Nonoptical Determinants of AniseikoniaArthur Bradley, Jeff Rabin,* and R. D. Freeman
Interocular differences in apparent size (aniseikonia) are typically associated with interocular differ-ences in refractive error (anisometropia). Aniseikonia is generally thought to reflect disparities inretinal image size that often accompany anisometropia. This assumption was examined with sevenhighly anisometropic subjects who were tested under conditions in which no substantial retinal imagesize differences were present. Using a dichoptic size matching task, consistent and large (mean = 22%)aniseikonias were found. Myopic anisometropes exhibit perceptual minification, while hyperopesdemonstrate perceptual magnification when using their more ametropic eye. Both ultrasonic andfundus examinations of these subjects indicate that differential retinal growth or stretching is re-sponsible for these findings. Invest Ophthalmol Vis Sci 24:507-512, 1983
Substantial interocular differences in apparent size(aniseikonia)1 are typically associated with interocu-lar differences in refractive error (anisometropia),2
although small amounts can occur in isometropicsubjects.3 It has been suggested that both optical andanatomical or physiologic differences between theeyes may be responsible for aniseikonia.1 However,the critical factor is generally assumed to be the dif-ference in retinal image size produced by the aniso-metropia or its correction.24"7
Most anisometropias of greater than 2 diopters re-sult from interocular differences in axial length ratherthan optical power.8 Therefore, regardless of the mag-nitude of the anisometropia, refractive errors can becorrected and retinal image sizes equated in the twoeyes by a simple spectacle correction placed at theanterior focal plane of the eyes. This relationship isdescribed by Knapp's Law,9 which often serves as arule of thumb for correcting anisometropia and elim-inating aniseikonia.10 However, several recent studiesreport substantial amounts of aniseikonia present inanisometropes corrected with spectacle lenses.""13
These apparent failures of Knapp's Law could resultfrom one or more of several reasons. The spectaclelens positions may have differed substantially fromthat of the anterior focal plane of the eye, or theanisometropias may have originated from optical andnot axial length differences. In addition, it is possiblethat large interocular anatomical or physiological dif-
From the School of Optometry, University of California,Berkeley, California.
* Present address: DDEAMC, Fort Gordon, Georgia.Supported by Grant EY01175 and Research Career Develop-
ment Award EY00092 from the US National Eye Institute.Submitted for publication March 22, 1982.Reprint requests: R. D. Freeman, School of Optometry, Uni-
versity of California, Berkeley, CA 94720.
ferences were responsible. However, because com-plete information about lens position, corneal pow-ers, and ocular dimensions was not provided it is im-possible to discriminate between these alternatives.
In the present study we have attempted to examinethe origins of aniseikonia in highly anisometropicsubjects and tried to evaluate the relative importanceof optical and neural factors. Under conditions ofapproximate equality of retinal image size in the twoeyes we find large amounts of aniseikonia, which ismost likely the result of differential growth of the twoeyes.
Materials and Methods
Subjects
Seven highly anisometropic subjects (five myopesand two hyperopes) were chosen for this study. Allwere examined carefully in the university eye clinic,and the resulting refractive information is presentedin Table 1. The anisometropias in our sample variedfrom 5 to 20 diopters, and they were therefore at thevery edge of the normal distribution of interocularrefractive error differences.6 However, very little in-terocular difference in corneal power was found(mean = 0.5 diopters). Also, the average cornealpower of our sample was 43 diopters, which is at thecenter of the normal distribution.14 Therefore, to afirst approximation, it was reasonable to assume thatwe had a sample of axial anisometropes who hadapproximately equal and typical optical powers intheir eyes. Consequently, using the calculations ofGullstrand15 for the typical eye, we estimated the an-terior focal plane to lie 15 mm anterior to the cornea.Large deviations from this value are unlikely in oursample because of the homogeneity of the cornealpowers (standard deviation = 1.4 diopters).
R = right eye, L = left eye, H = horizontal, V = vertical, SL = spectacle lens, CL = contact lens.
Procedure
A Moller-Wedell phase differences haploscope wasused to measure aniseikonia. This instrument pro-vides a dichoptic view by phase-coupling projectionand exposure of alternate images to each eye. The lefteye viewed a 3° X 20 min luminous bar, while theright eye viewed a similar bar of adjustable size. Bothbars were viewed in a large empty field, which helpedminimize the effects of size constancy by providingvery little distance information. Direct comparisoneikonometry1 was used to evaluate the aniseikonia.All subjects were instructed to vary the size of theadjustable bar until both appeared equal. The exper-imenter randomly adjusted the length of the variablebar between each setting, and the mean and standarddeviation of a minimum of eight settings were ob-tained. Aniseikonia (%) was calculated in the follow-ing way: Aniseikonia (%) = ([E - A]/E) X 100%.Where E and A represent the actual lengths of thebars seen as equally long by the least and most ame-tropic eyes respectively. Positive values indicate per-ceptual magnification and negative values minifica-tion for the more ametropic eye.
