104432149 optical metrology of lenses immersed in water

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OPTICAL METROLOGY OF LENSES IMMERSED IN WATER

A FOURTH YEAR THESIS IN Physics

In partial fulfilment of the requirements for the degree

BACHELOR OF SCIENCE

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Abstract An experiment was conducted with the aim of completely characterising the optical and physical properties of an intraocular lens (IOL). A theoretical software model of the IOL would then be used to verify the experimental metrology.

A FISBA OPTIK μPhase® HR interferometer was used to characterise a 21.5D IOL of the type Bausch & Lomb Akreos™ Adapt AO. The optical properties were measured as wave aberration in double transmission through the IOL; physical properties were measured as anterior-posterior surface radii of curvature and deviation from a perfect sphere, apparent apical thickness and back focal length. The hydrophilic nature of this particular IOL material necessitated measurement of the IOL submerged in liquid. The success of a previously performed experiment within the group was built upon, whereby the design and development of a new experimental apparatus allowed measurement of total wave aberration in transmission through the IOL. Accordingly, a high-quality mirror was submerged in the liquid.

Some problems encountered in measurement at autocollimation required measurement of a dry Pharmacia 17D IOL in air. ‘Dry’ IOLs are packaged in a dry atmosphere, thus they are well-suited to measurement in air. Measurement in air was assessed as perfectly adequate; however, measurement in balanced salt solution (BSS) would more closely represent the in situ environment.

The anterior and posterior surface deviations and radii of curvature were used together with the apical thickness to create a lens model in Zemax ray-tracing software. The software was then used to confirm experimentally determined values of total IOL transmission wavefront error. The modelled and experimental values of root mean square error differed by just 2.5%.

Further refinement of the experimental method and software model would allow transformation of this qualitative proof-of-concept model into an accurate quantitative analysis. With consequent reduction and/ or removal of variables, it would be possible to determine the source of discrepancy between experiment and theory. Complete control of all variables would in fact allow for attribution of any discrepancies to internal lens material inhomogeneities.

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List of Figures Figure 1.1. IOL Variations. .................................................................................................... 1

Figure 1.2. Schematic diagram of a cataracteous crystalline lens. ........................................ 2

Figure 2.1. 3D render of Zernike polynomials two to eleven. ................................................. 4

Figure 2.2. Schematic diagram of the relative measurement positions. ................................. 5

Figure 2.3. Schematic diagram of the confocal position. ....................................................... 5

Figure 3.1. Photograph of the Interferometer. ....................................................................... 8

Figure 4.1. Photograph of the initial IOL stage. ................................................................... 10

Figure 4.2. Photograph of the prototype Meccano stage and liquid bath. ............................ 11

Figure 4.3. Pharmacia (AMO) 17D IOL [8]. ......................................................................... 13

Figure 4.4. Photograph of the prototype Meccano ‘dry’ stage. ............................................. 14

Figure 4.5. 3D-rendered simulation of the experimental setup. ........................................... 17

Figure 4.6. 2D side-view of the Zemax double pass model. ................................................ 17

Figure 4.7. 2D side-view of the Zemax single pass model. .................................................. 18

Figure 5.1. Interferogram of the water meniscus. ................................................................ 19

Figure 5.2. Confocal interferogram of Bausch & Lomb 21D IOL in water............................. 20

Figure 5.3. Confocal interferogram of Pharmacia 17D IOL in air. ........................................ 21

Figure 5.4. Autocollimated interferogram of Pharmacia 17D IOL anterior surface in air. ...... 21

Figure 5.5. Autocollimated interferogram of Pharmacia 17D IOL posterior surface in air. .... 22

Figure 5.6. Comparison of modelled and experimental anterior 17D IOL surface. ............... 23

Figure 5.7. Comparison of modelled and experimental posterior 17D IOL surface. ............. 23

Figure 5.8. Comparison of modelled and experimental 17D IOL wave aberration. .............. 23

Figure 5.9. Final Zemax user-interface showing lens editor fields. ...................................... 24

Figure 5.10. Final Zemax user-interface showing total wave aberration and 2D layout. ...... 24

Figure 6.1. Examples of the lensing effect of the water meniscus. ...................................... 27

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Contents

Abstract................................................................................................................................... ii

List of Figures......................................................................................................................... iii

1. Introduction .................................................................................................................... 1

1.1 Intraocular Lens ...................................................................................................... 1

1.2 Cataract Surgery ..................................................................................................... 1

1.3 Project Aims............................................................................................................ 2

2. Background .................................................................................................................... 3

2.1 Aberration Theory ................................................................................................... 3

2.2 Interferometry ......................................................................................................... 3

2.3 Phase-Shifting Interferometry ................................................................................. 3

2.4 Zernike Polynomials ................................................................................................ 4

2.5 The ‘Cat’s Eye’ Position .......................................................................................... 4

2.6 The Autocollimated Position .................................................................................... 5

2.7 The Confocal Position ............................................................................................. 5

2.8 Characterising the IOL ............................................................................................ 6

2.9 IOL Selection and Metrology Criteria ...................................................................... 6

3. Instrumentation .............................................................................................................. 8

3.1 The Twyman-Green Interferometer ......................................................................... 8

3.2 Zemax Ray-Tracing Software ................................................................................. 9

3.3 Meccano ................................................................................................................. 9

4. Techniques .................................................................................................................. 10

4.1 Design and Construction of the IOL Stage ............................................................ 10

4.2 Calibration of the Interferometer ............................................................................ 11

4.3 Characterisation of the Retro-Reflective Return Mirror .......................................... 12

4.4 Characterisation of the Water Meniscus Lensing Effect ........................................ 12

4.5 Metrology of Bausch & Lomb 21.5D IOL in Water ................................................. 12

4.6 Metrology of Pharmacia (AMO) 17D IOL in Air ...................................................... 13

4.7 Zemax Ray-Tracing Analysis ................................................................................ 15

5. Results ......................................................................................................................... 19






6. Discussion. .................................................................................................................. 25

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6.1 Design and Construction of the IOL Stage ............................................................ 25






7. Conclusion ................................................................................................................... 30

8. Acknowledgements ...................................................................................................... 31

9. References .................................................................................................................. 31

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1. Introduction

1.1 Intraocular Lens

This project was specifically concerned with the optical metrology of intraocular lenses

(IOLs) immersed in water. IOLs are small plastic lenses of typically 6mm diameter and less

than 1mm thick. Two particular IOL models are shown in Figure 1.1 below. The central

region is called the optic, whereas the odd-shaped features extending from the optic are

called the haptics. The haptics’ shape, size and angulation can vary largely, depending on

the manufacturer. IOLs are usually implanted in the eye to replace the existing crystalline

lens because it has been clouded over by a cataract, or as a form of refractive surgery to

change the eye's optical power.

Figure 1.1. IOL Variations.

Bausch & Lomb Akreos Adapt AO Aspheric IOL (a) and

Bausch & Lomb Akroes M160 IOL (b) [1].

1.2 Cataract Surgery

Cataract surgery is one of the world’s most successful procedures, with approximately 20

million carried out globally and 20,000 carried out in Ireland each year [2]. Due to the ageing

society, there are currently 5 million new cataract patients annually, worldwide.

The surgery typically involves the replacement of the aged, cataracteous, partially

opaque crystalline lens (see Figure 1.2 below) with an artificial intraocular lens (IOL) [3].

When the crystalline lens is removed, the eye is said to be aphakic; with subsequent

implantation of the IOL, the eye is said to be pseudophakic. The procedure dramatically

reduces internal light scattering and provides for unobstructed retinal image formation [4].

