instrument Components

The following section lists the main instrument components and features chosen for

each optical path in the EM. These components were either sourced from external

suppliers or manufactured in‐house at the Brien Holden Vision Institute by Colm Dolphin.

6.3.2.1 Deflection System

Mirrors

All but two of the mirrors used in the deflection system are aluminium coated, front

surface mirrors with a surface flatness of 1/10 λ accuracy and a reflectance of

approximately 85% at a wavelength of 830 nm. These 32 front surface mirrors are quartz

coated to increase their hardness and to protect the aluminium layer. The majority of

the mirrors had to be custom shaped to fit into the EM’s mechanical design constraints.

The other two mirrors in the deflection system are the central mirror (M1) closest to the

eye, which is the hot mirror (multi‐layer dielectric coating, >95% reflectance, 4 λ

accuracy) used for the insertion of the fixation path, and the scanning mirror (protected

silver coating, >94% reflectance, 1/4 λ accuracy) that is required for the peripheral

refraction scan.

6.3.2.2 Illumination Path

Single Axis Galvanometer Scanner and Light Source

By use of the previously selected single axis galvanometer scanner (Section 5.2.1.3), the

EM scans the narrow SLD beam (wavelength 830nm, Section 5.2.1.1) sequentially and

rapidly across the retina. At each of the 11 retinal locations, the duration of the single

spot exposure is 0.065 seconds. With respect to safe exposure limits, Chapter 5

previously addressed the different sub‐exposures (spot, line, circle and scanning), which

were to be assessed for the on‐and off‐axis ring‐scan illumination. For the updated

wavefront sensing EM, only one relevant exposure had to be assessed; now being a small

spot exposure (Section 5.2.2).


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From Section 5.2.2.2.1 it is known that a small source exposure corresponds to a retinal

spot diameter of 25 μm (visual angle αmin = 1.5 mrad). According to the previous

calculations done in ZEMAX (Section 5.2.2.4.2), the distance between each retinal spot is

greater than the distance of 1.7 mm (visual angle α = 100 mrad), which according to ANSI

standards is the minimum distance where each retinal spot can be considered as an

individual exposure. Consequently, the performance of a peripheral refraction scan using

the wavefront sensing EM can be considered as an illumination of 11 independent retinal

spots, rather than a scan illumination.

With respect to safely repeating measurements, the maximum permissible exposures for

single and repetitive measurements were calculated for small source exposures

according to the ANSI rules (Section 5.2.2.2.1). The EM uses a power level of 0.90mW

with an exposure duration of 0.065 seconds per retinal location. According to Table 6.2,

this would allow 50 repeated measurements per day. In total, the peripheral refraction

scan with the EM takes only 0.75 seconds.

Table 6.2: Maximum permissible exposure limits (mW) for the EyeMapper.

Calculations were performed for a wavelength of 830 nm, an exposed retinal area that corresponds to a small source exposure (visual angle αmin= 1.5 mrad) and a single spot exposure duration of 0.065 seconds.

Number of Measurements per Day

1 2 5 10 20 30 50

Maximum Permissible Exposure Limits in mW

2.50 2.10 1.67 1.40 1.18 1.07 0.94

Shutter

A spring loaded mechanical shutter (Section 5.2.2.4.3) in the EM provides an additional

control for the exposure duration to the eye. This shutter blocks the light beam (Figure

6.3) until a solenoid pulls the shutter open briefly while the refraction scan is performed.

6.3.2.3 Reflection Path

HASO wavefront sensor

The wavefront sensor chosen for the EyeMapper is the HASOTM – 32 eye (Imagine Eyes,

France). This sensor provides high resolution and a wide dynamic range. Its effective


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pupil diameter is 3.65 mm and 1280 sub‐apertures are located in a monolithic 40 × 32

microlens array. The focal length of each lenslet is 2.30 mm.

Lenses and Polarising Optics

The EM comprises lenses with anti‐reflection coating to permit greatest transmission of

light and to avoid unwanted reflections occurring inside the instrument. Moreover,

polarising optics, such as a polarising cube beam splitter (PCBS) and a polariser were

used to reduce unwanted ocular reflections from cornea and crystalline lens surfaces

(Section 5.3.1).

6.3.2.4 Fixation Path

Fixation Target and Translation Stage

The EM’s distance fixation target features a green illuminated cross on black

background, which similarly to the target used in the COAS aberrometer, promotes

distance viewing. The target is mounted on a fast and precise linear translation stage

(Physik Instrumente (PI) GmbH & Co. KG, M‐122.2DD Precision Micro Translation Stage)

with a travel range of 25 mm and a maximum velocity of 20 mm/s. The 25 mm linear

movement of the fixation target can stimulate accommodation in the range from 0.00D

to 5.00D.

6.3.2.5 Pupil Imaging Path

Pellicle Beam Splitter

The pellicle beam splitter (PBS) selected for the reflection path transmits 92% of light

towards the HASO wavefront sensor and reflects 8% of light, which is used for the pupil

imaging path (Edmunds Optics, NT 39‐478, 8R/92T). The advantage of the pellicle beam

splitter is its thin membrane, which avoids both ghost images from second surface

reflections and changes in optical path lengths.

Pupil Imaging CCD and Single Axis Galvanometer Scanner for Pupil Alignment

The previously selected Sony CCD sensor ICX445 (Section 5.3.2) is the CCD sensor used to

capture the images from the pupil. For the pupil alignment task, the galvanometer


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scanner’s frame rate is set to 50 scans per second in order to permit simultaneous

alignment of the pupil for all three observation angles.

Pupil Illuminating LEDs

To permit the alignment of the pupil from all three observation angles (central, 30° nasal

and 30° temporal) the pupil area is illuminated with small infrared LEDs. These LEDs are

attached to the outside of the instrument cover in front of the eye and only emit light

during the pupil alignment procedure. Once the pupil is aligned and the peripheral

refraction scan is initiated, the LEDs switch off and thus do not interfere with the


6.3.2.6 Other Instrument Parts

Aluminium Alloy Instrument Parts

Following the development of the mechanical instrument design in SolidWorks and the

performance of the tolerance analysis in ZEMAX, the individual instrument parts (e.g.

mounts, base plate etc.) were drawn for production by Darrin Falk. The alloy parts were

manufactured in the workshop at the Brien Holden Vision Institute by Colm Dolphin.

Figure 6.11 presents a set of pictures taken during the manufacture process of these

parts.

Figure 6.11‐A shows the manufacture of the mirror holding bridge and Figure 6.11‐B

illustrates some components for the deflection system. A majority of the manufactured

alloy parts is shown in Figure 6.11‐C. These were assembled on an available OCT

instrument body (Zeiss OCT‐2, Figure 6.11‐D). Figure 6.11‐D shows the EM base plate

with all its assembled parts adjusted at the 90° position, whilst Figure 6.11‐E shows the

base plate position of the EM at the 180° position, the latter being the position used for

the measurement of the horizontal visual field meridian. Following the manufacture of

all parts, the parts were anodised in black colour and re‐assembled (Figure 6.11‐F).

Having all alloy parts anodised in black minimises unwanted reflections which could

interfere with the refraction measurements.

Alignment and Calibration Tools

For the alignment of lenses and mirrors, several alignment and calibration tools were

used.


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Figure 6.11: Pictures taken during the manufacturing process of the EyeMapper.

(refer to text for details)

One such tool was a single‐pass reduced model eye, which consists of a 3 mm pupil

aperture, a biconvex lens and an extended flat retina. This was mounted on a rotary axis

A B

C D

E F


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to permit alignment and calibration of the components along the 11 configurations. The

pivot of the model eye was located at the entrance pupil position, which was aligned

conjugate to the pivot of the scanning mirror and to the Hartmann‐Shack sensor. An LED

placed at the centre of the model eye’s retina was used to generate a ‘reflection beam’

(out‐of‐the‐eye single‐pass).

Instrument Cover

Lastly, an instrument cover was custom‐built to protect the instrument’s delicate

components against dust, ambient light, and accidental knocks, and to give it the

appearance of a clinical instrument.