All subjects were tested with their refractive errorsneutralized with trial lenses placed at a vertex distanceof approximately 15 mm from the cornea. This dis-tance was carefully obtained by adjusting variablehead and chin rests until the subject's closed eyelidjust touched a 15-mm protrusion from a lens blankmounted in the haploscope lens carrier. The triallenses were chosen to have a small and constant shapefactor of less than 1%, and therefore they magnifiedprimarily on the basis of power. Two subjects were
also tested with their contact lens corrections insteadof with trial lenses.
Additional examinations were conducted with sev-eral subjects to obtain fundus photographs and alsoA- and B-scan ultrasonographs in order to assess rel-ative sizes and differential growths of the two eyes.A Zeiss fundus camera was used to photograph thehorizontal meridian from the nasal to temporal oraserrata. Both axial lengths and overall shapes of theeyes were measured with A- and B-scans, respectively.A Sonometrics System was used, and the B-scanswere obtained with a sector scan technique.
Results
Knapp's Law states that, in axial anisometropia,retinal image size is equal in the two eyes if the cor-recting lenses are placed at the anterior focal planeof the eyes. Consequently, if aniseikonia is dependentprimarily on retinal image size differences, it shouldbe negligible in our sample when corrected at a vertexdistance of 15 mm. This prediction can be examineddirectly in Figure 1, which shows aniseikonia in per-cent as a function of anisometropia in diopters. Con-trary to the prediction, all of our sample exhibit largeamounts of aniseikonia when corrected at or aroundthe anterior focal plane (filled circles). In fact, thereis a systematic relationship between anisometropiaand aniseikonia. All of the myopic anisometropesobserved the 3° bar to be smaller with their moreametropic eye (perceptual minification), while theconverse was true for the hyperopes.
There are several alternative explanations for theresults. First, it is possible that large errors were made
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No. 4 NONOPTICAL DETERMINANTS OF ANISEIKONIA / Bradley er ol.': 509
in placing the trial lenses. Although conceivable thisis unlikely, because errors of more than 15 mm wouldbe required to account for these data.1 The consis-tancy of the measurements make such large errorsunlikely. However, we have tested the possibility ofsuch a positioning error directly by repeating themeasurements with two of our sample (AN and JR)while they wore their contact lens corrections (Fig.1, open circles). Large position errors could not occurwith a contact lens correction. Therefore, assumingthe refracting surface of the contact lens to lie about3 mm anterior to the entrance pupil of the eye,15 theformula for spectacle magnification (M = 1/1 - zF,where M = % magnification, z = distance of lensfrom entrance pupil, and F = power of correcting lensin diopters) allows the trial lens position to be esti-mated based on the measured aniseikonia differencesunder these two conditions. For example, subject ANexhibited a 28% increase in minification with hermyopic eye when the trial lens was used. This placesthe trial lens at approximately 16 mm anterior to theentrance pupil of the eye. The corresponding predic-tion for subject JR was approximately 14 mm, in-dicating spectacle lens positions slightly closer to theeye than expected. Therefore, it is very unlikely thatthe observed aniseikonias were produced by signifi-cant lens positioning errors. In fact, to produce suchlarge minification for the myopic eyes of these sub-jects (34% for AN and 10% for JR) the lenses wouldneed to be much farther, rather than a little nearerto the eye than the anterior focal plane.
The results shown in Figure 1 are only surprisingif the ametropias are axial. However, these data areentirely consistant with those expected from refrac-tive anisometropia,1 where there should be very smalldifferences in retinal image size with contact lens cor-rection but much larger ones with spectacle correc-tions. Because most anisometropias greater than 2diopters are axially produced,8 it is improbable thatall seven of our sample have refractive anisometro-pias. The similarity in the keratometric measure-ments for each eye (see Table 1) also makes this un-likely. However, it is possible, for example, that dif-ferences in anterior chamber depth, or lens thicknessare responsible. Therefore, in an attempt to evaluatethe relative roles of both optical and axial length dif-ferences, we examined two of our sample with A-scanultrasonography (Fig. 2). The data from each eye ofsubjects AN and JR are given in Table 2. The anteriorchamber depths and lens thicknesses are essentiallyidentical in both eyes of each subject. However, thedifferences in axial length are very close to those ex-pected if the anisometropias were axial. Subject ANhas 20 diopters of myopic anisometropia and an axiallength difference of 7.7 mm, which could account for
30 ~
2VIN
O)
ISE
IH
z<
CPoE
min
10
0
10
20
30
40 "~
-20
ANISOMETROPIAFig. 1. The amount of aniseikonia in percent is plotted as a
function of anisometropia in diopters for each subject. All subjectswere tested with trial lens corrections (filled circles), and two werealso tested with their contact lens corrections (open circles). Ver-tical bars indicate ±1SE.
over 90% of her anisometropia. The axial length dif-ference for subject JR can account for at least 95%of his anisometropia. In conclusion, then, it is verylikely that the anisometropias in our sample resultprimarily from axial length differences between thetwo eyes.