(a) (b)

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Figure 1.2. Schematic diagram of a cataracteous crystalline lens.

IOL power calculation is currently based on regression analysis and has effective outcomes

for people with ‘normal eyes’. ‘Unusual eyes’ are those which are unusually long or short or

belong to those patients who have previously had refractive eye surgery. For unusual eyes,

the IOL selection method is ineffective in 80% of cases, where post-operative vision is

characterised by blurriness and lack of contrast and where satisfactory vision necessitates

the use of spectacles. Post-operative retinal image quality is not solely based on correct IOL

power calculation; it is also based heavily on the true post-operative position of the IOL and

its optical aberrations.

1.3 Project Aims

The main aim of the project was to completely determine the optical and physical

characteristics of a particular IOL and subsequently fully characterise their effect on

pseudophakic retinal image quality. The anterior and posterior IOL surfaces, together with

the apical thickness, could be modelled in Zemax ray-tracing software. The software could

then be used to determine the IOL’s imaging properties using this simple lens model.

However, as already stated, this method only gives a measure of the total wave aberration

attributable to individual surface imperfection and does not take into account any aberrations

introduced due to IOL material inhomogeneity. Therefore, to completely determine the

pseudophakic retinal image quality, it is necessary to experimentally measure the total wave

aberration in transmission through the IOL, with subsequent confirmation using the Zemax

ray-traced model. Any discrepancies between the two data sets can then be assigned to

inhomogeneities in the lens material.

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2. Background

2.1 Aberration Theory

The properties of an optical system can be determined through the examination of wave

aberration introduced in single (or double) transmission through the system. For a single

optical element (e.g. a lens), this method only gives information about the optical

imperfections of the system as a whole, however, and does not portray any information

about the individual surfaces of the lens. Furthermore, it is impossible to determine whether

certain aberrations are due to surface imperfection or internal inhomogeneity. In order to

completely characterise the lens, it is necessary to measure not only both lens surfaces and

total wave aberration in transmission through the lens, but also the apical lens thickness.

The entire lens and consequent image degradation can then be modelled using ray-tracing

software.

The optical properties of a lens can be measured using an interferometer. The

associated software computes the lens imperfections and generates a set of Zernike

polynomials, which can be subsequently used to describe the lens properties in ray-tracing

software.

2.2 Interferometry

For many years interferometry has been an invaluable tool for the measurement of optical

surfaces and systems. Its capability was greatly extended with the advent of highly

monochromatic and coherent laser light. It was enhanced yet further with the development of

advanced numerical analysis techniques made possible by the power of computers in the

1990s. As a measurement technique it is extremely sensitive and can easily resolve

distances that are just a fraction of the wavelength of light. The measured parameter in

interferometry is usually the wavefront distortion, with interferometers measuring precisely

how an ideal wavefront is modified when it is reflected from a surface or transmitted through

an optical window or lens assembly.

2.3 Phase-Shifting Interferometry

The phase-shifting interferometric technique has an important advantage over static fringe

analysis whereby seemingly identical concave and convex surface maps can be deciphered.

The technique usually involves moving the reference surface, which is perpendicular to the

optical axis, by half a wavelength along the axis. This movement is effected by a piezo-

electric device and is usually separated into four or five steps, with measurements taken at

each step. The five step method has an advantage over the four step method whereby the

first and fifth measurements should be identical; thus the method is self-checking. The data

can then be ‘phase-unwrapped’ and the wavefront characterised to a very high degree of

accuracy.

If φ is the phase of the wave in radians, where:

,

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then φ1 – φ2 = Δφ is the phase difference between the test and reference beams

and if OPD is the optical path difference between two beams, then:

Δφ

[5]

2.4 Zernike Polynomials

Zernike polynomials are a compact set of polynomials which are often used to describe the

aberrations of optical assemblies. The wave aberration of a given wavefront is described as

its deviation from a perfect wavefront of the same type. The aberration is then decomposed

into a finite number of Zernike polynomials so that the total root mean square (RMS)

wavefront aberration is minimised.

Zernike polynomials form a complete set in two variables that are orthogonal in a

continuous fashion over the unit circle, thus necessitating normalisation of pupil co-

ordinates. They are orthogonal only in a continuous fashion and will not, in general, be

orthogonal over a discrete set of data points [6-7]. Several common definitions exist for

Zernike polynomials, so caution must be exercised when comparing coefficients. For

example, the notation adopted in the FISBA µShape® software differs from that in the

Zemax ray-tracing software; see Section 4.7.

Figure 2.1 below is a 3D mesh-type render of Zernike polynomials two to eleven.

Figure 2.1. 3D render of Zernike polynomials two to eleven.

2.5 The ‘Cat’s Eye’ Position

If a surface is placed directly at the focus position of a convex lens, then an interference

pattern is observed, and this is referred to as a ‘cat’s eye’ reflection. The interferogram

obtained is generally unhelpful in terms of surface evaluation, as one of the characteristics of

the cat’s eye position is wavefront inversion i.e. the light rays are not retro-reflected. The

cat’s eye is, however, very useful for measuring the radius of curvature, vertex length, and

apparent thickness of an optical system.

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2.6 The Autocollimated Position

The autocollimated position occurs where light from a focussing lens is normally incident on

a test surface, so that the beam is retro-reflected, with imperfections of the test surface

showing up as abnormalities in the interferogram. At this position, the focal point of the

focussing lens is coincident with the centre of curvature of the test surface, and is therefore

useful for measuring radius of curvature.

Figure 2.2. Schematic diagram of the relative measurement positions.

Top cat’s eye (Green)

Bottom cat’s eye (Blue)

Autocollimation (Red).

Note: The diagram is not to scale.

2.7 The Confocal Position

The focussing lens of the interferometer is positioned so that light enters through the focus

position of a convex test piece and emerges collimated (to be retro-reflected by a return flat).

The retro-reflected light then propagates back through the test piece and in this way,

information about the double pass aberration of the piece can be obtained. In this

arrangement, the focus positions of both the interferometer focussing lens and the test piece

are coincident.

Figure 2.3. Schematic diagram of the confocal position.

Note: The diagram is not to scale.

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2.8 Characterising the IOL

There are many ways of characterising optical surfaces and systems. The particular setups

used in this experiment allowed the determination of:

1. Radius of Curvature. The radius of curvature was measured as the displacement

between the cat’s eye reflection from the top surface of the IOL and the

autocollimated position.

2. Apparent Central Thickness1. The apparent thickness was measured as the

displacement between the cat’s eye reflections from the top and bottom surfaces of

the IOL respectively.

3. Back Focal Length. The back focal length was measured as the displacement

between the cat’s eye reflection from the top surface of the IOL and the confocal

position. Information about the back focal length can be used to calculate the

refractive index of a lens material.

4. Double Pass Wave Aberration. Information about the double-pass wave aberration of

the IOL was obtained from double-pass measurements in the confocal arrangement.

5. Surface Deviation in Single reflection at Normal Incidence. Pits/hollows in the IOL

surface will cause any light incident there to be phase delayed, with bumps/hills

causing phase advancement. In this way, surface abnormalities show up as visible

fringes in the interferogram, with each fringe representing an area of equal phase.

The phase-shifting software can be used to process the resulting interferogram and

calculate the corresponding Zernike coefficients.

2.9 IOL Selection and Metrology Criteria

A dioptric series of Bausch and Lomb Akreos Adapt AO IOLs were received prior to

experimentation. It was decided to measure the 21.5D Bausch & Lomb IOL, which, out of the

series of received IOLs, best matched the most commonly implanted IOL power of 21D

[2].The particular type of IOL material was a hydrophilic acrylic copolymer, with the IOLs

packaged in liquid. A model of the IOL is shown in Figure 1.1 (a); the haptic features are

seen on the top right and bottom left and serve to indicate that the anterior lens surface is

facing forwards.