6.3.3 The EyeMapper

In Figure 6.12, pictures of the final EM instrument without (A) and with (B) cover are

shown. Figure 6.13 shows a picture of the EM’s user interface. The user interface

consists of the three pupil alignment images, which show the pupil from the three

observation angles (central, 30° nasal and 30° temporal). Each image has purple marks

superimposed on the pupil to assist with the alignment. The user interface also displays

a graph in the bottom left which can either be used to plot the refractive vector

components, M, J180 and J45, or the sphere and cylinder values, or any individual higher

order aberrations.

The table above the graph lists the values of the sphero‐cylindrical refraction output

measured at each visual field position. Moreover, for each of the 11 measurements, the

Hartmann‐Shack raw images, and optionally the slopes, irradiance and phase images can

be presented. A double click on any of the 11 images enlarges the wavefront map for the

selected visual field angle and the individual aberrations can be assessed.

The user‐interface also displays minor and major pupil diameters, which represent the

smallest and the largest of the 11 pupil axes, as well as a user‐defined pupil diameter.

Either pupil diameter can be selected for the calculation of the aberrations, which

transforms all of the different peripheral elliptical pupil shapes into the one selected

circular pupil diameter.


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Figure 6.12: The EyeMapper instrument without (A) and with cover (B).

A B


218

Figure 6.13: The user‐interface of the EyeMapper developed by Darrin Falk.

The pupil is viewed simultaneously from three observation angles (central, 30° nasal and 30° temporal) and is aligned using the purple marks superimposed. The graph in the bottom left shows an example of a peripheral refraction profile plotted for M (red), J180 (green) and J45 (blue). In addition, the Hartmann‐Shack raw images (as well as slopes, irradiance and phase images) for each of the 11 measurements are shown in the bottom right.


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It should be noted that in addition to transforming the ‘elliptical’ pupil into a small, large

or user‐defined circular apertures, another approach that has previously been suggested,

is the stretching of the ‘elliptical’ pupil into a circular aperture. Lundström et al.125

compared the currently used representations on the quantification for peripheral

aberrations. Whereas the representation of the stretched ellipse shows advantages

when calculating the RMS error, it encounters drawbacks for the interpretation of the

individual Zernike coefficients. As varying degrees of pupil stretching is required when

analysing different peripheral angles, no direct comparison between those coefficients

can be made. Conversely, the use of the non‐stretched (small, large or user‐defined)

circular aperture has the advantage that it can be used to compare the coefficients

between different peripheral angles. However, when determining the RMS value using

the circular aperture, wavefront information would either be cut off or extrapolated.

Overall, the investigation by Lundström et al.125 emphasised that studies using different

representations for the quantification of peripheral aberrations cannot be directly

compared, as the individual Zernike coefficients will differ and the trend of the

coefficients as a function of peripheral angle is different for the three representations.

As the EM’s primary aim is to measure the sphero‐cylindrical refraction output as a

function of visual field angle, direct comparison of the individual second order Zernike

coefficients is required for the different measurement angles and hence, the software in

the EM was developed to permit the transformation from the ‘elliptical’ pupil into a

small, large and user defined circular aperture.

6.4 Instrument Validation

The aim of this section was to validate the EM, by assessing its repeatability,

reproducibility and accuracy. For this, measurements were performed on a peripheral

refraction model eye and on ten human eyes.

6.4.1 Methods

6.4.1.1 Peripheral Refraction Model Eye

For the validation of the EM, a peripheral refraction model eye was developed, which

comprises a combination of stationary, translational and rotational components. The

optical design (ZEMAX) and a picture of the model eye are shown in Figure 6.14. The


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stationary optical components comprise two lenses (f’=40 mm and f’=60 mm, Edmunds

Optics) and the pupil (5 mm), which in a simplified manner, represent the optics of the

cornea, pupil and crystalline lens. A retinal arm, with a translational retinal surface, is

mounted on a rotary axis with its pivot closely behind L2. While the translational retina

movement permits the adjustment for different refractive states, the rotational

movement permits the alignment for the different peripheral visual field angles. This

model eye permits peripheral refraction measurements up to ±50° and was used to

assess accuracy and to verify the detection of a wide range of spherical and astigmatic

errors as required when measuring the peripheral optics of the eye.

Figure 6.14: Peripheral Refraction Model Eye.

LEFT: Optical design layout of the peripheral refraction model eye; RIGHT: The physical peripheral refraction model eye.

Firstly, the model eye was adjusted for zero defocus . A template on top of the model

eye’s base plate was used to align the retinal arm at angular positions corresponding to

the visual field angles to be measured, i.e. ranging from ‐50° to +50° in 10° steps. The

model eye was then placed in front of the EyeMapper and measurements were taken

sequentially by moving the retinal arm along each of the 11 angular retinal positions.

This procedure was repeated five times. Refraction data were retrieved for a pupil

analysis diameter of 3.5 mm, which enclosed the minor elliptical pupil axis at 50°. To

assess instrument accuracy, a well‐calibrated commercially available aberrometer, the

COAS (Complete Ophthalmic Analysis System COAS, high resolution) was used as control

instrument (pupil analyis diameter was set to 3.5 mm). Moreover, an open‐view

0°

10°

20°

30°

40°

50°Visual Field Angles

L1L2

Pupil

Retina Pivot


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autorefractor (the Shin‐Nippon NVision K5001 (Shin Nippon)) was chosen for additional

comparison. When measuring the model eye’s peripheral refraction profile with these

conventional instruments, the model eye required alignment not only for the 11

different retinal positions, but also for the 11 different visual field angles. Measurements

were performed in sequential angular steps by re‐aligning both positions (visual field

angle and retinal angle) and the procedure of measuring the peripheral refraction profile

was repeated five times. Measurements with the autorefractor were limited to visual

field angles of ±10°, ±20° and ±30°. This was due to the fact that large reflections did not

permit on‐axis measurements and that the limited cylinder measurement range provided

results only up to 30°.

6.4.1.2 Human Eyes

6.4.1.2.1 Participants

Besides testing the peripheral refraction model eye for instrument validation, peripheral

refraction measurements were also performed on 10 participants, for which the study

protocol was approved by the institutional research and ethics commitee (VIHEC,

Syndey). To investigate the feasability of measuring eyes of various central refractive

errors and different peripheral refraction profiles, the participants recruited were four

hyperopes (M≥0.50D), four myopes (M≤‐0.50D) and two emmetropes (‐0.50D<M>0.50D).

Study demographics are summarised in Table 6.3.

Table 6.3: Study demographics

Mean Age

(years ± SD)

Mean Spherical Equivalent

(D ± SD)

Emmetropes (n=2) 38.0 ± 18.4 ‐0.08 ± 0.22

Myopes (n=4) 28.5 ± 1.0 ‐4.98 ± 2.57

Hyperopes (n=4) 56.0 ± 7.5 2.48 ± 1.60

In addition to determining the participants baseline peripheral refraction profiles, the

profiles of the same participants’ eyes were measured when wearing commercially

available contact lenses. The lenses selected were two single vision contact lenses

(power ‐3.00D); Acuvue 2 (Johnson Johnson) and Focus Night and Day (FND, CIBA

VISION), which feature opposed power profiles across the optic zone. Whereas the


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Acuvue 2 lens exhibits an increase in negative power towards the periphery, the FND

lens increases in positive power.219 The prime aim of including contact lens wear into this

study protocol was to investigate the EM’s capability of being able to differentiate

peripheral refraction profiles with different contact lenses on eye and to assess

measurement repeatability when compared to the baseline measurements. Refraction

measurements were always performed on the participants’ right eyes. The left eyes were

occluded during the measurement procedure in order to maintain stable fixation and

accommodation. To assess instrument reproducibility, the right eye of one participant

was measured on a different occasion by a different operator both with and without

contact lenses.

6.4.1.2.2 Instrumentation, Set‐up and Procedure

Central and peripheral refraction measurements along the horizontal visual field

meridian were performed using three instruments: the EM, the COAS and the Shin

Nippon. Each of these instruments required a slightly different set‐up and alignment

procedure to permit the measurement of the peripheral optics of the eye.

