reading fields of magnifying loupes

1820 J. Opt. Soc. Am. A/Vol. 4, No. 9/September 1987

Reading fields of magnifying loupes

Frans J. J. Blommaert and Johan J. Neve

Institute for Perception Research, Den Dolech 2, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Received May 23, 1986; accepted April 1, 1987

For the purpose of understanding the influence of the use of magnifying loupes on the reading process, the readingfield is a relevant concept. Three possible reading fields are distinguished: the monocular reading field, thebinocular reading field, and the composite reading field. Theoretical expressions for the widths of reading fields arederived as a function of the physical parameters of the loupe and the geometry of the reading situation. Variation ofreading-field width as a function of magnification is illustrated. For verification, experimentally determinedreading-field widths were compared with the theoretical ones. There were small systematic deviations, probablycaused by achromatic aberrations. In order to learn about the strategies that subjects use when reading with the aidof a loupe, loupe displacement was measured while subjects read text under conditions that provided a variety ofreading-field widths. It was found that individual subjects use different strategies (i.e., they use different reading-field widths).

INTRODUCTION

This paper deals with the process of reading with a loupe, orreading magnifier. Throughout this paper we will use theword loupe, by which we mean any positive lens that is usedfor enlarging the retinal image of an object (especially text)and that can be used as a hand magnifier. A fundamentalapproach of this topic should include an examination ofoptical, psychological, and ophthalmic aspects of readingwith a loupe. From a review of the literature on readingmagnifiers, we learned that most of the papers on this sub-ject are written from an ophthalmic point of view. Thesepapers often deal with either the classification of optical aidsor procedures for prescribing them to the visually im-paired.1-6 Among the psychological aspects of reading witha loupe are disturbances of the reading process that occur asa result of magnification and limited reading-field width.7

The effect of these disturbances, such as the influence of textmagnification and the influence of loupe movements on eyemovements, has not been properly investigated until now, asfar as we know.

If the psychological and ophthalmic aspects are to bestudied, the physical properties must first be understood.Therefore, as a start, we focused our attention in an earlierpaper on three physical quantities that seem to be of majorimportance, viz., the magnification of the retinal image, thedistance between the virtual image and the eyes, and thereading field of the loupe.8 Together with lens aberrations,these factors determine the retinal image and thus the imag-ing properties of a loupe.

In this paper we report on the reading-field width as afunction of the geometrical position in which the loupe isused. Apart from the work of Bouma et al.,7 the scarceliterature information on this subject deals with the monoc-ular reading field. Linksz, 1 for instance, gives only the theo-retical expression for this field. The difference between themonocular field of view for foveal vision of the rotating eyeand that for peripheral vision of the stationary eye is pointedout by Westheimer. 9 Sloan and Jablonski' 0 show data onthe monocular fields for different magnifiers, although the

geometrical positions of the loupes have been chosen ratherunrealistically in their study, i.e., loupes used as eyeglasses.Bouma et al.7 show experimental data on the magnificationfactor versus the binocular reading-field width for a numberof commercially available loupes.

We distinguish three different reading fields: the monoc-ular reading field, which is the horizontal size of the unmag-nified text portion that can be seen through a loupe with oneeye; the binocular reading field, defined as the overlappingpart of the two separate monocular fields; and finally thecomposite reading field, which is a mixture of both. Thevariations of these fields as a function of the geometricalposition in which the loupe is used are calculated theoreti-cally and compared with experimental data on the fieldwidth obtained in a preliminary experiment.

When reading through a loupe, one may use differentstrategies for integrating loupe magnification and loupemovements into the reading process. For instance, any oneof the three reading fields may be used, or subjects may findit convenient to use only the middle part of the loupe forreading. In order to gain more insight into what strategiesare being used, loupe movements made by six subjects whilereading texts were determined, both when subjects werereading with one eye and when they were reading with twoeyes. The results of the experiment show clearly that not allsubjects use the same reading field when reading through aloupe with both eyes.

THEORETICAL READING FIELDS

Since magnifying glasses have edges, the magnified part ofan object is limited in height and width. When the observerlooks through a loupe with both eyes, two partially overlap-ping images of the object may be seen: one with the left eyeand one with the right eye (see Fig. 1).

Therefore observers in principle have the possibility ofusing the information contained in both image fields. First,one may use either only the left or only the right (monocular)reading field. This might be expected if the reader has a

0740-3232/87/091820-11$02.00 © 1987 Optical Society of America

F. J. J. Blommaert and J. J. Neve

Vol. 4, No. 9/September 1987/J. Opt. Soc. Am. A 1821

text

L_H- v -4i&< a -4

Fig. 1. Definitions of the monocular (Wi), binocular (Wb), andcomposite (W,) reading fields. WR and WmL indicate the monocu-lar fields for the right and the left eyes, respectively. The parame-ters v, a, L, and D, denote the object-to-loupe distance, the eye-to-loupe distance, the loupe width, and the distance between the twoeye pupils, respectively.

dominant eye. Second, both reading fields may be seenbinocularly, i.e., when both reading fields are seen fused,while one experiences them as only a single image. A thirdpossibility (henceforward referred to as the composite read-ing field) is that the reader uses the information of the twomonocular fields alternately; i.e., appropriate text parts areviewed with the one eye, whereas other parts are viewed withthe other eye, and some parts may even be viewed binocular-ly. In this way the reader may make efficient use of theavailable information contained in both images.