A recent experiment performed by the author, in collaboration with Matt Sheehan,

indicated that measuring this IOL material in air was highly problematic. The thin layer of

liquid that covered the IOLs after removal from their containment was unsurprisingly found to

dry out. However, this drying out of the liquid caused any interferograms to fluctuate wildly

due to the induced constantly-changing aberrations. Thus problems similar to, for example,

the drying of the tear film in retinal imaging were encountered. Without the use of a

sophisticated adaptive optic system, the method of hydrophilic IOL measurement in air was

deemed impossible. Furthermore, there was some ambiguity as to whether the IOL’s

physical characteristics changed through drying out in air. Consequently, it was decided to

measure the IOL submerged in liquid.

The measurement of an IOL is a difficult task. The lens itself is small and fragile and

requires delicate manipulation using a tweezers or other sensitive instrument. Care must be

taken to ensure that at no point is the optic region touched with anything but the cleanest

and smoothest of devices, lest any damage be caused there. It is not simply sufficient to

1 Note that due to refraction at the air/ IOL interface, it was necessary to model the system in

ZEMAX® to calculate the real thickness of the IOL.

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place the IOL on an optical bench, since that would damage or dirty the optic region.

Furthermore, the haptics which extend from the optic would be weighted downwards,

causing strain on the (often flexible) optic and incorrectly introducing artefacts there.

Therefore, it is necessary to place the IOL on a stage which not only allows light to pass

unobstructed through the IOL, but also provides adequate haptic and optic support.

When measuring an IOL, particular care must be taken to ensure that the rotation of

the IOL about its optical axis is kept constant, or at least well-defined, for all measurements.

If it was not, then the surfaces would be measured as being incorrectly rotated relative to

each other. For example, when measuring the anterior and posterior IOL surfaces, the IOL

must be flipped about a particular known axis; otherwise the measured surfaces will give

incorrect total wavefront aberration when modelled in software.

The aforementioned recent experiment was carried out to determine the

characteristics of the Bausch & Lomb IOL series. However, the particular experimental

technique adopted allowed only determination of the anterior & posterior surface deviations,

radii of curvature and back focal lengths; and apical thickness. It was deemed too difficult,

too time-consuming, or too complicated to measure the wave aberration in double

transmission through the IOL. Improvement upon the success of this previous experiment

therefore necessitated the design and development of a new apparatus and experimental

technique which would allow effective measurement of wave aberration in double pass

through the IOL.

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3. Instrumentation

3.1 The Twyman-Green Interferometer

All measurements of IOL properties were performed using a FISBA Optik µPhase® HR

Twyman-Green Interferometer. It allows implementation of the phase-shifting interferometric

method owing to the inclusion of a piezo-electric actuator contained within the device. It

operates using a frequency-stabilised He-Ne auxiliary laser ( =632.8nm). The interferometer

was mounted vertically on a µPhase® ophthalmic platform. Vertical translation of the

interferometer was accurately performed using the in-built micrometer with smallest ruled

division of 0.01mm. A photo of the apparatus is shown in Figure 3.1 below.

The interferometer was accompanied by µShape® interferometry software. The

software facilitates calibration of the system and measurement of surface deviation in single

reflection at normal incidence and wave aberration in double transmission, amongst others.

The phase-shifting technique is utilised in deciphering interferograms, with the resultant

wave aberration displayed as measurement maps on the user interface. The software can

then be used to resolve the maps into a user-specified number of Zernike coefficients for

subsequent export.

Figure 3.1. Photograph of the Interferometer.

The interferometer is a two-beam system, whereby an expanded and collimated

beam of the highly monochromatic He-Ne laser light is incident on a beam splitter, where

equal beam intensities are reflected and transmitted. One of these beams is referred to as

the reference beam and is created by reflection from an extremely accurate reference

surface. The second beam is reflected from the test surface, and is referred to as the object

beam. The two beams are then made to interfere, with the resulting interferogram on the

CCD camera displayed as a live image intensity distribution on the software interface.

The interferometer functionality can be extended through the use of spherical

objectives. A µLens EF 15/43 spherical objective, together with a µLens DCI 2 10/∞ beam

Interferometer

Coarse

Adjust

Screw

Micrometer

µPhase®

Ophthalmic

Mount

Tip/Tilt Table

Objective

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expander were employed in this experiment. The notation for lens specifications is µLens

[Model] [Diameter/Focal_length]. Thus, the employed objective had an f-number of f/2.9.

3.2 Zemax Ray-Tracing Software

Zemax is a comprehensive ray-tracing software package which allows the design,

optimisation and characterisation of optical systems and lens assemblies. It has a user-

friendly and intuitive interface allowing easy description and modification of optical element

parameters. It is a powerful tool for the analysis and visualisation of system performance

such as spot diagrams and ray-fan plots and boasts a comprehensive suite of in-built

optimisation tools for the optimal design of a particular optical arrangement.

In this experiment, the measured IOL surface deviations, radii of curvature and apical

thickness could be inserted into Zemax, with the software used to calculate the resultant

total wave aberration. This theoretical result could then be compared to the experimentally

determined value of double pass aberration.

3.3 Meccano

Meccano is a robust construction system comprising re-usable metal components, with nuts

and bolts to connect the pieces. It enables the construction and implementation of simple

working models and mechanical devices. The combination of its relatively low cost and large

range of components makes it ideal for constructing almost any conceivable structure.

Meccano was highly suitable for this project since it required custom-built structures over a

short period of time. It would have been impractical to wait for the manufacture of such

structures in the department workshop.

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4. Techniques

4.1 Design and Construction of the IOL Stage2

As already stated, the design and development of a new apparatus and experimental

technique was necessary to improve upon the success of previous experiments. The

particular difficulty which previously hindered the measurement of double pass wave

aberration was the availability of an apparatus which allowed independent tip/tilt and

translation of both the high-quality retro-reflective mirror and the IOL itself. Consequently, a

considerable amount of time was spent in designing and constructing an IOL stage which

not only provided adequate IOL support, but also provided for relative tilt of the IOL and

return mirror. Note that measurement of the submerged IOL also necessitated submersion of

the IOL platform and the high-quality return mirror in a liquid bath.

Initially, an IOL stage was successfully constructed using Linos optical bench

components, shown in Figure 4.1 below. Although optical bench components are

manufactured to exacting dimensions, they are relatively expensive and typically only a few

components will be readily available in the laboratory environment. Due to the lack of

multifarious components, the apparatus design was not ideal. In particular, the small rod

suspending the IOL platform entered the water quite close to the IOL itself, resulting in large

curvature of the water meniscus due to larger surface tension at that point; see Figure 4.1.

Figure 4.1. Photograph of the initial IOL stage.

The outer ‘legs’ would surround the liquid

bath, with the IOL and supporting platform submerged in the liquid.

It became increasingly clear that high-quality components were not necessary, and

that a large variety of components was highly desirable. Accordingly, it was decided to

create a new prototype stage using Meccano. A suitable stage was constructed, with the

Meccano components offering a much wider range of customisation possibilities. A photo of

the stage is shown in Figure 4.2 below. The IOL stage rested on the µPhase® ophthalmic

table, enabling tip, tilt and horizontal translation of the IOL.

2 The ‘stage’ is defined here and throughout as the entire structure used to hold the IOL, whereas the ‘platform’ is that

particular part of the stage which the IOL actually rested on.