Due to its dedicated purpose and optical design, the set‐up and alignment procedure

with the EM was fastest, as it only required the alignment of the participant's pupil

(simultaneous alignment of the central and two peripheral pupil images) with the

instrument axis. Conversely, peripheral refraction measurements with the Shin‐Nippon

autorefractor and the COAS aberrometer required further modifications and numerous

re‐alignments by both participants and operators. Using the Shin‐Nippon autorefractor,

the same set‐up and alignment procedure as described in detail previously (Section

3.2.1.2) were followed. Refraction measurements were extended to horizontal visual

field angles ranging from ‐40° to +40° in 10° steps. Whilst measurement of this angular

visual field range could be achieved using the autorefractor's open‐view design, this set‐

up was not implementable when using the closed‐view COAS aberrometer. Instead, a

custom‐made peripheral fixation device was developed for the COAS to present

peripheral fixation targets for the 30° nasal and 30° temporal visual field angles (Figure

6.15). To provide targets that are presented at distance, high power focusing lenses were

used in the peripheral fixation device and the targets were mounted on a common block

which could be moved to adjust (de‐)focus.


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The measurement of the horizontal peripheral refraction profile, consisting of either 11

(EyeMapper), 9 (Shin Nippon) or 3 (COAS) field positions, was performed three times.

Figure 6.15: Custom‐made peripheral fixation device for the COAS.

For all participants, the above mentioned measurements were performed along the

horizontal visual field meridian. In addition, in one out of the ten participants, the EM’s

rotational feature was tested. For this, the participant’s peripheral refraction profile was

measured along the seven visual field meridians, ranging from 0° to 90° in 15° steps. The

measurement of each visual field meridian was repeated three times.

6.4.2 Results

6.4.2.1 Peripheral Refraction: Model Eye

Figure 6.16 shows the model eye’s peripheral refraction profile for M, J180 and J45 as

measured with the EM, the COAS and the Shin Nippon. The overall agreement of the

refractive vector components between the three instruments was good. On average, the

measurements with the autorefractor were about 0.30D more myopic when compared to

the EM and the COAS. For the common visual field angle data (i.e. ±10°, ±20° and ±30°),

J180 agreed well between the three instruments. The greatest differences in J180 between

the COAS and the EM were found at the ±50° angles. Some variation was noted in the

EM data for J45 at the +30°, +40° and ±50° angles. The raw data indicated that this

difference was related to the combination of large magnitude in cylinder and a small axis

deviation of 1‐2° from the 90° cylinder axis. Whereas standard deviations for M and J180


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were smallest for the EM when compared to the other two instruments, for J45 they were

greatest with the EM.

Figure 6.16: Peripheral refraction profiles of the model eye when measurements were performed with the EyeMapper, the COAS aberrometer and the Shin‐Nippon NVision K5001 autorefractor.

6.4.2.2 Peripheral Refraction: Human Eyes

6.4.2.2.1 Peripheral Refraction Profiles

Figure 6.17, Figure 6.18 and Figure 6.19 show the refractive vector components M, J180

and J45 plotted as a function of visual field angle for all three instruments, the EM, the

COAS and the Shin‐Nippon. Data are plotted for the three refractive groups when

measurements were performed at baseline and when wearing contact lenses on eye.

The baseline data plotted in Figure 6.17 show that the mean peripheral refraction

profiles as measured with all three instruments exhibited relatively more myopia in the

periphery for the emmetropic and the hyperopic group. Conversely, the myopic group

exhibited a more hyperopic shift in the periphery when measurements were performed

with the Shin Nippon and the EyeMapper. For the COAS, peripheral measurements

obtained in the hyperopic group also showed a relative hyperopic shift in the temporal

visual field, but a more myopic shift in the nasal visual field.

‐10

‐8

‐6

‐4

‐2

0

2

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

Power in D

Visual Field Angles in °

M (COAS) J180 (COAS) J45 (COAS)

M (EyeMapper) J180 (EyeMapper) J45 (EyeMapper)

M (Shin‐Nippon) J180 (Shin Nippon) J45 (Shin Nippon)


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Emmetropes (n=2) Myopes (n=4) Hyperopes (n=4)

Figure 6.17: The refractive vector component M (in D) plotted as a function of visual field angle when measured with the EyeMapper, the COAS aberrometer and the Shin Nippon NVision K5001 autorefractor.

Mean data for the three refractive groups are shown for baseline measurements (top, absolute values) and measurements with the contact lenses on eye (bottom, relative values).

‐6

‐4

‐2

0

2

4

6

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

M (in D)


EyeMapper ‐ BL COAS ‐ BL Shin‐Nippon ‐ BL

Temporal Nasal

‐6

‐4

‐2

0

2

4

6

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

M (in D)



Temporal Nasal

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4

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M (in D)



Temporal Nasal

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0

1

2

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

RPRE of M (in D)


EyeMapper ‐ FND COAS ‐ FND Shin‐Nippon ‐ FND

EyeMapper ‐Acuvue 2 COAS ‐Acuvue 2 Shin‐Nippon ‐Acuvue 2

Temporal Nasal

‐2

‐1

0

1

2

3

4

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‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

RPRE of M

(in D)




Temporal Nasal

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‐3

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‐1

0

1

2

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

RPRE of M

(in D)




Temporal Nasal


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Figure 6.18: The refractive vector component J180 (in D) plotted as a function of visual field angle when measured with the EyeMapper, the COAS aberrometer and the Shin Nippon NVision K5001 autorefractor.


‐8

‐6

‐4

‐2

0

2

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

J 180(in D)



Temporal Nasal

‐8

‐6

‐4

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0

2

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

J 180(in D)



Temporal Nasal

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0

2

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J 180(in D)



Temporal Nasal

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0

2

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RPRE of J 180(in D)




Temporal Nasal

‐8

‐6

‐4

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0

2

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

RPRE of J 180(in D)




Temporal Nasal

‐8

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‐4

‐2

0

2

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

RPRE of J 180(in D)




Temporal Nasal


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Figure 6.19: The refractive vector component J45 (in D) plotted as a function of visual field angle when measured with the EyeMapper, the COAS aberrometer and the Shin Nippon NVision K5001 autorefractor.


‐4

‐2

0

2

4

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

J 45(in D)



Temporal Nasal

‐4

‐2

0

2

4

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J 45(in D)



Temporal Nasal

‐4

‐2

0

2

4

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

J 45(in D)



Temporal Nasal

‐4

‐2

0

2

4

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RPRE of J

45(in D)




Temporal Nasal

‐4

‐2

0

2

4

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

RPRE of J

45(in D)




Temporal Nasal

‐4

‐2

0

2

4

‐60 ‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50 60

RPRE of J

45(in D)




Temporal Nasal


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For the myopic group, the EM measured more plus (on‐axis 0.41D) when compared to

the COAS and more minus (on‐axis 0.52D) when compared to the Shin Nippon. For on‐

axis measurements, the same trend but with smaller differences was found in the

emmetropic group, where the shift of the COAS was 0.26D more plus and the shift of the

Shin Nippon was 0.13D more minus when compared to the EM. For the hyperopic group,

the EyeMapper measured more minus when compared to the COAS (0.20D) and the Shin

Nippon (0.31D).

In general, the baseline peripheral refraction profiles obtained with the three

instruments were in agreement. However, there were some obvious differences in M at

nasal 30° in the myopic group, where the COAS measured more minus than the other

two instruments (1.09D when compared to the EM, and 1.57D when compared to the

Shin Nippon) and at nasal 40° in the hyperopic group, where the EM measured more

minus (1.09D) when compared to the Shin Nippon.

In addition, Figure 6.17 shows the relative peripheral refraction profiles measured with

the two contact lenses on eye. For all refractive groups and for all three instruments a

difference in peripheral refraction profiles between the two lens types was detected.

Measurements with the FND lens on eye always showed a more myopic shift, when

compared to the measurements with the Acuvue 2 lens one eye. When compared to the

measurements obtained with the EM, the Shin Nippon measured a more hyperopic

peripheral refraction profile.