Since it is not yet clear which field is used during loupereading, we traced the variation of the different fields, themonocular field Wm, the binocular field Wb, and the compos-ite field Wc, as a function of the loupe properties (focallength and width) and the geometrical position (eye-to-loupe distance and object-to-loupe distance) in which theloupe is used. For the stationary eye on the optic axis, onemay derive for the monocular reading field (see Appendix A)that

(1)

where Wm is the width of the monocular reading field, v isthe object-to-loupe distance, a is the eye-to-loupe distance, fis the focal length, and L is the loupe width.

The eye-to-loupe distance a for the stationary eye is moreprecisely defined here as the distance from the second nodalpoint of the eye to the principal plane of the loupe.

The binocular reading field equals the overlapping part ofthe separate monocular ones. It can be derived (see Appen-dix A) that

Wb= Wm -- D,a(2)

where DP is the distance between the two eye pupils.The composite reading field by definition equals the total

part of the object that can be seen through a loupe by usingboth eyes. It is clear from Fig. 1 that

Wc = 2Wm Wb. (3)

In order to illustrate the variation in reading-field width

as a function of the geometrical position, the binocular read-ing field has been calculated as a function of the object-to-loupe distance v and some specific values for a, as shown inFig. 2. In this calculation a practical numerical value for thewidth of a loupe of 10 D (f = 10 cm) was taken to be 6.5 cm(this choice will be explained further on).

From Fig. 2 it can be seen that the binocular reading fieldvaries largely with the geometrical position in which theloupe is used. Especially for v = 10 cm, that is, if the objectis situated in the focal plane, the binocular reading field mayvary from zero to infinity, depending on the eye-to-loupedistance a. For small a values, Wb will be large, whereas forlarge a values, the reading field will decrease to very smallvalues. When the loupe is used in such a way that thevirtual image is formed at a point closer to the eyes than thenear point of accommodation (-b + a < 25 cm), the retinalimage is blurred and thus becomes inferior with respect tovisibility. Therefore we regarded accommodation for dis-tances smaller than 25 cm to be impossible. This assump-tion leads to the hatched areas in Fig. 2, which are notallowed when sharp retinal imaging is demanded. Thedashed curve in Fig. 2 corresponds to an eye-to-image dis-tance -b + a of 25 cm, where -b is the (virtual) image-to-loupe distance and where the distance of 25 cm correspondsto a near point of accommodation of a 45-year-old human.1

The curve is obtained by using the thin-lens equation (A4)(see Appendix A).

From Eqs. (1)-(3) it can be seen that the width of a loupeshould be known in order to calculate the reading-fieldwidths. From physical constraints it follows that the widthof a loupe is not unlimited and will depend on the focallength of the loupe. In order to gain some insight into thismatter, we plotted the widths L of 29 commercially available

3-W*0

V(U.

to0C

EI

f

image to eye distance-b+a=25cm

lI I

o0 4/ / / /7/7 Z /F,7t10 5 10

, v(cm)object distance

Fig. 2. The theoretical binocular reading field Wb as a function ofthe object-to-loupe distance v for a loupe with f = 10 cm. Thestraight lines have been calculated for some values of the eye-to-loupe distance a (in centimeters). The dashed curve corresponds toan eye-to-image distance -b + a of 25 cm. The hatched areas arenot allowed (see the text).


VW.=(i+"- L,a f)


E? ZL

21f-J

0.a 100

00 10 20

focal distance f (cm) -Fig. 3. The width L of 29 commercially available loupes, plotted asa function of the focal length f. The straight line obeys the expres-sion L = f/4 + 4 (in centimeters).

09

0

0)

32

16

8

4

2

0 0 1 2 4 8

retinal magnification M25

Fig. 4. Theoretical field width W of the unmagnified text portionthat can be viewed binocularly, monocularly, and with both eyesalternately, as a function of the magnification M2 5. The curves havebeen calculated for a fixed ratio v/f of 0.75 and for an eye-to-loupedistance a of 15 cm. As is indicated in the figure, the focal distance fvaries monotonically from large values on the left-hand side to smallvalues on the right-hand side. The pupil distance DP was taken tobe 6 cm.

loupes as a function of their focal distances f, as shown in Fig.3.

The straight line through the data points is fitted by theeye and obeys the equation (in centimeters)

L f + 4. (4)4

This relation was used to investigate the variation of thethree different reading fields as a function of magnification.For the magnification of a loupe it can be derived (see Ap-pendix A) that

M25 = 25v + a - avif (5)

where M25 is the commonly used magnification factor calcu-lated with respect to an unmagnified object viewed from adistance of 25 cm (see, for example, Ref. 5).

In order to illustrate the difference among the three read-ing fields, we plotted these fields separately as functions ofM25 in Fig. 4.

For clarity, the object-to-loupe distance was fixed at 0.75times the focal length, and the eye-to-loupe distance a waschosen to be 15 cm. These values are close to what subjectsactually seem to prefer, although they may not be optimalfor all loupes. Furthermore, the distance Dp between thetwo eyes was taken to be 6 cm.