IOL Platform

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Figure 4.2. Photograph of the prototype Meccano stage and liquid bath.

The outer ‘legs’ can be seen to surround the bath, with the IOL platform and

mirror submerged in the bath. Note that the IOL platform was covered

with black tape to avoid any unwanted reflections there from.

As can be seen from the photo, the water bath with submerged mirror was also placed

on its own tip & tilt platform. The construction of this bath platform was vital to the success of

the experiment, since it allowed essential alignment of the mirror with the interferometer.

This therefore ensured that any collimated light emerging from the aligned IOL would re-

trace its path back to the interferometer. The bath platform was supported using Linos

cageplates and rods, with the delicate tip & tilt control achieved using three upward-facing

potentiometer-type screws.

4.2 Calibration of the Interferometer

Calibration of the interferometer was necessary in order to remove aberrations inherent in its

optical assembly, thus ensuring that the measurements obtained related directly to the part

under test. When measurements were performed using collimated light, the system was

calibrated using a large plane FISBA calibration surface of 4% reflectivity and surface

flatness of greater than /20 ( =632.8nm). Calibration of the µLens EF 15/43 spherical

objective employed in the experiment required use of a spherical reference. A FISBA

spherical calibration surface with a radius of curvature of 10mm, surface accuracy of /20

( =632.8nm) and reflectivity of 4% was used for this purpose. At the confocal position, the

rays of light striking the surface at 90o were retro-reflected and a ‘null fringe condition’ was

obtained.

A virtual electronic ‘Calibration Mask’ was used in the µShape® software to mask out

any undesirable outer fringing due to diffraction effects, ghost images on the CCD camera

and indistinct aperture edges.

IOL Platform

Mirror

Liquid Bath

Bath

Tip/Tilt

Controls

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4.3 Characterisation of the Retro-Reflective Return Mirror

It was desired to measure the optical properties of an IOL using a spherical objective. This

required calibration using the FISBA spherical calibration surface. However, at the confocal

position, the light is retro-reflected from the plane mirror and thus any imperfections in the

mirror would incorrectly show up as aberrations in the IOL. If the system has already been

calibrated for use with the spherical objective, then it can only be used with that objective

and cannot be used to account for imperfections in the mirror.

Consequently, it was necessary to characterise the mirror prior to any measurements

of wave aberration in double transmission through the IOL. The interferometer was fitted with

a diameter 10mm beam expander and was first calibrated using the large FISBA flat. The

mirror was then aligned with the collimated interferometer output and a measurement of the

mirror surface was taken sixteen times. The average mirror surface error could then be

added to the ‘error budget’ of the double-pass wave aberration measurements.

4.4 Characterisation of the Water Meniscus Lensing Effect

Due to the finite radius of the employed water bath, surface tension caused some curvature

of the water meniscus at the periphery. Note that this lensing effect occurs even for a

perfectly flat water surface and can be easily modelled in Zemax; however extra care must

be taken to measure and account for the meniscus curvature.

To reduce curvature of the water meniscus, a large diameter of approximately 9cm

was chosen for the water bath. It was decided to measure the meniscus curvature by simply

reflecting collimated light from the top surface of the water. The resultant interferogram could

then be studied with the Zernike defocus term indicating the amount of curvature. A large

amount of time was spent aligning the water surface with the interferometer. It was not

simply a case of tilting the water bath, since the bath simply ‘moved around’ the water, with

the water surface remaining flat according to gravity. It was thus a case of aligning the entire

interferometer mount with the (level) water. After much deliberation, a satisfactorily low

number of tilt fringes were observed in the interferogram and so a measurement of the water

surface was taken. It was found to take an unreasonably large amount of time to completely

remove all tilt fringes. Since the primary interest was in determining the curvature of the

water, it was decided to ignore any rotationally invariant terms obtained in the interferogram;

the tilt fringes were accordingly ignored.

4.5 Metrology of Bausch & Lomb 21.5D IOL in Water

Prior to any measurement/alignment, it was necessary to switch on the laser, after which a

20 minute period was required to facilitate stabilization of the laser output.

The IOL, IOL platform and mirror were submerged in water, as per Figure 4.2 above.

However, before placement and alignment of the IOL stage, it was necessary to align the

mirror with the interferometer. The spherical interferometer objective was removed, and the

mirror adjusted using the three bath platform screws to obtain a null fringe condition.

The IOL was handled by the haptics and centred over a hole of diameter approx

6.5mm in the IOL platform. The hole was slightly larger than the IOL optic body to eliminate

the possibility of damaging the optic through contact with the platform. The hole was also

small enough to ensure that the optic was adequately supported, and that the IOL was not

suspended purely by the outer regions of the haptics. This therefore reduced possible effects

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of strain caused by suspension from the haptics, such as flattening of the top surface and

introduction of surface artefacts. Below the IOL platform was the aligned mirror, which

allowed the confocal position to be determined.

Alignment of the IOL was carried out by ensuring that each of the confocal, cat’s eye

and autocollimated fringe patterns were centred on the CCD camera when the

interferometer was at their respective vertical locations. Any misalignment saw the patterns

drift to one side with vertical movement of the coarse adjustment/ micrometer gauge, and

was removed with suitable adjustment of the tilt and/ or lateral translation of the IOL stage.

After alignment of the mirror and IOL, it was decided to proceed with measurements.

The micrometer screw was used to accurately move the interferometer between successive

points of interest, with the value on the micrometer scale recorded at any particular point. At

the confocal and autocollimated locations, a virtual electronic ‘Measurement Mask’ was

applied to mask out any unwanted fringing due to edge effects of the IOL and/or the

interferometer’s optical assembly itself.

To ensure that the orientation of the IOL was well-defined when measuring the

anterior and posterior surfaces, one of the non-featured haptics was marked. It was

consequently possible to not only determine which of the IOL surfaces was facing forwards,

but also the rotation of that particular surface. Between measurements, the IOL was flipped

carefully about a vertical axis through the IOL.

Unfortunately, some complications were observed while measuring the anterior and

posterior surface deviations at the autocollimated position. Firstly, a weak reflection caused

by the small change in refractive index at the water/IOL interface resulted in very low

contrast interferograms. Secondly, the water meniscus served to diverge the converging

objective beam at the autocollimated position. This resulted in a slower beam in the water,

and consequently only a small portion of the IOL surface was covered at that position.

Without the availability of a faster objective lens, it was decided to alternatively measure a

dry-packed hydrophobic IOL in air.

4.6 Metrology of Pharmacia (AMO) 17D IOL in Air

Without a faster objective lens, the unavoidable complications associated with metrology in

water necessitated measurement of a dry IOL. It was decided to measure a Pharmacia

(AMO) 17D IOL, since, due to limited availability of various IOL powers, it best matched the

most commonly implanted 21D. The IOL is shown in Figure 4.3 below. Note in particular the

‘s’, or ‘backwards s’ shaped haptics as distinct from the haptics of the Bausch & Lomb

model.

Figure 4.3. Pharmacia (AMO) 17D IOL [8].

14

Measurement of the IOL in air obviated the need for the water bath and accordingly,

the IOL stage could be made less unwieldy. A new IOL stage was constructed, as illustrated

in Figure 4.4 below.

Figure 4.4. Photograph of the prototype Meccano ‘dry’ stage.

The outer ‘legs’ can be seen to surround the mirror.

Note that the IOL platform was again covered with black tape to avoid unwanted reflections.