Figure 6.18 shows the peripheral refraction profiles for the refractive vector component

J180. All three instruments produced similar profiles for the three refractive groups,

which demonstrated the typical nasal‐temporal asymmetry of astigmatism across the

visual field. The hyperopic group showed the greatest peripheral astigmatism, followed

by the emmetropic and then the myopic group. The greatest difference in J180 (0.93D)

was found in the 40° nasal visual field for the hyperopic group between the Shin Nippon

and the EM.

The peripheral refraction profiles obtained with either contact lens type on eye showed

a similar trend for J180 as previously seen in M. Figure 6.18 demonstrates that in the


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emmetropic and myopic group, measurements with the FND lens on eye produced

greater peripheral J180 when compared to the measurements with the Acuvue 2 lens on

eye. A smaller difference between the two lens types was found in the hyperopic group

when measurements were performed using the EM. For all refractive groups, with and

without contact lenses on eye, the Shin Nippon measured less peripheral astigmatism

when compared to the EM.

The peripheral refraction profiles for the refractive vector component J45 are shown in

Figure 6.19. Apart from some fluctuations across the visual field, the baseline

measurements obtained from the three instruments compared well with each other.

Greatest fluctuations were found in the hyperopic group, the group which had the

greatest peripheral astigmatism (J180). The difference in relative J45 between the

peripheral refraction profiles obtained with the two contact lens types was small when

measured with all three instruments.

6.4.2.2.2 Repeatability

Figure 6.20 shows the coefficients of repeatability (2.77 × within participant SD, three

repeats) plotted for M, J180 and J45, for all three instruments, for all visual field angles

and for the with‐ and without‐contact lens condition. In general, it can be seen that

independent of the instrument used for the measurements, the coefficients were always

lower when measurements were performed without contact lenses on the eye.

Repeatability generally decreased with increase in peripheral field angle.

For the refractive vector components M and J180, the coefficients of repeatability were

larger for measurements obtained with the Shin Nippon when compared to those

obtained with the EM. This was the case for measurements performed with and without

contact lenses on the eye. For some visual field positions (e.g. for M at temporal and

nasal 40°, without contact lens), the coefficients reached twice those for the Shin Nippon

when compared to the EM. For most, but not all visual field positions, the coefficients of

repeatability for J45 were also larger for the Shin Nippon when compared to the EM.

The coefficients of repeatability for the three visual field positions (0° and ±30°)

measured with the COAS compared to those to the EM, obtained without contact lenses

on eye were very similar. However, in relation to the “with contact lens” measurements,


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the coefficients for M were larger for the COAS when compared to the EM and the

coefficients for J180 and J45 were larger for the EM when compared to the COAS.

Without Contact Lens on Eye With Contact Lens on Eye

Coefficient of

Repeatability for M

Coefficient of

Repeatability for J 1

80

Coefficient of

Repeatability for J 4

5

Figure 6.20: Coefficients of repeatability for M, J180 and J45 (in D).

For each visual field angle and each instrument, data were plotted for measurements performed without and with contact lenses on eye.

6.4.2.2.3 Reproducibility

Figure 6.21 shows the peripheral refraction profile for M of one participant as measured

with the EM by two different operators at two different occasions.

The participant’s distinct peripheral refraction profile was noticeable for all conditions,

with and without contact lens wear and when measurements were performed by

operator 1 (visit 1) and operator 2 (visit 2). On average, measurements performed by

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

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Visual Field Angle (°)

EyeMapper COAS Shin Nippon

Temporal NasalTemporal NasalTemporal Nasal

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50



Temporal NasalTemporal NasalTemporal Nasal

0.00

0.20

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0.60

0.80

1.00

1.20

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Temporal NasalTemporal NasalTemporal NasalTemporal Nasal

0.00

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0.80

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Temporal NasalTemporal NasalTemporal NasalTemporal Nasal

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0.60

0.80

1.00

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Temporal NasalTemporal NasalTemporal NasalTemporal NasalTemporal Nasal

0.00

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0.80

1.00

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1.40

1.60

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50



Temporal NasalTemporal NasalTemporal NasalTemporal NasalTemporal Nasal


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operator 1 were slightly more myopic when compared to measurements performed by

operator 2 (average difference 0.17D at baseline, 0.15D with FND and 0.04D with Acuvue

2) with standard deviations of the repeats being similar for each operator [operator 1:

±0.24D (BL), ±0.24D (FND), ±0.25D (Acuvue 2) and for operator 2: ±0.22D (BL), ±0.24D

(FND), ±0.41D (Acuvue 2)].

Figure 6.21: The peripheral refraction profile for M measured by two independent operators on two different occasions.

Data are shown for one participant (mean of three repeats).

Table 6.4 provides a summary of the coefficients of reproducibility (2.77 × within

operator SD) for M, J180 and J45. Overall, reproducibility for M and J180 was best for

measurements performed with the Acuvue 2 lens, followed by the measurements

performed at baseline, and then the FND lens. Reproducibility for J45 was best at

baseline, followed by the FND lens and then Acuvue 2.

Table 6.4: Summary of the coefficients of reproducibility (in D).

Coefficient of Reproducibility

Baseline

M 1.12

J180 0.73

J45 0.37

Acuvue 2

M 0.86

J180 0.72

J45 0.57

FND

M 1.41

J180 0.73

J45 0.45

‐3

‐2

‐1

0

1

2

3

4

5

6

7

8

‐50 ‐40 ‐30 ‐20 ‐10 0 10 20 30 40 50

M in D

Visual Field Angle

Operator 1 ‐ BL Operator 1 ‐Acuvue 2 Operator 1 ‐Night & Day

Operator 2 ‐ BL Operator 2 ‐Acuvue 2 Operator 2 ‐Night & Day

Temporal Nasal


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6.4.2.2.4 Refraction Map

Figure 6.22 shows the relative peripheral refraction data of the right eye of one

participant measured with the EM and plotted as a function of visual field meridian and

visual field angle. The size of the red circles represents the magnitude of the spherical

error across the visual field, which was more positive in the temporal and superior visual

field when compared to the nasal and inferior visual field. The length of the blue dotted

arrow indicates the magnitude of the minus‐cylinder and the direction of the arrow

represents the direction of the minus‐cylinder axis.

Figure 6.22: The relative refraction data measured with the EM and plotted as function of visual field meridian and visual field angle (n=1).

The size of the red half circles represents the magnitude of the spherical error. The solid red line indicates positive spherical error and the dotted red line indicates negative spherical error. The astigmatic error is represented by the blue dotted arrow. Size of the arrow indicates the magnitude of the minus‐cylinder and its direction indicates the minus‐cylinder axis. Data are plotted as mean values (3 repeats).


233

It can be seen that the magnitude in astigmatism increases towards the periphery, with

higher astigmatism found in the nasal and inferior visual field when compared to the

temporal and superior visual field. The direction of the minus‐cylinder axis is

approximately orthogonal to the measured visual field meridian, with slight deviations in

the nasal visual field. Five out of seventy measured visual field positions could not be

plotted for this participant, due to some eye lid obstructions of the pupil.

6.4.3 Discussion

6.4.3.1 Accuracy: Model Eye

The overall agreement between the model eye’s peripheral refraction profile as

measured with all three instruments was good, with the COAS and the EM providing the

most comparable results.

The small myopic shift measured with the Shin Nippon, when compared to the EM and

the COAS aberrometer, could be due to the different operation principles (ring‐

autorefraction principle versus aberrometry) as well as the difference in pupil size

dependency. Whereas refraction (aberration) data from the EM and the COAS were

retrieved from a wavefront exiting the eye which was analysed using a 3.5 mm pupil

analysis diameter, the Shin Nippon autorefractor uses a fixed size ring (2.3 mm) to

project a ring image onto the retina, and based on its reflected size and shape the

sphero‐cylindrical refractive error is determined.