It can be seen from Fig. 4 that the theoretical readingfields decrease strongly with increasing magnification. On adouble-logarithmic scale, the values of the three readingfields as a function of the magnification can be approximat-ed by straight lines with slopes -2, -1.5, and -1.5 for thebinocular, monocular and composite fields, respectively.The slope of -2 for the binocular field versus magnificationis in accordance with the experimental results of Bouma etal.7 Values for a and v differing from a = 15 cm and v = 0.75fwould yield combinations of magnification and field widthdifferent from the ones shown here. The general tendency,

g \49; m~~vea

stationary eye

I0 a r

text loupe fovearotating eye

Fig. 5. Comparison of the reading-field widths for peripheral vi-sion of a stationary eye (1/2yi) and for foveal vision of a rotating eye(

1/2Y2)- (Top) The nodal point N of the eye is the reference point for

the eye-to-loupe distance a. (Bottom) The center of rotation C isthe reference point for the eye-to-loupe distance ar in the secondcase. The reading-field width is always larger for peripheral visionthan for foveal vision, since a is always smaller than a,.

CI

I

U

I I I


I

0o

Iz


however, would be the same, namely, that field width de-creases strongly with increasing magnification.

When one is reading through a loupe, the eyes do notremain stationary but rotate in order that relevant text partscan be viewed foveally. The eye rotation will have conse-quences for the three reading-field widths defined by Eqs.(1)-(3). This effect was already pointed out by West-heimer 9 for the monocular field width. As can be seen fromFig. 5, the theoretical values for the reading fields have to becorrected by a small amount that can be expressed in achange in the eye-to-loupe distance a for the stationary eye.

To compensate for the effect of eye rotation, we will sub-stitute for a the distance a, from the principal plane of theloupe to the rotation point of the eye, which is situated about1 cm farther away from the loupe than is the second nodalpoint (see Fig. 5). In what follows, when theoretical readingfields are calculated, the effect of eye rotation will be takeninto account. In cases in which the magnification M25 iscalculated, the distance a to the second nodal point has beentaken.

EXPERIMENTALLY DETERMINED READING-FIELD WIDTHS

In order to evaluate the theoretical reading fields, an experi-ment was carried out in which values for the monocular fieldWm and the composite field W, were measured separately.Values for the binocular reading-field width Wb cannot bedetermined directly, and so they will be derived from theexperimental values from Wm and W, according to Eq. (3).

The experiment was designed in such a way that the read-ing fields varied from a few centimeters up to about 20 cm forWm and up to about 30 cm for W,. This was done by usingloupes of the same focal length while the eye-to-loupe dis-tance a was varied from 10 to 40 cm. Furthermore, the loupewidth L was varied by using four similar rectangular loupesfrom which an increasing amount of the edges had been sawnoff, resulting in loupe widths L of 6, 8, 10, and 11.9 cm,respectively. The object-to-loupe distance was fixed at 0.75f= 23.1 cm. In order to make sure that no interaction couldoccur between magnified and unmagnified text parts, theloupes were surrounded by opaque edges. HN (one of theauthors) acted as a subject.

The object consisted of a white sheet of paper that con-tained a line of randomized alphabet letters that were typedabove a line of different numerals and placed horizontally inthe object plane. The subject was asked to report whichcombination of letter and number he perceived at the ex-treme right and left loupe edges. The distance betweenthese positions was measured and defined the reading-fieldwidth with an accuracy of about one letter position (about0.5 cm). When only one eye was used, the experimentalresults were interpreted as the monocular reading field W,,.When both eyes were used, the results were interpreted asbeing values for the composite reading field W, (see Fig. 1).

During the experiment the subject used a forehead rest inorder to ensure that his head remained steady in the appro-priate position. The experiment was recorded on videotape, from which the values for the eye-to-loupe distance arwere obtained later.

From the known values for a, v, f, and L, the theoreticalvalues for the reading-field widths W, and W, were calculat-

ti2

0

subj. HN

-~~~~~-A

10~~~~~~~~~~~~~~~.15.O

theor. field widthW(cm)

Fig. 6. The experimental reading-field widths measured for sub-ject HN, versus the corresponding theoretical reading field widths.The experimental W values are obtained for loupes with a focallength of 30.8 cm and different loupe widths (L = 6, 8, 10, and 11.9cm, respectively). For each loupe, the distance v was fixed at 23.1cm while the eye-to-loupe distance a was taken to be 10, 20, 30, and40 cm, successively. For each value of f, L, v, and a, the theoreticalfield width W was calculated; the effect of eye rotations was takeninto account. Open circles represent the experimental values forthe monocular field, and filled squares represent the experimentalvalues for the composite field. The straight line represents equalvalues for the experimental and theoretical reading-field widths.

ed. In Fig. 6 the experimentally determined reading fieldsW. and We are shown plotted against their theoretical val-ues.

It can be seen that for larger reading fields the experimen-tal values increasingly deviate from the theoretical ones.This can probably be explained by an increasing effect ofachromatic aberrations, which leads to a higher magnifica-tion factor at the edges than in the middle of the loupe (forthese particular loupes) and thus results in smaller readingfields.