Once again, pre-alignment of the mirror with the interferometer was necessary and

was performed using the three vertical tip/tilt screws. The IOL stage was then placed

carefully over the mirror, taking great care not to touch it directly. The IOL was handled

carefully by the haptics and was placed over a diameter 6.5mm hole in the platform.

As was the case for wet metrology, alignment of the IOL was carried out by ensuring

that each of the confocal, cat’s eye and autocollimated fringe patterns were centred on the

CCD camera when the interferometer was at their respective vertical locations. Any

misalignment was removed with suitable adjustment of the tilt and/ or lateral translation of

the IOL stage.

After alignment of the mirror and IOL, it was decided to proceed with the dry

measurements. The micrometer screw was again used to move the interferometer between

successive points of interest, with the value on the micrometer scale recorded at any

particular point. The points of interest were located and recorded four times for each IOL

orientation. At the confocal and autocollimated locations, another (different) virtual electronic

Measurement Mask was applied to mask out any unwanted fringing.

To ensure that the orientation of the IOL was well-defined when measuring the

anterior and posterior surfaces, one of the s-shaped haptics was marked with a felt-tipped

pen. Thus, it was possible to determine which of the IOL surfaces was facing forwards, and

also the rotation of that particular surface. Between measurements, the IOL was flipped

carefully about an axis joining the meeting points of the haptics with the optic region.

Clear measurement maps were obtained at both the confocal and autocollimated

positions, with full coverage of both the anterior and posterior surfaces in the autocollimated

position. With this in mind, it was decided to begin modelling of the measured IOL

parameters in Zemax.

IOL Platform

Mirror

IOL

Mirror

Tip/Tilt

Controls

15

4.7 Zemax Ray-Tracing Analysis

Before deciding the orientation of the IOL in Zemax, it was first necessary to determine

which IOL surface was actually anterior, and which was posterior. In terms of balancing

aberrations when illuminated by collimated light, it is advantageous for the most curved

surface of a lens to face the collimated light, with the less curved side facing the focal region

[2]. Measurements of the IOL surfaces indicated that one surface was indeed more curved

that the other. This surface was initially deemed the anterior surface since, when implanted

in the eye, the anterior lens surface is facing (almost) collimated light. Note that the light is

not actually collimated, due to corneal refraction; however, it will suffice to assume so in this

approximation. Furthermore, it seemed reasonable to assume that wave error in double pass

through the lens would exhibit less spherical aberration when the anterior surface faced the

collimated light. Indeed, it was found experimentally that least spherical aberration was

observed when the preliminarily appointed anterior surface faced the collimated light. With

these evidences, it was decided to model the appointed anterior surface as facing the

collimated light in Zemax.

It was noted that the experimentally determined apical IOL thickness was an

apparent thickness caused by refraction at the air/IOL interface. It was therefore necessary

to convert this to a real distance using Zemax. However, it was not simply a case of

multiplying by the refractive index of the IOL since the surface sag needed to be taken into

account.

The measurement maps obtained in the µShape® software were resolved into the

first eleven Zernike coefficients, up to and including spherical aberration. The coefficients

were exported to a text file after each successful interferometric measurement. Analysis of

the text file indicated that the µShape® convention for Zernike polynomials differed from that

in Zemax. It was therefore necessary to rearrange and normalise the exported µShape®

Zernike coefficients before subsequent importation to Zemax.

Table 4.1 below indicates the discrepancy between the two conventions.

µShape® Zemax

Coefficient Polynomial Description Polynomial Description

1 1 1

2

3

4

5

6

7

8

9

10

11

Table 4.1. Indication of the discrepancy between conventions adopted in µShape® and Zemax

16

The anterior and posterior IOL surfaces were modelled as ‘Zernike standard sag’

surfaces in Zemax. This option allowed definition of the optical characteristics of both

surfaces in terms of their standard (rearranged and normalised) Zernike coefficients

obtained from the µShape® software. The interferometer µLens 15/43 objective was

modelled as a paraxial lens. In Zemax, “the paraxial surface acts as an ideal thin lens” [9].

To simulate double pass wave aberration of the IOL, it was necessary to model the

system in the confocal arrangement i.e. when the emergent light was collimated. The

problem of optimising the objective-IOL distance for collimated emergent light was solved

using a second paraxial lens directly behind the IOL. The distance between this second

paraxial lens and the image plane, and its focal length were fixed to 100mm (the default

paraxial lens focal length in Zemax is 100mm). Now, the image plane RMS spot size is

clearly minimised if collimated light is incident on the paraxial lens, since that is the definition

of a lens’ focal length. Since the paraxial lens is placed directly after the IOL, it is therefore

clear that the minimum image plane RMS spot size occurs for collimated light emerging from

the IOL. The optimal objective-IOL distance can thus be found by minimising the image

plane RMS spot size. This was performed using a Zemax merit function. The merit function

is, after [10], “a numerical representation of how closely an optical system meets a specified

set of goals”. In this case, the goal is minimal image plane RMS spot size with the objective-

IOL distance as the single variable. After optimisation, the technique can be qualitatively

verified by ignoring the second paraxial lens; collimated light should emerge from the IOL.

The collimated light was then reflected by a MIRROR surface type. In Zemax, after

reflection from a mirror, surfaces are modelled a second time, as though the light propagates

through the mirror, with distances entered as negative values. Extra care must be taken,

however, when entering radii of curvature after the mirror element. “The convention is that a

radius is positive if the centre of curvature is to the right (a positive distance along the local z

axis) from the surface vertex, and negative if the centre of curvature is to the left (a negative

distance along the local z axis) from the surface vertex. This is true independent of the

number of mirrors in the system” [11]. Thus, on reflection from the mirror, the radii are not

negated as with distances. Figure 4.5 below is a 3D-render of the experimental setup, as

modelled in Zemax; Figure 4.6 is a 2D side-view of the Zemax model. Note that the light

does not appear to exactly re-trace its path through the IOL. This was an un-avoidable effect

caused by the spherical aberration induced in single pass through the IOL and was not

simply an error in objective-IOL distance optimisation. Note also that the IOL-mirror distance

was approximated experimentally by photographing a ruler beside the apparatus.

17

Figure 4.5. 3D-rendered simulation of the experimental setup.

Figure 4.6. 2D side-view of the Zemax double pass model.

The objective beam (left) enters the IOL at the confocal position and emerges collimated, to be retro-reflected

from the mirror (right). The beam then passes back through the IOL to the image plane (centre). Note

that the posterior surface is facing to the left, with the anterior surface facing to the right.

The next step was to define the surfaces in terms of their Zernike coefficients.

Particular difficulty arose when entering those coefficients for the first anterior surface (which

faced to the right) and the second anterior and posterior surfaces after the mirror. It was

noted that when measuring a surface with the interferometer, that surface ‘faced’ the

interferometer. However, when modelling the first anterior surface in Zemax, the light

entered from the ‘back’ of that surface. Thus, the sign of all coefficients required inversion to

account for looking at the back of the surface, with certain coefficients requiring inversion to

account for anti-symmetry about the vertical axis [2]. Taking these two factors into account,

coefficients three, four, six, seven, nine and eleven were inverted for the anterior surface

(using the Zemax naming convention). Further difficulty was encountered when entering the

coefficients for the surfaces after the mirror, since those post-mirror distances are negative.

It was decided to use the original anterior coefficients since the light faced that surface, with

the posterior coefficients inverted accordingly, with all coefficients inverted again to account

for post-mirror distances being negative. Finally, the image plane was modelled at the focal

18

point of the objective lens, where the wave aberration in double transmission through the

lens could be studied.