With respect to M and J180, instrument repeatability was shown to be best for the EM

when compared to the other two instruments. It is possible that repeatability results

were slightly affected by the different model eye alignment requirements. Whereas for

the EM, the model eye was simply placed in front of the instrument and the retinal arm

was sequentially realigned to measure the peripheral refraction profile, for the other

two instruments the model eye was also rotated to permit alignment for the different

visual field angles (the equivalent of the ‘eye or head‐turn’ by participants). This

additional alignment requirement may have led to slightly less‐repeatable results when

measurements were performed with the COAS and the Shin Nippon. Although, the COAS

and the EM were in good accordance with each other up to a visual field angle of ±40°,

there was a noticeable difference for J180 at ±50°. It is possible that this is due to the EM


234

using a more advanced wavefront sensor featuring higher resolution/sampling and wider

dynamic range than the COAS. Although, a ray‐tracing approach was attempted to

calculate the theoretical peripheral refraction profiles for the model eye by use of the

previous equations in ZEMAX (Section 4.2.1.2), the profiles for M and J180 were

increasingly more positive as field angle increased when compared to the profiles

measured with the three instruments. This difference between the results obtained for

the analytical and physical model eyes requires further investigation. The COAS

instrument is generally considered the reference standard for central ocular

aberrometry.165 On the basis that the model eye data obtained from the EM were in

good agreement and showed even better repeatability when compared to the COAS

measurements, it was demonstrated that the EM is an accurate and repeatable

instrument for central and peripheral refraction measurements.

6.4.3.2 Peripheral Refraction Profiles and Repeatability: Human Eyes

As scattering, dispersion and light efficiency differ between human eyes and model eyes,

the second part of this validation study aimed to also perform measurements in human

eyes. It should be noted however, that when measuring human eyes, several other

inherent factors can affect measurements which may be assessed in more detail in

future. These factors include, for example, the impact of: lead and lag of

accommodation, clarity in optical media, the size and location of the blind spot area,

fluctuating fixation, pupil size, eye lid shape etc.

The first aim of the current validation study on human eyes was to assess the

measurements and repeatability of peripheral refraction profiles obtained with and

without contact lenses on eye, for hyperopic, emmetropic and myopic eyes when using

the three instruments, the EM, the COAS and the Shin Nippon.

Due to the COAS and the Shin Nippon being dedicated on‐axis instruments, some

modifications to the set‐up and alignment procedure were required to permit

measurement of the peripheral optics of the eye. Certain instrument boundaries did not

permit the number of visual field angle measurements possible with the EM. While the

COAS could only measure two peripheral positions (±30°), Shin Nippon measurements

were possible up to ±40°. Due to some missing data points for the Shin Nippon and the

COAS, the peripheral refraction profiles as obtained with the EM could not be compared


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entirely. Perhaps a different peripheral refraction set‐up for the COAS, such as used by

Mathur et al.123 or by Baskaran et al.130 (COAS HD‐VR) could be used in a future

validation study in order to permit the measurement and comparison of more peripheral

visual field angles.

All peripheral refraction profiles were assessed in terms of refractive power vectors,

which overall showed good agreement between the measurements obtained from the

three instruments. Some on‐axis differences were found for M at baseline for the

different instruments and refractive groups. It was shown that for both the myopic and

the emmetropic group, the COAS measured more minus when compared to the EM, and

the EM measured more minus when compared to the Shin Nippon. This effect was

greater for the younger myopic group when compared to the young emmetropic group,

but this trend was not seen in the older hyperopic group. It is reasonable to suggest that

this difference was caused by the impact of accommodation and instrument myopia in

the younger groups when measurements were performed using the EM and the COAS.

Whereas the Shin Nippon is an open‐view autorefractor, the EM and the COAS are

closed‐view instruments with a working distance of 100 mm and 50 mm, respectively.

This suggests that the COAS, with its smaller working distance may have produced

greater instrument myopia when compared to the EM. That this on‐axis difference is

likely to be due to some accommodation effect is also supported by the results obtained

on the model eye, which showed an opposite shift in M between instruments, with the

Shin Nippon producing a small myopic shift when compared to the EM and the COAS.

When assessing the peripheral refraction profiles with contact lenses on eye, all

instruments indicated the same anticipated trend. The FND lens, which exhibits an

increase in positive power towards the periphery, produced a more myopic peripheral

refraction profile when compared to the Acuvue 2 lens. Conversely, the Acuvue 2 lens,

which exhibits an increase in negative power towards the periphery, produced a more

positive peripheral refraction profile when compared to the Focus Night and Day lens.

With respect to J180, there was a trend for the Shin Nippon measuring less peripheral

astigmatism (J180), when compared to the EM. This was particularly evident for larger

visual field angles and in hyperopic eyes, which exhibited a large degree of peripheral

astigmatism. However, this effect was not observed in the previous measurements


236

performed on the model eye, which also exhibited large amounts of peripheral

astigmatism. Nevertheless, Shin Nippon measurements performed with the model eye

were only possible for field angles up to ±30°. Moreover, the retina of the model eye

differs to the human retina, as it is plane and not curved in shape. Thus, one reason for

the J180 difference found in human eyes between the Shin Nippon and the EM,

particularly at large peripheral angles, may be explained by the previous modelling

approach for which a schematic model eye with curved retina was used.

It was demonstrated that when using the ring‐autorefraction principle the peripheral

retinal ring images are asymmetrically distorted (Section 5.4.3.2.2) and that this

distortion could potentially interfere with the sphero‐cylindrical refraction output

provided by the autorefractor. For measurements with contact lenses on eye the same

difference was found, with the EM measuring more minus for M and J180 when compared

to the Shin Nippon.

Besides some small fluctuations across the peripheral refraction profile, the overall

profile of J45 was consistent for all three instruments. The greater J45 fluctuations found

in the hyperopic group can be explained by a combination of greater magnitude of

peripheral astigmatism (J180) and a small deviation from the 90° cylinder axis.

With respect to repeatability, the EM produced more repeatable results when compared

to the Shin Nippon. This was particularly so for measurements performed without

contact lenses on eye. There are many factors that could have led to the lower

repeatability when using the Shin Nippon including the decreased tolerance to pupil

misalignment when performing peripheral refraction measurements using the Shin

Nippon (Chapter 2 and 3). Unlike with the EM, where a fast measurement scan is

performed, with the Shin Nippon, measurements were performed sequentially for each

visual field position and thus numerous re‐alignments were required by both participants

and operators. Another reason, as in Chapter 5, could be related to the ring‐

autorefraction principle being not a suitable operation principle, when performing


Although, it was demonstrated that measurements with contact lenses on eye are

possible with the EM, repeatability is still lower when compared to baseline


237

measurements. One factor could be lens movement on the eye or small amounts of lens

prism, but more work is required to further understand and improve the accuracy of

measuring peripheral refraction profiles with contact lenses on eye.

6.4.3.3 Reproducibility

For one participant, measurements with the EM were repeated on a second occasion by

an independent operator. The measured peripheral refraction profiles were similar

between operators for all conditions, whether measurements were performed with or

without contact lenses on eye. However, there was a small trend for operator 1

measuring more myopic peripheral refraction profiles compared to operator 2

(difference < 0.17D). This may be related to a consistent small difference in pupil

alignment between both operators, which would also explain why the standard

deviations of the repeats were similar for both operators. The small difference in M

measured between operators resulted in the higher coefficients of reproducibility. It

should be noted, however, that due to the small sample size of only one participant, the

current analysis on instrument reproducibility is limited. A larger sample sized study,

where measurements are performed by more than two operators, is therefore

recommended to provide clinically more useful information on the EM’s reproducibility.

6.5 Discussion

6.5.1 Peripheral Refraction Instruments

During the last few years, interest in the measurement of peripheral refractive errors has

increased enormously. For the measurement of peripheral refraction, commercially

available instruments are commonly used (Chapter 1), which when adopted for this

purpose require some form of modification to the instrument set‐up and alignment

procedure. However, alignment requirements, for both, participants (eye/head turn) and

operators (pupil/instrument) can become very time consuming when using such

instruments, and the precise alignment of the pupil was found to be a critical parameter

in peripheral refractometry (Chapter 2). Hence, a new peripheral refraction instrument,

the EyeMapper, was developed with the aim to perform fast and accurate refraction

measurements across a wide visual field.


238

The need for such fast peripheral refraction instruments has been recognised over the

last few years, and besides the EM presented in this thesis, three additional peripheral

refraction instruments have been developed during this time.42, 128, 155 All of these new

instruments require some form of scanning in order to permit the refraction

measurements across the visual field. Table 6.5 lists some of the main features for each

of the four peripheral refraction instruments.