It is furthermore obvious from Fig. 6 that, for the samevalues of the theoretical reading fields, the experimentalmonocular fields deviate by a larger amount from the theo-retical values than do the composite ones. This result canbe explained by the fact that in order to achieve equal ex-perimental values for the monocular and the compositefields, the loupe has to be brought closer to the eye when oneis looking through the loupe with one eye than when one islooking through the loupe with both eyes. With decreasingeye-to-loupe distance, however, the amount of achromaticaberrations increases. Therefore it is plausible that at equalexperimental Wm and W, values, the monocular field widthdeviates more than the composite field width does from thetheoretical values.

LOUPE DISPLACEMENTS

In the previous section reading-field width was defined asthe unmagnified text portion that can be viewed through aloupe. When such a text portion is smaller than the totaltext width, one has to move the loupe along the text lines inorder to read the complete text.

F. J. J. Blonunaert and J. J. Neve

u v la Mu Ha TV .IQ


ES

3.

._

I

0

0 1U 15 s0 25 30 35theor. field width W(cm)-

Fig. 7. Experimental reading-field widths, measured for all sub-jects, versus theoretical field widths. The experimental values forthe monocular field Wm are given by the open symbols (o, f = 19.1cm; 0, f = 30.8 cm) respectively, and the filled symbols (m, f = 19.1cm; 0, f =30.8 cm) represent the experimental values for the com-posite field W,. The dashed curves are taken from Fig. 6. Thestraight line again represents equal values for the experimental andtheoretical field widths.

C

axEl

0

X - 2aE

-X

1. (a)0o

CL x

aEu)

C.CL

0.In

0

x.a)

-E

3.xa3

20'

(b)

0

0,0 W-Wm one eye covered

0 10 20 30exp. field width W(cm)-

___ W=Wm one eye covered, El W-Wm both eyes uncovered

0 10 20 30exp. f iel d width W(cm)-

Since the widths of the three possible reading fields arenot the same, we expected that a measurement of the widthsof these fields, together with the determination of the hori-zontal loupe displacement, would give information aboutwhich reading field is actually used by a person when readingtext through a loupe. In other words, loupe displacementsmight reveal whether subjects use both eyes simultaneouslyor alternately or use only one eye. For this purpose weconducted the following experiment.

We measured the horizontal displacements of two loupesfor six subjects (five had normal acuity, and one, KW, had avisual acuity of about 0.2) for four different observationconditions. The loupes had focal distances of 19.1 and 30.8cm and widths of 8.0 and 11.9 cm, respectively. The fourdifferent observation conditions for each loupe wereachieved by changing the eye-to-loupe distance a, paramet-rically in four steps from approximately 10 cm to approxi-mately 40 cm. The ratio v/f was kept constant at 0.75.

For each geometrical reading situation, which was pre-sented in random order for each loupe, the subjects wereasked to read silently different text samples with a length ofabout seven lines and with a fixed line width of 20 cm. Thesubjects performed this task while reading through the loupesometimes with both eyes and at other times with one eye.

The movements of the loupe were recorded on video tape,from which afterward the values for the eye-to-loupe dis-tance a, and the horizontal loupe displacement AXL wereobtained. For each geometrical position in which text wasto be read, the reading-field widths W, and W, were mea-sured for each subject by using the procedure that has beendescribed for the reading-field measurements. Owing to thechanges in the eye-to-loupe distance from approximately 10to approximately 40 cm, the monocular reading field W.,,varied from about 4 to 9 cm and from about 8 to 18 cm for theloupes with f = 19.1 cm and f = 30.8 cm, respectively. The

Ca)E

0

Qa)0

a)

CL

._

E

a

._

U)V

0

C

x

At

E

VI)

._

CL

X

c

E

x<3

--- W=WmA, A W-W C

one eye coveredboth eyes uncovered

20~

10

(c)

n

<3.

(d)

0

0 10 20 30exp. field width W(cm)-

--- W=Wm one eye covered

*,c W=Wb both eyes uncovered

0 10 20 30exp. field width W(cm)--

Fig. 8. Horizontal reading-field displacements, for subject HM, asa function of experimental reading-field widths. (a) Axwversus themeasured Wm values when one eye is covered. These curves arereproduced in (b)-(d) (dashed curves). For the case in which botheyes are uncovered, the solid curves represent Axw versus (b) theexperimental Wm values, (c) the experimental W, values, and (d) theexperimental Wb values. The open symbols represent data ob-tained by using a loupe with f = 19.1 cm and L = 8 cm, and the filledsymbols represent data obtained by using a loupe with f = 30.8 cmand L = 11.9 cm.

30subj.HMI

NH~TD

25

1 5 _ __- - _ _ _ _ _ _

0 0~~~0

10 _.

F. J. J. Blornmaert and J. J. Neve


one eye covered W=Wm

both eyes uncovered W=Wb

subj. MvdV.

C

E

Qa)C._

._

0.

M

x)

06.xLa)

1'

C.

?x<3

___ w=wm one eye covered

*uj K-w, | both eyesuncovered

subj. KW

20 k

10.

(d)

0

10 20 30exp. field width W(cm) )--

Ca)

Ea)

Qa._

IV

U:0

d.x

--- one eye covered W=Wm

* X A both eyes uncovered W=Wc

subj. W K

\ -

10 20 30exp. field width W(cm)--

tE

X<

0

10.