After modelling the system in double pass, it was noted that the coefficient negation

system could be erroneous, and that any slight variation of coefficients was time consuming;

a simpler model was therefore sought. It was remarked that the wave aberration induced in

double pass through a system is simply double that induced in single pass [2]. Accordingly,

the system could be modelled in single pass, with the resultant wave aberration simply

doubled to simulate double pass. Moreover, it was noted that the FISBA µShape® software

outputs the results of double pass measurements as single pass wave aberration errors [12].

Therefore, in any case, it was necessary to only model half of the experimental setup i.e.

reflection from the mirror and the subsequent second pass through the IOL did not have to

be modelled.

The mirror and second IOL surfaces were thus removed. As before, the objective-IOL

distance was optimised to minimise image plane RMS spot size when focussing using the

second paraxial lens. The method was again qualitatively checked by temporarily ignoring

the paraxial lens; the emergent light was indeed collimated. This time, however, the second

paraxial lens remained in place to focus the collimated emergent light onto the image plane,

with the single pass wave aberration errors viewed there; see Figure 4.7 below.

Figure 4.7. 2D side-view of the Zemax single pass model.

The objective beam (left) enters the IOL at the confocal position and emerges collimated. It is then

focussed onto the image plane (right) by a paraxial lens placed directly after the IOL. Note

that the posterior surface is facing to the left, with the anterior surface facing to the right.

19

5. Results


The sixteen measurement values for the retro-reflective mirror were found to be highly

consistent. The surface peak-to-valley and root mean square (RMS) values are quoted as a

fraction of the wavelength of the laser light ( =632.8nm). The errors were calculated as the

standard error of the mean.


Characterisation of the water meniscus lensing effect was found to be problematic. The

water meniscus was found to fluctuate constantly, even after extended periods with no noise

or movement in the laboratory. Figure 5.1 is an example interferogram of the water

meniscus.

Figure 5.1. Interferogram of the water meniscus.

Note the false ripples on the map due to movement of the water meniscus.


A series of measurements were taken for the Bausch & Lomb IOL in the confocal position.

The IOL was oriented with the anterior surface facing the collimated light (toward the mirror).

For each measurement, the corresponding surface deviation map and Zernike polynomials

were saved to disk. At the end of the measurement trial, the surface deviation maps were

studied to see which gave the most complete coverage, or which were missing the least data

points, if any. Data points were missed in the interferogram if the image intensity at that point

20

was not high enough and occurred, for example, if a dust particle was present. Figure 5.2

below represents the best map obtained.

Figure 5.2. Confocal interferogram of Bausch & Lomb 21D IOL in water.

The image on the left is the interferogram as seen on the CCD camera. The image

on the right is the interferogram as interpreted by µShape®.

As already stated, the water meniscus caused divergence of the objective beam at the

autocollimated position and hence the beam was slower in the water. The autocollimated

measurement maps were accordingly small. They therefore only represent a small portion of

the surface near the centre and do not represent the surface as a whole. Consequently, they

are deemed useless and are not included here.


The same procedure was carried out for the dry as for the wet measurements, whereby

several measurements were taken for each of the positions of interest. In this case, two

different sets of maps were obtained for the IOL in the autocollimated position, one set for

each lens surface facing the mirror. As previously outlined, it was reasoned that the anterior

surface should be facing the collimated light (the mirror) when the maps exhibited the least

spherical aberration. Subsequent analysis of the Zernike coefficients indicated that one of

the orientations did indeed exhibit less spherical aberration; thus, it was decided to use

those maps as the wave aberration of the lens, with the surface facing the mirror deemed

the anterior surface. Figure 5.3 is the best obtained confocal interferogram for that lens

orientation. To the left of the software map is the interferogram as seen on the CCD camera,

shown here again for completeness.

21

Figure 5.3. Confocal interferogram of Pharmacia 17D IOL in air.

The image on the left is the interferogram as seen on the CCD camera. The image

on the right is the interferogram as interpreted by µShape®.

The anterior and posterior surfaces were completely filled by the objective beam at

the autocollimated position, in strong contrast to the same position in the wet measurements.

Several measurements of both surfaces were again taken, with the fullest map chosen as

the representative measurement; they are shown in Figure 5.4 and Figure 5.5 below. The

interferograms as seen on the CCD are not shown here, since they do not contribute

anything in particular to the discussion.

Figure 5.4. Autocollimated interferogram of Pharmacia 17D IOL anterior surface in air.

22

Figure 5.5. Autocollimated interferogram of Pharmacia 17D IOL posterior surface in air.

The micrometer reading was recorded for each of the confocal, top and bottom cat’s

eyes and the autocollimated positions for each IOL orientation. The procedure was carried

out four times, with the values subsequently used to calculate back focal lengths, radii of

curvature and apparent apical thicknesses. All values are included in Table 5.1 below. Note

that the error values were calculated as the standard error of the mean.

It was deemed necessary to only determine the real apical thickness for one lens

orientation and so only that thickness is included; see Section 6.6 for a discussion on its

error. Its value was calculated as:

Anterior surface

Posterior Surface

Trial # Back Focal Length Radius Apical Thickness Back Focal Length Radius Apical Thickness

1 18.020 15.530 0.580 17.950 21.865 0.575

2 18.020 15.545 0.570 17.990 21.905 0.570

3 17.975 15.575 0.575 17.960 21.890 0.570

4 17.965 15.625 0.580 17.970 21.870 0.570

Average 17.995 15.569 0.576 17.968 21.883 0.571

Error 0.015 0.021 0.002 0.009 0.009 0.001

Table 5.1. Experimentally measured physical parameters of the 17D IOL.


The rearranged and normalised Zernike coefficients obtained from the µShape® software for

the anterior and posterior surfaces were entered into Zemax, as outlined above. The

resultant surfaces are shown below beside the experimental maps, for comparison, in Figure

5.6 and Figure 5.7.

23

Figure 5.6. Comparison of modelled and experimental anterior 17D IOL surface.

The experimental map is shown on the left, with the resultant Zemax model on the right.

Figure 5.7. Comparison of modelled and experimental posterior 17D IOL surface.

Again, the experimental map is shown on the left, with the resultant Zemax model on the right.

After definition of the anterior and posterior surfaces, the wave aberration in transmission

through the IOL was modelled. The simulated interferogram is compared to the experimental

interferogram in Figure 5.8 below.

Figure 5.8. Comparison of modelled and experimental 17D IOL wave aberration.

24

The values and percentage differences for the respective experimental and modelled peak-

to-valley and root mean square errors are listed in Table 5.1 below. The wavefront errors are

quoted as a fraction of . ( =632.8nm)

Peak-to-valley Root mean square

Experimental 1.99 0.39

Modelled 1.62 0.40

% Difference 18.6% 2.5%

Table 5.1. List of experimental vs modelled total wavefront errors, including % difference.

Figure 5.9 and Figure 5.10 below are screenshots of the final Zemax user interface showing

lens editor fields, and total wave aberration and 2D layout, respectively. The lens editors are

those in which the lens data parameters were entered.

Figure 5.9. Final Zemax user-interface showing lens editor fields.

Figure 5.10. Final Zemax user-interface showing total wave aberration and 2D layout.

25

6. Discussion.

6.1 Design and Construction of the IOL Stage

The design and construction of the IOL stage required a considerable amount of effort and

time. The particular difficulty arose in allowing independent tip, tilt and translation controls for

both the IOL and the mirror. The choice of potentiometer-type screws for the bath tip/tilt table

may seem trivial, or even ridiculous; however it was only through the use of such random

components that said table could have been built.