The accurate lens positioning and confirmed axialnature of the anisometropia emphasize that the an-iseikonias reported by our subjects did, in fact, occurwith approximately congruous retinal images. There-fore, some very significant nonoptical interocular dif-ferences must be responsible. The large amount ofneural processing that intervenes between the retinalimage and the appreciation of size (the "ocular im-age"1) provides many possible locations for the sourceof the aniseikonia. It is certainly possible that centraldifferences between the inputs from the two eyescould exist in visual cortex, but the eye itself is a morelikely candidate because differences in size alreadyexist here.
In order to evaluate what ocular variables were re-sponsible for the aniseikonias, we made a detailedexamination of the globe and retinae of some of oursample. First, to assess how differences in axial lengthaffected the shape of the eye, we obtained B-scan ul-trasonographs from subjects AN and JR. Completescans of both eyes are shown in Figure 3A for onesubject (AN). To facilitate interocular comparison theright and left halves of the sonographs of the rightand left eyes respectively have been placed side by
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INVE5TIGATIVE OPHTHALMOLOGY b VISUAL SCIENCE / April 1983 Vol. 24
SUBJECT AN
LE piano RE -20.25
mmm
AL = 23.56mm AL = 31.22 mm
1 SUBJECT JR
LE -12.50 RE - 3 . 2 5
AL = 29.13mm AL = 25.51 mmFig. 2. A-scan ultrasonographs were obtained to evaluate the
role of axial length in producing the anisometropias in our sample.Scans are shown from subjects AN (A) and JR (B). Peaks, fromleft to right, are produced by the following sources: First, on thefar left, is the emitter artifact. The second peak indicates the po-sition of the cornea. Then comes the peaks from the front andback surface of the lens. Finally, a large peak can be seen from theretina, choroid, sclera, and orbital tissue. AL = axial length. Thequantitative details of these scans are tabulated in Table 2.
side (Fig. 3B). Several aspects of globe shape can beevaluated by simple inspection of these figures. First,from the symmetry of the anterior segments it is ev-ident that the ocular length differences are restrictedto the posterior section of the eye. Also, the moremyopic eye does not exhibit much shape distortion.These pictures indicate that the area of the globe cov-ered by the retina has grown considerably larger inthe more myopic eye. Therefore, when retinal imagesizes have been equated in the two eyes, the imagein the larger more myopic eye covers a smaller pro-
portion of the retina. It is these subjects who reportminification in their more myopic eye when the ret-inal images are matched in size. Therefore, it seemslikely that the proportion of the retina covered by animage, and not its absolute size may determine itsapparent size.
Although these pictures show conclusive evidenceof differential eye growth in anisometropia, it is notclear where the extra (in the case of myopes) growthoccurs. Are these differences in growth spread outuniformly over the globe posterior to the ora serata,or are they concentrated at the posterior pole of theeye? The interpretation of our size matching datadepends on the answer to this question, because wesampled only a very small and select region of theretina (1.5° on either side of the fovea). Therefore,to examine differential growth, or stretching acrossthe retina we took a series of fundus shots across thehorizontal meridian of the eyes from several subjects.Sample data are shown in Figure 4. A fundus com-parison of an emmetropic (left) eye and highly my-opic (right) eye of subject AN can be made from Fig-ure 4A. The fundus of the left emmetropic eye isophthalmoscopically normal. The uniform coloringof the retina is typical. However, the fundus of theright myopic eye exhibits many features commonlyfound in highly myopic eyes that have undergoneexcessive growth or stretching. First, the separationof the retina, pigment epithelium, and choroid fromaround the optic disc is typical. Second, the pale andnonuniform fundus is indicative of stretching andthinning. Third, the thin retinal vessels, and the vis-ible choroidal vessels also indicate stretching. It isclear from these two pictures that the area of retinathat manifested perceptual minification has under-gone excessive stretching. Therefore, in our experi-ment, where retinal image size was held constant inthe two eyes of this subject (AN), the image in themyopic right eye fell on a retina containing fewer
Table 2. A-scan ultrasonography data: oculardimensions in millimeters for two myopicanisometropes whose ultrasonographsare shown in figures 2 and 3.
Ocular dimention
Anterior cornea/anterior lens
Lens thicknessVitreous chamber
depthAxial length
LE
3.73.4
16.423.6
AN
RE
3.63.7
23.831.2
Subject
LE
4.04.1
20.929.1
JR
RE
3.83.8
18.025.5
LE = left eye, RE = right eye.