(e)

00

10 20 30exp. field widthW(cm) -

___ w:wm one eye coveredA, A W:W 1* , a w-w lboth eyes uncovered*, 0 WWbsubj. TD

10 20 30exp. field widthW(cm) 0

C

QAE

C.)

xE E

z C.)

'i X0<3

Xa)

20

10

(c)

0J-

one eye covered W=Wm

both eyes uncovered W=WcA__

subj. NH

0 10 20 30exp. field width W(cm)-i-

composite field width W, varied from about 6 to 14 cm andfrom about 11 to 26 cm for the loupes with f = 19.1 and f =30.8 cm, respectively.

By following this procedure, we obtained for each subjectexperimental data for Wm, W,, and the loupe displacementAXL (with and without one eye covered) for each geometrical

Fig. 9. The horizontal displacements Ax wfor all subjects as afunction of the experimental reading-field widths. Dashedcurves represent Ax w versus the measured Wm values obtainedwhen one eye is. covered. Solid curves represent the valuesobtained when both eyes are uncovered. (a) Axw versus theexperimental Wb values. (b), (c) Axxwversus the experimentalW, values, for subjects WK (b) and NH (c). (d), (e) Axwversusthe experimental Wm,. Wb, and W, values for subjects KW (d)and TD (e), since these subjects only use a small part of theloupe. The open symbols represent the results obtained byusing a loupe with f = 19.1 cm and L = 8 cm, and the filledsymbols represent the results obtained by using a loupe with f= 30.8 cm and L = 11.9 cm.

situation given by the values of a, v, f, and L and a line widthof 20 cm. From these data the binocular reading field Wbwas calculated according to Eq. (3).

Figure 7 shows the experimentally determined readingfields Wm and W, for all subjects, plotted against their theo-retical values, which were calculated from the values of a,, v,

C0)E

0Q'a.)

la E_ I2 <

X

20

10

(a)

Ca)E

C._)

LX

0<

a)t

20

10

(b)


20K


f, and L. It can be seen that the fields of the several individ-uals are positioned close together and vary in the same wayas shown for the fields in Fig. 6. In fact, the dashed curves inFigs. 6 and 7 are identical.

From the loupe displacement AXL the corresponding dis-placement Ax, of the reading-field center in the text planewas obtained by making use of the following expression,which is derived in Appendix A:

Ax a, + AXL- (6)XW-a,.

In the case in which subjects are reading with one eyecovered, it is clear which reading-field width they use duringreading, namely, the monocular field width. The results onthe horizontal reading-field displacement Axw can then beplotted as a function of the measured monocular field Wm, asis illustrated in Fig. 8(a) for subject HM. In this figure, thedashed curves represent the measured field displacementsAx., and the straight line gives the least theoretical fielddisplacement necessary to read a text line of a width of 20 cmcompletely. It can be seen from the dashed curves that,although the subject moves the loupe more than is strictlynecessary, the measurements follow the line of minimal fielddisplacement nicely. This indicates that the subject makesuse of the increase of the monocular field width by movingthe loupe over a smaller distance. It should be noticed thatthe AxW values are obtained by using two different loupes.In Fig. 8(a) the open symbols represent the data obtained byusing the loupe with f = 19.1 cm and L = 8 cm, and the filledsymbols represent the data obtained by using a loupe with f= 30.8 cm and L = 11.9 cm.

When subjects are reading through a loupe with both eyesuncovered, we do not know whether they use the binocular,the monocular, or the composite reading field. This prob-lem was approached by plotting the measured field displace-ments Ax w for both eyes uncovered as a function of the threepossible reading fields Wm, Wb, and W, [Figs. 8(b), 8(c), and8(d), respectively]. The curves obtained in this way arethen compared with the curve for field displacement versusreading field for the true monocular case (one eye covered)given in Fig. 8(a). The curve that best matches the curve forthe true monocular case is then interpreted as representingthe reading field that is actually used in the case of readingwith both eyes. This is illustrated in Figs. 8(b)-8(d) forsubject HM. In Fig. 8(b), the curves with the squares depictthe field displacements Axw obtained when both eyes wereuncovered as a function of the measured monocular fieldWm, and the triangles in Fig. 8(c) give the Axw values ob-tained when both eyes were uncovered as a function of W,.Neither of these follows the dashed curves for the true mon-ocular case. Therefore we conclude that the subject doesnot use the monocular field or the composite field whilereading through the loupe with both eyes. In Fig. 8(d), thecurves for Axw values versus Wb values show much morecorrespondence with the curves for the monocular case, indi-cating that HM probably uses the binocular reading field.

The same procedure was followed for all six subjects. Theresults are given in Fig. 9, where, for the case in which botheyes were uncovered, we have given the horizontal field dis-placements Axxw directly as a function of the reading fieldsthat the subjects actually appear to use during reading.

It can be seen from Fig. 8(d) and from Figs. 9(a)-9(e) that

the group of subjects can be divided roughly into four sub-groups according to the field width that they appear to useduring reading.

Subjects HM and MvdV [see Figs. 8(d) and 9(a)] seem tomake use of the binocular reading-field width, and subjectsWK and NH [see Figs. 9(b) and 9(c)] seem to use the com-posite reading field. For subjects KW and TD [see Figs.9(d) and 9(e)] it is hard to tell whether they read through theloupes monocularly or binocularly. In fact, they do not usethe full width of their reading field but read through a smallpart of the loupe. This can be seen clearly for subject KW[see Fig. 9(d)]. In the monocular case (one eye covered),subject KW displaces his reading field in a constant way overa distance of approximately 19 cm, which is close to the fullline width of 20 cm, while his reading-field width varies fromnearly 4 to 20 cm.