The initial Linos stage was discarded since the rod suspending the platform entered

the water too close to where the IOL would be located. Moreover, the rod was not symmetric

about the IOL location, so the meniscus would not only have been highly curved, but it would

also have been anti-symmetric; this anti-symmetric meniscus would have been exceedingly

difficult to measure and account for in the Zemax model. Thus, it was decided to opt for the

Meccano model, since the platform supports entered the water symmetrically much farther

from the IOL location. The Meccano stage also allowed greater customisation possibilities.

Furthermore, the IOL stage had to be designed such that it could be removed and

replaced without disturbing the mirror. This was useful for example when pre-aligning the

mirror with the interferometer. In the end, a satisfactory prototype was designed which

allowed all of the above and also minimised the IOL-mirror distance. Minimum IOL-mirror

distance was necessary to reduce errors due to mirror misalignment in the light re-tracing its

path back through the IOL.


Measurements of the retro-reflective mirror were found to be highly consistent, evidenced in

the values for the standard error of the mean. The mirror was measured as having zero RMS

surface error. However, it is non-physical to assume that the RMS surface error was exactly

zero; it was simply zero within the specified number of decimal places in the µShape®

software. It seemed reasonable to assume that the mirror could be so flat, since it had a

relatively large diameter and ample thickness. It was noted that the manufacture of optical

flats is far easier for those which are relatively large; thus, that sizeable mirror could be

manufactured to a high degree of flatness.

As previously stated, it was not possible to simultaneously calibrate the

interferometer for measurement of plane and spherical surfaces. It was therefore necessary

to include the mirror surface error in an error budget for the double pass wave aberration

errors. Owing to the mirror RMS surface error figure of zero, it was decided to simply ignore

any mirror surface error, since the aberrations introduced in double pass through the IOL

would be an order of magnitude greater in any case.


As previously stated, characterisation of the water meniscus was found to be highly

problematic. The appeal of interferometry as a measurement technique is in its ability to

resolve extremely small distances. However, without the use of sophisticated self-correcting

interferometers, this sensitive technique is highly susceptible to mechanical vibration. Thus,

26

the sensitivity is self perpetuating. It was observed that the movement of cars outside the

building and the closing of doors in the corridor caused turbulent meniscus motion. It is

important to note that the meniscus appeared perfectly still to the eye. However, a single

fringe on the interferogram represented surface error of one wavelength of light. Accordingly,

surface motion of just ~700nm would cause a fringe to continuously drift across the

interferogram, rendering it unreadable.

The effects of meniscus motion can be seen in Figure 5.1. The µShape® software

phase-unwrapping algorithm can be seen to have broken down in regions where motion was

excessive. In regions where the interferogram was successfully captured, the measurement

map is characterised by a rippling effect incorrectly introduced by the meniscus motion. This

rippling effect erroneously introduces large amounts of higher-order Zernike terms in the

map and so the map is deemed futile. Furthermore, as with the mirror surface error, the

small peak-to-valley and RMS values of 0.26 and 0.02 (expressed as a fraction of

=632.8nm) would be an order of magnitude less than the IOL wave aberration errors in any

instance.


The high-quality double pass interferogram of the 21.5D IOL in water is shown in Figure 5.2.

It represents a breakthrough in IOL metrology which was previously thought impossible, due

to the inherent complications in measurement at the confocal position. A very slight amount

of shading is barely visible in the CCD interferogram on the left-hand side. This shading,

which is characteristic of an astigmatic wavefront, was clearly resolved by the µShape®

software in the image to the right. Thus, the phase-shifting interferometric technique is highly

accurate and is capable of resolving features that are scarcely visible to the human eye.

The choice of water as the submersion liquid is a contentious issue. It is important to

note that this project was concerned in particular with the proof of the concept of double

pass IOL metrology in water. The main focus was not in obtaining quantitative results for the

exact determination of IOL aberration, but was in qualitatively confirming a metrology that

was previously thought impossible. However, the choice of water is still reasonable [2].

Water is readily available, its index of refraction has been well characterised for a range of

wavelengths and temperatures and it is physicochemically representative of the in situ

environment [13-15]. It was noted that the use of balanced salt solution (BSS) would have

been preferable since it would better mimic the in situ environment; however, lack thereof

rendered its employment impossible.

The main limiting factor to the wet measurement technique was the small size of the

obtained autocollimated maps, due to diversion of the objective beam at the air/water

interface. According to Snell’s law [16], light bends toward the normal at the point of

incidence when passing from a rarer to denser medium. With the interferometer at the

autocollimated position, the objective beam is converging at the air/water interface, thus the

water meniscus serves to bend the light rays away from the optical axis. With the

interferometer at the confocal position, the objective beam is diverging and so the meniscus

serves to bend the light rays toward the optical axis. An illustration of the effect is shown in

Figure 6.1 below. Thus, at the autocollimated position, the objective beam was accordingly

slower and hence poor coverage of the IOL surface resulted.

27

Figure 6.1. Examples of the lensing effect of the water meniscus.

Shown is a converging beam (left) and

diverging beam (right). The water was modelled as having a refractive index of 1.33.

Due to time constraints, it was not possible to obtain a faster objective of such quality

as the µLens 15/43. Without availability of a faster beam, measurements of IOL surface

deviation were limited to only a small portion in the central region of the surface. It is

important to note that the Zernike polynomials are orthogonal on the unit circle. Hence, when

describing particular surfaces, they are meaningful only when used across the same

physical size across all surfaces i.e. they cannot be extrapolated to account for larger

diameters. The particular problem associated with the small autocollimated measurement

maps was that their Zernike coefficients were useful only for those small sizes. This

therefore also rendered useless the larger high-quality double pass measurement maps.

Moreover, the obtainment of high-quality measurement maps was hindered by

distinctively low-contrast CCD interferograms. This lack in contrast was attributable to the

low-intensity reflection from the water/IOL interface due to the small refractive index

differential there. The amount of light reflected from the interface between two media can be

calculated using the fresnel reflection coefficients for s and p polarised light, respectively

[17]. It was attempted to improve the map acquisition performance by increasing the

integration (or exposure) time of the CCD camera. However, increasing the exposure made

the system more susceptible to error due to mechanical vibration.

Note that these adverse effects also plagued the previously performed experimental

measurements of surface deviation [18]. Consequently, it was decided to measure a dry IOL

in air.


Initially, it was decided to attempt the wet measurements since it was anticipated that they

would be hardest to perform, and indeed they were. Furthermore, as previously outlined, the

Bausch & Lomb 21.5D IOL best matched the most commonly implanted 21D.

However, measurement of an IOL submerged in water was not pivotal to the success

of the experiment; measurement of a dry IOL would prove just as useful. The downside of

dry IOL measurements in this case, however, was the fact that the best matched 17D did not

very closely match the most commonly implanted 21D. This minor disadvantage could easily

be overcome by simply acquiring a 21D IOL. However, such an IOL was not available at

time of experimentation.

Air

Water Meniscus

Air

Water Meniscus

Water Water

28

The high-quality measurement maps obtained, visible in Figure 5.3, Figure 5.4 and

Figure 5.5, owe to the relatively large refractive index differential at the air/IOL interface.

Prior to measurement of the IOL, it was anticipated that a large amount of spherical

aberration would be present in the confocal position. This would result in a possibly

indeterminate exact null fringe condition, since spherical aberration serves to elongate the

focal region into a paraxial and marginal focus. i.e. there is no single definite focal point.

Thus, there would be a relatively large distance over which the confocal position could be

defined. Fortunately, excessive spherical aberration was not observed and so the confocal

position was relatively well-defined.