Table 6.5: Features of current peripheral refraction instruments.

Instrument Operation Principle

Peripheral Refraction is

achieved with…

Visual Field Range Measurement Duration (in s)

Scanning Photo‐

Refractor

(Tabernero et al.42)

Photo‐

refractometry

a rotational and

translational hot

mirror

‐45° to +45° in 0.4°

steps

4

Scanning Shack

Hartmann

Aberrometer (Wei

and Thibos128)

Aberrometry three‐element,

double‐ pass scanning

lenses and a scanning

mirror

‐15° to +15° in 5°

steps (along 6 visual

field meridians)

7 to 8

Scanning

Hartmann‐Shack

Wavefront Sensor

(Jaeken and

Artal155)

Aberrometry a rotation stage and

fixed mirrors

‐40° to +40°

(continuously)

2

The EyeMapper Aberrometry a deflection system

and a scanning mirror

‐50° to +50° in 10°

steps (along 7 visual

field meridians)

currently 0.45

per visual field

meridian

The first peripheral refraction instrument was introduced by Tabernero et al. in 2009.42

This instrument is a scanning photo‐refractor, which permits continuous refraction

readings across the horizontal visual field. For this, a rotational and translational hot

mirror is used to achieve the peripheral refraction scan. Measurements with this

instrument take approximately 4 seconds. The scanning photo‐refractor is currently

limited to the measurement of spherical errors and thus, astigmatic errors, which are

particularly present in the periphery of the eye, cannot be investigated when

measurements are performed using this instrument.

The Scanning Shack Hartmann Aberrometer by Wei and Thibos uses custom‐designed,

three‐element, double‐pass scanning lenses and a scanning mirror to perform the

peripheral refraction scan.128 By use of these lenses, the instrument permits


239

measurements ranging from ‐15° to +15° in 5° steps along 6 visual field meridians. Thus,

a total of 37 refraction measurements can be obtained within 7 to 8 seconds. Currently,

however the central and all peripheral measurements along the horizontal meridian are

not possible as strong backward scattering of light interferes with the measurements.

Like Tabernero et al.’s scanning photo‐refractor, Jaeken and Artal’s open‐view scanning

wavefront sensor measures refraction continuously across the wide horizontal visual

field.155 This instrument comprises a combination of moving (rotation stage, a caging

system and a high speed camera) and fixed components (mirrors). As with the EM, one

design goal of this wavefront sensing technique was to maintain equal path lengths at

each measuring angle. A peripheral refraction scan with this instrument currently takes 2

seconds and further adjustments to the current instrument are required to provide a

clinically more useful version.

The EM uses a deflection system, which comprises numerous stationary mirrors and a

scanning mirror to permit the refraction scan across the visual field. This deflection

system presents some advantages over the other three instruments. Unlike the scanning

aberrometer by Wei and Thibos, where all peripheral measurements are performed via

the same double‐pass scanning lenses, the deflection system of the EM has individual

paths for each peripheral measurement angle and thus, permits measurements up to

±50°. Compared to the instruments by Tabernero et al. and Jaeken and Artal, which

require some moving elements to perform the peripheral refraction scan, the advantage

of the EM’s deflection system is that the scan can be performed very rapidly. In fact

although in the current study the EM’s measurement time was 0.75 seconds, latest

improvements to the instrument have increased the measurement speed even further

and the instrument permits now measurements in only 0.45 seconds. Consequently, the

impact of fluctuating accommodation and/or fluctuating fixation on the refraction

measurements is smallest with the EM compared to the other instruments. On the other

hand, the scanning principles used in the peripheral refraction instruments by Tabernero

et al. and Jaeken and Artal have the advantage that they permit continuous refraction

measurements, which allow the assessment of the complete peripheral refraction

profile. The main advantage of the Scanning Shack Hartmann Aberrometer by Wei and

Thibos is, that during one scan, this instrument permits measurements along 6 (currently

5) visual field meridians. Although the rotational feature of the EM also permits the


240

measurement of the vertical and five oblique visual field meridians, these measurements

have to be performed independently from each other.

With respect to its size, appearance and user interface, the EM was designed to be used

in clinical practice by a clinician with minimal training. While there is potential for

further refinement of the design to make it a commercial instrument, the EM is closest

to a marketable clinical instrument for routine use.

When comparing the features of the current four peripheral refraction instruments, it is

evident that each instrument has its own advantages and disadvantages. Being in the

early development stages with some limitations still present, it is anticipated that more

refinements are soon to follow for each instrument. Ultimately, these peripheral

refraction instruments have the potential to be used as general myopia monitoring tools

not only in research institutions but also in clinical and optometric practices.

6.5.2 Limitations and Suggestions for Future Work

Being a prototype instrument, the EyeMapper has room for further improvement. The

knowledge gained during the design and development phase, in which many obstacles

had to be overcome, can now assist in the further refinement and testing of the

instrument. The following points list some of the current main limitations of the EM and,

where possible, provide suggestions to address them in either this prototype and/or

future instrument versions:

Peripheral refraction measurements on the model eye have shown that a small

cylinder axis deviation caused some fluctuations in the refractive vector

component J45, particularly at far‐peripheral angles. This is likely to be due to

some small mirror alignment errors in the deflection system which can and need

to be resolved.

The majority of mirrors used in the deflection system are aluminium coated,

front surface mirrors, with a reflectance of approximately 85% at the wavelength

of 830 nm. The use of silver mirrors with higher reflectivity would reduce light

loss, allowing a reduction in the power of the SLD.


241

The current mechanical beam shutter used in the EM is noisy and a potential

source of vibrations. Replacement by a smoother and less noisy shutter is

suggested.

A slightly larger diameter lens (L1) for the on‐axis alignment would improve

alignment, particularly, when measurements need to be performed for very

large pupils (e.g. under cycloplegia).

The EM is designed with the aim to measure peripheral refraction over wide

angles of view (from ‐50° to +50°). However, in some cases measurements at far

peripheral angles may be not possible due to the participant’s eye lid obstructing

the pupil.

The validation study on the EM has shown that when performing measurements

using closed‐view refraction instruments, adequate autofogging mechanisms

have to be incorporated. With the fixation target being positioned on a movable

translation stage, it would not be difficult to move the target to such a position.

Whether or not a real open‐view set‐up can be incorporated into the EM

instrument, is to be assessed further.

Currently, the EM can measure visual field meridians ranging from 0° to 90° in

15° steps. Perhaps a different rotation method could be implemented in a

future instrument to also permit the measurements of the visual field meridians,

ranging from 0° to 180°.

The EM’s fixation path was designed with the aim to measure the peripheral

refraction profile for different accommodative states. Further work is required to

test this feature and to investigate its implications on visual science.

6.6 Conclusion

A new peripheral refraction instrument, the EyeMapper, was developed at the Brien

Holden Vision Institute, Sydney, Australia. The instrument’s optical design is based on

the wavefront sensing principle, a principle which was deemed to be most suitable for an

instrument dedicated to the measurement of peripheral refraction. By means of a

deflection system and a scanning mirror, this instrument is able to provide global

refraction (aberration) measurements, ranging from ‐50° to +50°, in 10° steps.

Following development of the EM, a peripheral refraction model eye with a rotational

and translational extended plane retina was used to assess instrument accuracy. When


242

compared to refraction data obtained on a well‐calibrated commercially available

aberrometer, the results obtained with the EM were in good agreement and showed

overall better repeatability. Moreover, in 10 human eyes, measurements were

performed with and without contact lenses on eye, using three instruments; the

EyeMapper and the two commercially available instruments, the Shin Nippon and the

COAS. Overall, the comparability of the peripheral refraction profiles was good between

the instruments; however, the Shin Nippon measured slightly more positive M and J180

values with increasing visual field angle when compared to the EM. Better repeatability

for M and J180 was obtained with the EM, when compared to the Shin Nippon data. In

addition, the peripheral refraction profile of one participant was measured with the EM

by two different operators on two different occasions to demonstrate good

reproducibility.