DISCUSSION

The reading-field width of a certain loupe is a quantity thatis hard to define uniquely. This is clear from the followingobservations. First, when the subject is reading through aloupe with both eyes, two separate images of the text areformed that only partially overlap. Second, the widths ofthese images depend strongly on the physical properties ofthe loupe and the geometry of the conditions of observation.

As far as the physical properties of the loupe are con-cerned, it can be concluded from Fig. 4 that the field widthsstrongly decrease with decreasing focal length of the loupe.This effect can be partly explained by the relation that wasfound to exist between the width and the focal length ofloupes (see Fig. 3). This can be understood from Eq. (1),which shows that the monocular field width is proportionalto the loupe width.

Another factor that results in smaller field widths forshorter focal distances can be explained from the consider-ation that the magnification for loupes having shorter focallengths will, in general, be higher. Since higher magnifica-tion factors lead to smaller text portions visible within theloupe edges, this effect too will lead to smaller reading-fieldwidths, as was earlier recognized by Bouma et al.

7

As far as the geometry of the reading situation is con-cerned, all three reading-field widths depend strongly on theeye-to-loupe distance a and the object-to-loupe distance v,as is shown in Fig. 2 for the binocular field width. From thisfigure, it can be concluded globally that the larger readingfields occur for small values of the eye-to-loupe distance a(i.e., a loupe used as an eyeglass).

In the literature we have not yet encountered any classifi-cation of field widths into the monocular, binocular, andcomposite reading-field widths. Apart from the work ofBouma et al.,

7 who implicitly assume that the relevant fieldwidth is the binocular one, only the monocular field width isoccasionally mentioned." 9" 0

As can be seen from Fig. 4, there usually exists a largedifference among the widths of the three separate readingfields. This means that subjects, in principle, have the pos-sibility of choosing between a number of strategies whenreading through a loupe:

* A subject may use the information contained in boththe left and the right image fields economically. In that case



the subject will look with the right eye at the left edge andwith the left eye at the right edge. The composite reading-field width will be used by such subjects.

* The loupe reader may use only the image parts thatare seen fused when viewing with both eyes. Such subjectsuse the binocular field width Wb.

* In some cases the reader uses only the monocularfield. This may be caused by eye dominance usual for aparticular reader or by eye dominance caused by the specificreading situation that occurs during loupe reading. Forbinocular seeing, a certain amount of coherence between theseparate images is necessary.' 2 Whenever the two imagesseen through a loupe overlap only slightly, fusion of bothimages will be difficult, and hence the monocular field of oneeye will be used.

* The subjects may use only a small part of the loupewidth. This may be a strategy chosen, for instance, byreaders who prefer or need aberration-free images. Suchpersons may look either monocularly or binocularly througha loupe while using only the center part of the loupe forreading.

In fact, all six subjects who took part in the experimentscan be classified into one of these four groups, as was de-duced from the loupe displacements that they made whilereading text. This deduction was based on the implicitassumption that those fields are used whose displacementsbest match the result of the monocular reading experiment.However, other factors may be involved; therefore we mustdraw conclusions carefully. For instance, in the experi-ment, a change in reading-field width was accompanied by avariation in the magnification and image distance. An ef-fect of the variation of these quantities might be hidden inour results. Furthermore, subjects might have changedtheir strategies depending on the absolute size of the read-ing-field width. In our view, such factors should be thesubject of further investigation.

Some straightforward conclusions, however, can bedrawn. Some subjects (WK and NH) use such small loupedisplacements that they must have used the composite read-ing field at least for large values of this field width (see Fig.9). Another pertinent conclusion might be that some sub-jects (KW and TD) only used a small part of the loupe,presumably the middle part.

Concerning the particular difficulties of reading with aloupe, few experimental data are available. The specificreading situation may, however, be compared with ordinaryreading (without magnification). In such a comparison itmay be asked what the influence will be of the aspects inwhich loupe reading differs from normal reading.

Magnification will lead to an enlarged image of the textand its constituent letters. From the results of Bouma etal.13 and Aberson'14 who investigated the influence of lettersize on word recognition and reading speed, it can be con-cluded that visually impaired readers need a larger lettersize for optimal reading than do normal readers (at a readingdistance of 33 cm, an average height of 5 mm for the im-paired compared with 2 mm for normal readers). Compara-ble results were obtained by Legge et al.15 A limited amountof magnification of text will thus lead, in general, to a morenearly optimal reading condition for the visually impaired.

Limitation of the reading field width will, in general, dis-turb the normal reading process. If the horizontal binocularreading-field width is larger than (or equal to) the line width,not much influence can be expected from this factor, apartfrom the unknown influences of vertical field width and lensaberrations. If the magnified text part is smaller than theline width, horizontal loupe displacements relative to thetext are necessary, and eye movements must be tuned toloupe movements. This will certainly be the case for sub-jects who prefer the binocular reading field when loupe read-ing, since the binocular field is the smallest one of the threepossible fields. Subjects who prefer to use the monocular orthe composite reading field, will, in general, make fewerloupe movements. Their reading process will, however, beslow compared with normal reading. If the monocular fieldis employed, only a single retinal image is used. If, on theother hand, the composite field is employed, the retinalimages of both eyes will be used alternately, and the overlap-ping part of the images might be fused.