It can also be argued that measurement of the dry IOL in air is not representative of

the in situ environment. The IOL material may absorb some of the ocular fluid and in doing

so, change its physical characteristics. However, an experiment previously performed by the

author indicated that the IOL’s physics characteristics did not change when submerged in

water, even for extended periods. The minimal error values of all measured physical

parameters also indicate that the technique was highly consistent, even for just four

measurement trials. Thus, measurement in air was accordingly acceptable.


It is clear from Figure 5.6 and Figure 5.7 that the Zemax models faithfully recreated both the

anterior and posterior IOL surface deviations.

It is worth noting that the real apical thickness calculated in Zemax is not quoted with

any error. This does not mean that the value was calculated with infinite uncertainty. Instead,

the analysis of its error was simply omitted, since it was deemed unnecessary in this proof-

of-concept model. Its calculation would be performed by taking the error of the experimental

apparent thickness and using Zemax to compute the corresponding error of the real

thickness.

After calculation of the real apical IOL thickness, the anterior and posterior surfaces

were modelled to qualitatively determine the total wave aberration in transmission through

this modelled IOL. Figure 5.8 illustrates the agreement of the experimental and modelled

total wavefront errors. In comparing the two sets of data, some unexpected results were

observed. In particular, the peak-to-valley (PV), root mean square (RMS) and spherical

aberration errors of the modelled wavefront were considerably larger than the experimental

wavefront errors. The following are proposed as the reasons for this discrepancy.

Firstly, at the confocal position, it was initially assumed that light passed through the

entire optic region to be retro-reflected from the mirror. However, it is assessed that this

assumption is not correct. Edge effects at the optic periphery will cause any light rays

passing through there to be diverted largely and so these rays will not be retro-reflected by

the mirror; consequently, they do not form part of the interferogram. Thus, only a smaller

region of the optic is represented by the confocal interferogram. When the diameters of the

IOL surfaces were reduced in the Zemax model, the resultant PV, RMS and spherical

aberration values were found to decrease accordingly, in closer agreement with the

experimental wavefront.

Secondly, the posterior IOL surface was found to be slightly aspheric. It was aspheric

in the sense that it was difficult to obtain an exact null fringe condition at the autocollimated

position. The observed effect was similar to a spherically aberrated wavefront focussing on

an image plane, where the definite focal point is elongated between a paraxial and marginal

focus. In this case, the null fringe condition was found to be elongated between a focal

region for the paraxial rays and a focal region for the marginal rays. Therefore, a certain

29

error was present in the determination of the posterior radius of curvature. When the

posterior radius of curvature was increased slightly to a value of 23.5mm, the modelled

wavefront errors were found to more closely agree with the experimental values.

Furthermore, as previously stated, the IOL was observed to exhibit less spherical

aberration in double pass than was anticipated. Therefore, perhaps the IOL is designed for

minimal induction of spherical aberration, with the internal lens material and aspheric surface

acting to cancel it out. With the reduction in modelled lens diameter and increase in posterior

radius of curvature, the modelled RMS surface error is within just 2.5% of the experimental

value; thus the two are in relatively close agreement.

At this initial proof-of-concept stage with many undetermined variables, it is impossible to

ascertain as to what is causing the discrepancy between experiment and theory. If all

variables were removed, then the discrepancy could in fact be directly attributed to internal

lens inhomogeneities. However, without such removal of inherent variables, it is not possible

to confidently determine the source of discrepancy.

30

7. Conclusion

In conclusion, the concept of measuring double pass wave aberration in transmission

through an IOL has been proven. This previously deemed impossible measurement is not

only repeatable, but results obtained can be subsequently confirmed with software ray-

tracing analysis. The particular success of this project was in the design and development of

individual tip and tilt controls for the IOL and retro-reflective mirror.

A whole gamut of IOL types can be characterised through measurement in the wet or

dry. Measurement with the IOL submerged in water is not pivotal to experimental success;

however, it is more representative of the in situ environment. With this in mind, further work

performed in this area would employ balanced salt solution (BSS) as the submersion liquid.

The software confirmation of dry experimental measurements has been performed.

Particular care must be taken in future work to better determine the extent to which the

objective beam covers the IOL in both confocal and autocollimated measurements. It was

observed that incorrectly large coverage assumptions are highly erroneous. As for wet

measurements, it is clear that future success will necessitate the use of a faster high-quality

objective beam. Only then will the surfaces of higher-powered IOLs be completely covered

at the autocollimated position.

Finally, with future successful elimination of variables, the discrepancy between

experimentally and theoretically determined wavefront errrors can be attributed to internal

IOL material inhomogeneity.

31

8. Acknowledgements

The author wishes to acknowledge the expert advice and consultation of Dr. Alexander Goncharov and the consultation of Matt Sheehan. Worthy of acknowledgement also is the time spent bouncing physics trivia off my good friends Adam Beatty, Colm Lynch, Marieke van der Putten and other classmates over the occasional pint of Guinness. In addition, to my brother Brian who tirelessly proof reads all my documents. Without them, I would scarcely have survived.

9. References

[1] “Bausch & Lomb – MICS Platform IOL – Inheriting the best”. Available at:

http://millennium.micsplatform.com/mics-iol_inheriting_EN.php. (Accessed: 20 March 2012).

[2] Goncharov, A. V. (2012) Personal communication.

[3] 1. R. Bellucci, S. Morselli, and P. Piers. (2004) “Comparison of wavefront aberrations and

optical quality of eyes implanted with five different intraocular lenses,” J. Refract. Surg. Vol.

20, pp. 297-306.

[4] Pierscionek, B., Green, R. J. and Dolgobrodov, S. G. (2002) “Retinal images seen

through a cataracteous lens modelled as a phase-aberrating screen”. J. Opt. Soc. Am. A. 19,

pp. 1491-1500.

[5] E. Goodwin and J. Wyant (2006) Field guide to Interferometric Optical Testing. SPIE

press. Chapter 1, page 2.

[6] E. Goodwin and J. Wyant (2006) Field guide to Interferometric Optical Testing. SPIE

press. Chapter 3, page 24.

[7] Zernike, F. (1934) "Beugungstheorie des Schneidenverfahrens und seiner verbesserten

Form, der Phasenkontrastmethode". Physica 1, p. 689.

[8] Davison, J.A. “Endothelial cell damage, viscoelastics, anterior capsular tears, and

sutureless closure”. Available at: http://80.36.73.149/almacen/medicina/oftalmologia/

enciclopedias/duane/pages/v6/v6c011.html (Accessed: 22 March 2012).

[9] Zemax user manual. p. 376.



[12] FISBA Optik HR Interferometer user manual. Section 6.7.5.

32

[13] Thormählen, I., Straub, J. And Grigull, U. (1985) “Refractive index of water and its

dependence on wavelength, temperature and density”. J. Phys. Chem. Ref. Data. 14 (4). pp.

941-942.

[14] Schiebener, P., Straub, J., Levelt Sengers, J. M. H. and Gallagher, J. S. (1990)

“Refractive index of water and steam as a function of wavelength, temperature and density”.

J. Phys. Chem. Ref. Data. 19 (3). p. 708.

[15] Harvey, A. H., Gallagher, J. S. and Levelt Sengers, J. M. H. (1998) “Revised formulation

for the refractive index of water and steam as a function of wavelength, temperature and

density”. J. Phys. Chem. Ref. Data. 27 (4). p. 773.

[16] Hecht, E. (2002) Optics (4th ed.). Addison Wesley. Chapter 4. p101.

[17] Hecht, E. (2002) Optics. 4ed. Addison Wesley. Chapter 4.

[18] Sheehan, M. (2012). Private communication.

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