Compared to other peripheral refraction instruments, the EyeMapper permits the fastest

peripheral refraction scan across the visual field requiring only 0.75 seconds. In addition,

its rotational feature permits the measurements of 7 visual field meridians and its

clinically user‐friendly design, makes it a great myopia monitoring tool for future studies.

CHAPTER 7: SUMMARY AND CONCLUSIONS

243

CHAPTER 7:

SUMMARY AND CONCLUSIONS

7.1 Significance of Peripheral Refractometry

With the rapidly increasing prevalence of myopia in many countries, the discovered link

between myopia development and peripheral refractive error has stimulated great

interest in the critical assessment and monitoring of the peripheral optics of the eye. It

has therefore become paramount for myopia research activities to be able to develop

techniques that measure both central and peripheral refraction, quickly and accurately.

Currently, however, there are several limitations with commercially available refraction

instruments for the measurement of peripheral refraction.

The aims of this thesis were to investigate methodological limitations of current

peripheral refraction techniques, and to introduce and explore new concepts to improve

peripheral refraction.

7.2 Current Limitations

When using conventional instruments for the measurement of peripheral refraction,

modifications and numerous time‐consuming re‐alignments are required, by both

participants and operators.

7.2.1 Participant‐Related Alignment Limitations

To permit the measurement of a particular peripheral visual field angle, the participant is

commonly asked to either turn the eye or the head towards a peripheral fixation target.

The use of two different alignment methods has raised the concern over whether

peripheral refraction measurements obtained through eye and head turn differ (Section

1.4). It was hypothesised that external muscles from the eye may potentially affect eye

turn measurements. Several studies, each based on different study protocols (peripheral

visual field angles, instrumentation, viewing duration, etc.) have sought to answer this

question. Due to the inconclusive results obtained between studies, it was

recommended that, where possible, head turn should be used for peripheral refraction

measurements (Chapter 1). A further limitation associated with participant alignment is


244

the extensive testing time required, particularly when numerous peripheral positions

need to be measured for the determination of the participant’s peripheral refraction

profile. In general, the active and time‐consuming cooperation required by the subject

limits the use of commercially available instruments for the measurement of the

peripheral optics of the eye.

7.2.2 Operator‐Related Alignment Limitations

Besides the participant‐related alignment limitations, one aspect that had not yet been

investigated was whether alignment limitations also exist for the operator when

measuring peripheral refraction. By use of a conventional autorefractor (based on the

ring autorefraction principle) it was demonstrated that, as peripheral visual field angle

increased, tolerance to pupil misalignment by the operator decreased significantly, even

below normal alignment variability, making peripheral refraction measurements more

susceptible to error (Section 2.1). As a result it was concluded that precise pupil

alignment by the operator is critical to obtain accurate peripheral refraction results. In

addition, a three‐dimensional entrance pupil model demonstrated that the peripheral

entrance pupil shape is not elliptical, as currently assumed when aligning the instrument

(Section 2.3). This can lead, potentially, to small systematic alignment errors, particularly

at large peripheral angles.

With precise pupil alignment being such a significant parameter in peripheral

refractometry, a method that aimed to rectify pupil alignment related errors when using

conventional instruments was established, validated and tested (Chapter 3). This method

firstly required the development of a pupil alignment matrix, which was achieved by

measuring refractive error with a conventional autorefractor at pre‐defined pupil de‐

alignment positions for a number of selected visual field angles. In addition, the amount

of pupil misalignment was determined from the pupil alignment screen image, as

captured during the refraction measurement. The relevant correction algorithms for

pupil misalignment were derived from the matrix, and refraction values were corrected

with respect to the amount of pupil misalignment measured. Following correction of

pupil misalignment, the variability for the corrected mean peripheral refraction profile

was reduced by at least 25%. Despite the fact that the developed method was

demonstrated to reduce the variability caused by pupil misalignment, it is anticipated


245

that further reductions can be achieved by refining the correction algorithms and by

eliminating the small image capture delay.

7.3 A New Approach

With the ultimate goal to overcome peripheral refraction measurement limitations

related to both the time‐consuming re‐alignment (off‐axis fixation) requirements by the

participant and the strict requirements for precise pupil alignment by the operator, a

new instrument concept was introduced; the EyeMapper (EM) (Chapter 4). The initial

aim of the EM was to perform a rapid refraction scan, ranging from ‐50° to +50° in 10°

steps, using ten stationary deflecting prisms and one scanning mirror. As with most

autorefractors that are currently adopted for peripheral refractometry, the objective was

to determine the sphero‐cylindrical refraction output by means of the ring‐

autorefraction operation principle. On the basis of the EM reference model eye, the

optical sub‐paths of the proposed EM instrument were designed using the optical system

design software ZEMAX. Specifically, five intertwined optical paths; the deflection

system, the illumination, reflection, pupil imaging and fixation paths, were designed and

evaluated with respect to the individual pre‐defined path criteria.

Prior to testing of this instrument concept, a number of additional functions and

components required sourcing and evaluation to ensure the safe and effective operation

of the proposed EM instrument (Chapter 5). This process included assessment of the on‐

and off‐axis ring scan illumination and its optical radiation safety limits, as well

assessment of the speed and precision of the image detection. As a preliminary

validation step for the optical design, image capture and image analysis, the critical

components required for the EM’s on‐axis ring‐autorefraction principle were assembled

and tested. Although its operation for on‐axis measurements was confirmed and cross‐

validated with a conventional autorefractor, an obstacle relating to the ring‐image

analysis was identified, which would impair one of the main goals of the EM; the

performance of a peripheral refraction scan in less than one second. Additional

experimental testing and modelling also revealed that peripheral higher order

aberrations have the potential to interfere with the sphero‐cylindrical refraction

readings obtained when using this ring‐autorefraction operation principle. A technique

that segregates higher and lower order aberrations was therefore deemed more suitable

for an instrument dedicated to measuring peripheral refraction.


246

Based on the knowledge gained in Chapters 4 and 5, the optical and mechanical EM

design was updated to integrate the wavefront sensing principle. On the basis of the new

design, the first prototype instrument was built at the Brien Holden Vision Institute and

tested experimentally (Chapter 6). The updated EM instrument uses an intricate

arrangement of stationary mirrors and one scanning mirror that together permit global

(central and peripheral) refraction (aberration) measurements, ranging from ‐50° to +50°

in 10° steps. The rotational feature of the EM permits the measurements of seven visual

field meridians ranging from 0° to 90° in 15° steps. An entire peripheral refraction along

one visual field meridian scan can be completed within only 0.75 seconds, making it the

fastest of the four peripheral refraction instruments developed thus far. Finally, the EM

was validated by measuring peripheral refraction on a custom‐designed peripheral

refraction model eye and on 10 human eyes. Peripheral refraction profiles measured on

the custom‐designed model eye were in good agreement with the EM and a well‐

calibrated commercially available aberrometer. Improved repeatability was obtained

using the EM. Improved repeatability was also achieved with the EM when compared to

the Shin Nippon autorefractor for measurements performed on 10 human eyes. This was

true for measurements obtained with and without contact lenses on eye.

In summary, a new clinical instrument, the EyeMapper, was developed which permits

accurate, repeatable and reproducible real‐time global refraction measurements, which

are of particular importance for the monitoring and assessment of myopia progression.

7.4 Conclusions

This thesis comprises a body of work that has contributed to the improved

understanding of methodological limitations of current peripheral refraction techniques.

On the basis of the limitations identified, new methodologies for the advancement of

peripheral refractometry were introduced and explored. All the aims were achieved and

both hypotheses confirmed.

Findings from this thesis have reinforced the fact that when using an instrument for

purposes other than its intended use, it is not certain that the intrinsic application or

operation principle will generate accurate results when used in the modified fashion.


247

This work has implications for numerous research activities; in particular, when the

interpretation of accurate peripheral refraction profiles is required, and where

longitudinal and/or large sample sized studies require a number of repeated

measurements. In the current quest to understand, monitor and control myopia

progression, the clinically robust, fast and accurate EM instrument presented in this

thesis, provides the most advanced tool for the measurement of peripheral refraction

profiles in large population‐based studies, as well as detailed investigations into

peripheral refraction profiles of individuals. It is anticipated that in the near future

applications for peripheral refraction instruments will be found not only in research

institutions but also in general eye care, for example, in assessing retinal image profiles,

in detecting children who are at risk of developing myopia, and in prescribing specific

optical devices with designs to eliminate peripheral hyperopia or myopia. In addition to

refractive error development and control, there are many other research areas related

to the peripheral optics of the eye for which the use of such a fast peripheral refraction

instrument could also be of great benefit, including optimising peripheral visual function

for low vision subjects with absolute central skotoma or in sport and life in general.