Loupe displacements will cause visible movement of themagnified text relative to the unmagnified text. This maydisturb the normal reading process, especially if the begin-ning of a new line has to be found. Bouma16 estimated thatin reading without a loupe, the distance-over-line length(line angle) for normal reading should be larger than 2 deg toensure easy location of the beginning of a new line. It isunlikely that this rule gives an adequate description forloupe reading, the more so since the parallax effect will leadto a disorientation of the reader concerning the specificlocation of the magnified text part within the unmagnifiedtext.

As was shown before,'l 8the virtual image of the text will beformed at a distance from the eye that is farther away thanthe unmagnified text. In that sense, the reading distancewill generally be larger than under normal reading condi-tions. This distance will affect the accommodative state ofthe eye lens, in that less accommodation will be needed forreading with the aid of a loupe than for normal reading. Infact, loupes and reading glasses have this property in com-mon. Since visually impaired readers often have less ac-commodative power, this property may be helpful. If aloupe and reading glasses are used in combination, however,one should take care that the image distance does not exceedthe punctum remotum.

Lens aberrations and surface reflections will tend to de-crease the quality of the retinal image. Lens aberrations,such as spherical and chromatic aberration, usually occur atthe edges of loupes. Therefore readers may be inclined touse only the (middle) portion of a loupe that is more or lessaberration free. Presumably, the specific part of the loupethat is used by loupe readers depends to a great extent onsubjective factors. For severely impaired readers, for in-stance, it may even be the case that an aberration-free imageis needed for correct recognition of letters and words. Inthat case only the middle part of a loupe will be used.

Surface reflections may occur in any part of the imagefield, depending on external factors such as the presence andthe position of a lamp or window. They will cause localcontrast reduction of the magnified text. According to vanNes and Jacobs,'7 contrast reduction will lead to impairedrecognition of letters and words and consequently to a dis-turbance of the reading process.



CONCLUSIONS

It is difficult to define the reading-field width of a loupe orreading magnifier uniquely. Three different reading-fieldwidths, which depend on the physical properties of the loupeand the geometry of the reading situation, may be distin-guished.

Subjects appear to use different reading-field widthswhen reading through a loupe. This indicates that differentstrategies may be used for integrating loupe magnificationand loupe movements into the reading process.

Little is known concerning the particular difficulties ofreading with a loupe compared with normal reading. Aninvestigation of the influence of magnification, limited read-ing-field width, lens aberrations, and surface reflectionsmight reveal the differences between loupe reading and nor-mal reading processes more quantitatively.

APPENDIX A

In the derivations of the reading field and the retinal magni-fication, we have made the following assumptions:

* We are dealing with an infinitely thin lens.* The object is placed within the focal length of the

loupe.* The eye pupil is regarded as a point.* The eyes have a single nodal point.* The eyes do not rotate.

In the calculations of the reading-field displacements, how-ever, we allow for eye rotations.

Monocular and Binocular Reading-Field WidthsOne may calculate the monocular and binocular field widthsfrom Figs. 10 and 11, respectively.

In Fig. 10, one eye is situated on the optic axis of the loupe.The eye-to-loupe distance is given by a; the text is placed ata distance v from the loupe with a focal length f. The virtualimage of the text is formed at a distance -b + a from the eye.The portion y' of the virtual image that can be viewedthrough the loupe originates from the unmagnified text por-tion y. This unmagnified text portion gives us the monocu-lar reading field

Wm = y.

It can be seen from similar triangles in Fig. 10 that

y' b y' -b+ay v L a

(Al)

(A2)

virtual image

I

'/2 y'

\-1 - loupe\ H e _ _ _ _ _ I

I - -b

i eye

Lv a -,

Fig. 10. Definition of the monocular reading-field width.

virtual image

II A" -text

I "Z"I s21' -H

I l1

I. - -- a' --Fig. 11. Definition of the binocular reading-field width.

In Fig. 11 both eyes are situated at a distance 1/2D, fromthe optic axis of the loupe, where DP is the distance betweenthe eyes. The definitions of the parameters a, v, -b, f, and Lare the same as in Fig. 10. The binocular reading field isgiven by the unmagnified text portion z of which the virtualimage z' is seen through the loupe with both eyes simulta-neously. The binocular field is thus given by

Wb = z. (A6)

From similar triangles it follows that

Z- b z'-Dp -b+az = a _ IZ v Z 'L DP a

(A7)

where L represents the loupe width. After eliminating yand y' one obtains

W.m -~~(-ba+a )L.b (a)

By using the thin-lens formula'8

1+1v b f

W, can be written as

W.=(1+v_ L)L.