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248

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APPENDIX A

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APPENDIX B

Visual Field Angle (°) Equations RMSE

Horizontal Pupil

Alignment Meridian

M

nasal 40 1.65 5.50 10 1 1.215

3.66 10 1 2 1.95 2.04 10 1 0.936

nasal 30 1.17 1.77 10 1 0.806

1.05 10 1 2 1.17 5.86 10 2 0.799

nasal 20 6.75 10 1 4.03 10 2 0.534

6.70 10 2 2 6.75 10 1 3.51 10 2 0.530

central 0 1.59 10 1 2 8.39 10 3 1.63 10 3 0.299

temporal ‐205.05 10 1 8.46 10 2 0.533

6.70 10 2 2 5.05 10 1 9.28 10 3 0.529

temporal ‐30 8.65 10 1 3.61 10 2 0.535

3.41 10 2 2 8.65 10 1 7.45 10 2 0.534

temporal ‐40 1.47 1.40 10 1 0.786

7.75 10 2 2 1.47 5.32 10 2 0.783

nasal/temporal θ (‐/+) . . 0.776

J180

nasal 40 180 1.11 3.45 10 1

180 0.615

180 1.89 10 1 2 1.14 1.55 10 1180 0.565

nasal 30 180 5.83 10 1 9.76 10 2

180 0.415

180 5.69 10 2 2 5.83 10 1 3.36 10 2180 0.411

nasal 20180 3.20 10 1 5.12 10 3

180 0.337

180 3.11 10 2 2 3.21 10 1 4.00 10 2180 0.336

central 0 180 8.68 10 2 2 3.34 10 2 1.78 10 2180 0.161

temporal ‐20 180 2.33 10 1 2.85 10 2

180 0.228

180 3.34 10 3 2 2.38 10 1 2.38 10 2180 0.228

temporal ‐30 180 4.21 10 1 2.17 10 2

180 0.281

180 5.79 10 3 2 4.21 10 1 2.82 10 2180 0.281

temporal ‐40 180 7.79 10 1 5.25 10 3

180 0.458

180 2.64 10 3 2 7.78 10 1 8.21 10 3180 0.458

nasal/temporal θ (‐/+) . . 0.445

Appendix

303

Vertical Pupil

Alignment Meridian

J45

nasal 40 45 8.19 10 1 1.37 10 2

45 0.409

45 8.88 10 3 2 8.19 10 1 2.36 10 245 0.408

nasal 30 45 5.24 10 1 1.50 10 2

45 0.348

45 3.13 10 2 2 5.24 10 1 4.90 10 445 0.348

nasal 20 45 3.14 10 1 1.17 10 2

45 0.264

45 2.36 10 3 2 3.14 10 1 9.01 10 345 0.264

central 0 45 2.87 10 2 2 6.83 10 2 1.50 10 445 0.142

temporal ‐20 45 1.72 10 1 6.75 10 3

45 0.226

45 1.40 10 2 2 1.72 10 1 8.75 10 345 0.225

temporal ‐30 45 3.16 10 1 5.45 10 2

45 0.278

45 4.85 10 2 2 3.16 10 1 1.40 10 445 0.274

temporal ‐40 45 5.04 10 1 1.01 10 1

45 0.350

45 7.03 10 2 2 5.04 10 1 2.17 10 245 0.344

nasal/temporal θ (‐/+) 45 1.49 10 2 2.20 10 245 0.332

Horizontal Pupil

Alignment Meridian

M

inferior 20

4.55 10 1 6.10 10 2 0.519

8.65 10 2 2 4.55 10 1 2.29 10 2 0.513

inferior 30

7.58 10 1 2.03 10 2 0.643

3.26 10 3 2 7.66 10 1 2.60 10 2 0.643

inferior θ (+) 2.49 10 2 4.50 10 2 0.586

J180

inferior 20 180 2.21 10 1180 0.321

inferior 30 180 3.61 10 1180 0.456

inferior θ (+) 180 1.17 10 2180 0.394

Vertical Pupil

Alignment Meridian

J45

inferior 20 45 1.79 10 1 1.16 10 2

45 0.195

45 1.07 10 2 2 1.79 10 1 4.36 10 445 0.195

inferior 30 45 3.62 10 1 2.93 10 2

45 0.265

45 1.35 10 2 2 3.61 10 1 1.42 10 245 0.265

inferior θ (+) 45 1.11 10 2 8.89 10 345 0.237

Appendix

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APPENDIX C

Appendix

305

APPENDIX D

Publications and Presentations

Journal Articles

Fedtke C, Ehrmann K, Holden BA. A review of peripheral refraction techniques (2009).

Optom Vis Sci 86:429‐46.

Fedtke C, Manns F, Ho A. The entrance pupil of the human eye: A three‐dimensional

model as a function of viewing angle (2010). Optics Express 18:21:22364‐22376.

Fedtke C, Ehrmann K, Ho A, Holden BA. Lateral pupil alignment tolerance in peripheral

refractometry (2011). Optom Vis Sci 88:4.

Presentations

Fedtke C, Ehrmann K, Ho A, Holden B. The impact of pupil alignment on peripheral

refraction measurements using the Shin‐Nippon NVision K5001. Presented at the

American Academy of Optometry, Orlando, Florida; 2009.

Ho A, Fedtke C, Manns F. The peripheral entrance pupil. Presented at the American

Academy of Optometry, Orlando, US; 2009.

Ho A, Lazon de la Jara P, Martinez A, Kwan J, Fedtke C, Holden BA, Sankaridurg P.

Influence of accommodation on peripheral refraction: Effect of a novel optical design

contact lens for manupulating peripheral defocus. In: Presented at International Myopia

Conference, Tübingen, Germany; 2010. Optom Vis Sci 88:3:441‐42.

Sankaridurg P, Donovan L, Varnas S, Ho A, Kwan J, Fedtke C, Chen X, Ge J, Smith III E,

Holden BA. Impact of spectacle lenses on peripheral refractive errors. Presented at

International Myopia Conference, Tübingen, Germany; 2010. Optom Vis Sci 88:3:443‐44.

Appendix

306

Poster Presentations

Fedtke C, Lazon de la Jara P, Sankaridurg P, Kwan J, Ho A, Holden BA. Relationship

between annual refractive error changes and changes in ocular biometric data in Chinese

children. Presented at International Myopia Conference, Tübingen, Germany; 2010.

Optom Vis Sci 88:3:402

Kwan J, Sankaridurg P, Lazon de la Jara P, Chen X, Fedtke C, Donovan L, Ho A, Ge J,

Holden BA. Association between peripheral refractive error and myopia risk factors.

Presented at International Myopia Conference, Tübingen, Germany; 2010. Optom Vis Sci

88:3:402

Lazon de la Jara P, Sankaridurg P, Martinez A, Kwan J, Fedtke C, Ho A, Holden BA.

Manipulation of the peripheral retinal image using two novel contact lens designs.

Presented at International Myopia Conference, Tübingen, Germany; 2010. Optom Vis Sci

88:3:400

Lazon de la Jara P, Ehrmann K, Kwan J, Fedtke C, Falk D, Sankaridurg P, Holden BA. The

effect of contact lens power profile on peripheral refraction. Presented at the American

Academy of Optometry, San Francisco, US, 2010.

Fedtke C, Ehrmann K, Falk D, Harms‐Biβ E, Ho A, Holden BA. Means to rectify pupil

alignment errors in peripheral refractometry. ARVO. Fort Lauderdale, US, 2011.

Patent Applications

Ehrmann K, Fedtke C, Ho A. Determination of peripheral refraction. Patent Application

Number: AU2010901866

peripheral refraction: significance, current limitations and a

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