(A3)

After solving for z and z' from Eq. (A7) and making use ofEq. (A4), one obtains

Wb (1+a-v)L-kDP== W V--Dp.a f a m ap (A8)

The Retinal Magnification M25(A4) The retinal magnification of a loupe is commonly calculated

as that compared with the largest possible sharp image if noloupe is used, which is obtained if the object is placed in thepunctum proximum.1 For the punctum proximum a dis-

(A5) tance of 25 cm is usually taken, which corresponds to a nearpoint of accommodation of a 45-year-old human." The


" --, I--I-,

I

I


magnification, called M25, then determines the size of theretinal image of an object as seen through the loupe, com-pared with the size of the retinal image if no loupe is usedand the object is viewed from a distance of 25 cm.

From the definition of M2 5 and Fig. 12 it follows that

M25 =: 0 (A9)a

where a is the viewing angle for the unmagnified object at 25

cm and / is the viewing angle for the magnified object.

virtualimage object

1x2 y' - 1 _,

4

Provided that viewing angles a and A are not too large andthat the object is situated within the focal length of the loupe(v < f), one obtains

(A10)a;~y/2, 0 Z y'/2 25 -b + a

It can be seen from similar triangles in Fig. 12 that

;~~~~~~y -=-_ ._y

(All)V

From Eqs. (A9) and (All), expressions (A10), and Fig. 12, itfollows that M25 can be written as

25 V+ a-a25loupe

- v -a0 -bI

a -viewing angle for 1/2Yunmagnified object 2 5cat 25cm 25cm

: viewing angle formagnified object

M25= :

Fig. 12. Definition of the retinal magnification M25.

rotating eye

ar

X| textW-

.Wm-.

Fig. 13. Definition of the loupe displacement AXL and the reading-field displacement AxW for the monocular case.

rotating eyes

L. J IoupeI~~~~~ALK

+ X r x .' , ,-t~~~~~~~~ext -AXW ~ Ww, Wc W

Fig. 14. Definition of the loupe displacement AXL and the reading-field displacement AxW for the case of reading through a loupe withboth eyes.

(A12)

Reading-Field DisplacementsIn the monocular case, the reading-field displacement Axwcan be obtained directly from Fig. 13, in which AXL and Axwrepresent the distances over which the center of the loupeand the monocular reading field are moved, respectively.The text-to-loupe distance is given by v, and a, representsthe distance between the loupe and the center of rotation Cof the eye. The points labeled N and N' give the positions ofthe nodal point of the rotating eye. From similar triangles,one obtains

a,. + vAx w AxL.ar.

(A13)

The same equation is obtained in the case of readingthrough a loupe with both eyes. This is illustrated in Fig. 14,in which AXL, Axw, v, and a, have the same meaning as in Fig.12. The separation between the eyes is given by Dp. Thebinocular reading field is given by Wb and the composite oneby W,. The center points of these fields coincide and arepositioned on the straight line connecting the point 0 withthe center of the loupe. The points C, and C2 represent thecenters of rotation of the two eyes. Equation (A13) is againobtained by using similar triangles.

ACKNOWLEDGMENTS

We would like to thank H. E. M. M6lotte for his stimulatinginterest and H. Bouma for helpful criticism. The researchof Johan J. Neve was supported by the Dutch InnovationResearch Programme on Aids for the Handicapped (IOP-HG).

REFERENCES

1. A. Linksz, "Optical principles of loupe magnification," Am. J.Ophthalmol. 40, 831-840 (1955).

2. J. E. Lebensohn, "Newer optical aids for children with lowvision," Am. J. Ophthalmol. 6, 813-819 (1958).

3. S. Duke-Elder and D. Abrams, System of Ophthalmology(Kimpton, London, 1970), Vol. 5, pp. 793-807.

4. L. L. Sloan, Reading Aids for the Partially Sighted: A System-atic Classification and Procedure for Prescribing (Williamsand Wilkins, Baltimore, Md., 1977).

5. G. E. Fonda, Management of Low Vision (Thieme-Stratton,New York, 1981).

6. E. E. Faye, Clinical Low Vision (Little, Brown, Boston, Mass.,1976).


I

�_J


7. H. Bouma, H. E. M. M6lotte, and F. J. J. Blommaert, "On thefield width of reading magnifiers," IPO Ann. Prog. Rep. 19,133-136 (1984).

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11. Y. Le Grand, Optique Physiologique (Editions de la Revued'Optique, Paris, 1952), Vol. 1.

12. A. L. Duwaer and G. van den Brink, "What is the diplopiathreshold?" Percept. Psychophys. 29, 295-309 (1981).

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large print easy to read? Oral reading rate and word recogni-tion of elderly subjects," IPO Ann. Prog. Rep. 17, 84-90 (1982).

14. D. H. A. Aberson, "Simulation of poor visual acuity: composi-tion of silent-reading speeds," submitted to Vision Res.

15. G. E. Legge, G. S. Rubin, D. G. Pelli, and M. M. Schleske,"Psychophysics of reading-II. Low vision," Vision Res. 25,253-266 (1985).

16. H. Bouma, "Visual reading processes and the quality of textdisplays," in Ergonomic Aspects of Visual Display Terminals,E. Grandjean and E. Vigliani, eds. (Taylor and Francis, London,1980), pp. 101-114.

17. F. L. van Nes and J. C. Jacobs, "The effect of contrast on letterand word recognition," IPO Ann. Prog. Rep. 16, 72-80 (1981).

18. W. T. Welford, Geometrical Optics (North-Holland, Amster-dam, 1962), Vol. 1.

reading fields of magnifying loupes

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