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No. 4 NONOPTICAL DETERMINANTS OF ANI5EIKONIA / Bradley er al. 511
SUBJECT AN
LE RE SUBJECT
M J R
Fig. 3. The shape of the globe was evaluated using B-scan ultrasonographs. A, Full scans of both the right and left eyes of subject AN.Interocular comparison is facilitated in B, where the abutting left and right halves of the left and right eyes, respectively, are shown forsubjects AN and JR.
photoreceptors per unit area than the emmetropic lefteye. This deduction is not unreasonable consideringthat there is no evidence of additonal retinal .growthto compensate for the extra size of the eye. Conse-quently, it seems likely that apparent size is deter-mined by the number of retinal elements stimulatedand not the absolute size of the retinal image.
This conclusion is supported further by the evi-dence given in Figure 4B, showing the fundae of twomyopic eyes. The first is from the left eye of subjectJR who has slightly more anisometropia and myopiathan subject DG, whose right eye fundus is shown inthe lower picture. Although JR has more myopia, thefundus of DG shows considerably more signs ofstretching. The significance of this difference can beseen by comparing the amount of perceptual mini-fication exhibited by the myopic eyes of these twosubjects (Fig. 1). Subject DG exhibits twice as muchminification (20%) than JR (10%). Therefore, evenfor subjects with similar amounts of anisometropiathe degree of aniseikonia correlates well with theamount of retinal stretching. This emphasizes boththe importance of nonoptical factors in determininganiseikonia, and also the weakness of any opticallybased rule of thumb for correcting it.
Discussion
Although the possibility of nonoptical factors in-fluencing aniseikonia has been appreciated for sometime,1 such influences are generally assumed to besecondary, and most emphasis in the clinical litera-ture is placed on the role of retinal image size.4 How-ever, our results show convincingly that very sub-stantial aniseikonias can be observed with congruousretinal images. The findings also emphasize that pre-
vious reports of large amounts of aniseikonia in an-isometropes corrected with spectacle lenses1213 areprobably not due to retinal image size disparities.
A)
RE
B)
LE
RE
Fig. 4, Composite fundus photographs are shown here from threesubjects. A, Both the left (top and right (bottom) eyes of subjectAN. B, The more myopic left eye of subject JR (top) and moremyopic right eye of DG (bottom).
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At the outset we posed the question: are optical ornonoptical factors most important for producing an-iseikonia? It turns out that these two types of inter-ocular difference are always opposite in sign. Myopicanisometropes have optical magnification and neuralminification. Conversely, hyperopic anisometropeshave optical minification, but nonoptical magnifi-cation. Therefore, the relative importance of each fac-tor can be gauged by measuring the resultant anisei-konia when both are present, that is, for the uncor-rected eye. Unfortunately this experiment is verydifficult to do because of the poor image quality.However, we have already measured the neural mag-nification differences, and it is simple to predict theoptical differences. The uncorrected retinal image sizedifferences (%) in axial anisometropia are approxi-mately 1.7 X RX, where RX is the spectacle correc-tion necessary at the anterior focal plane. Only oneof our sample (JR) had a neural difference that issmaller than the predicted retinal image size differ-ence. All other subjects exhibited larger neural thanoptical differences. Therefore, we conclude that, ingeneral, there are likely to be larger neural than op-tical magnification differences between the two eyesin high anisometropia.
Although these findings are somewhat contrary tothose expected, the explanation seems straight-for-ward. As the eye grows, it increases in length andcircumference. Consequently, the retinal image sizeincreases, but so does the area of retina receiving theimage. To a first approximation these opposite effectscancel. However, our data indicate that the retinalstretching around the fovea may increase by a greaterproportion than the axial length of the eye. Therefore,although, for example, the retinal image in an un-corrected myopic eye is very large, it may actuallystimulate a smaller number of retinal photoreceptors.
The clinical implications of these data are clear.First, contrary to popular belief, Knapp's Law, al-though an adequate approximation for equating ret-inal image size, cannot be used as a rule of thumbfor eliminating aniseikonia in anisometropes. Sec-ond, it may seem from our data (Fig. 1) that, a contactlens correction would serve as a useful correction forthese patients. However, before accepting this con-clusion it is worth noting a major limitation of thisstudy. Our results only represent a very small regionof the retina, and it is clear from the fundus photo-graphs in Figure 4 that the retina is likely to bestretched in a very nonuniform way. Consequently,what may be the perfect correction for one part of
the retina may introduce large aniseikonias in anotherpart of the visual field. Indeed, it may be impossibleto correct for both the anisometropia and the ani-seikonia for any large region of the retina. Eliminatinganiseikonia in the central retina while ignoring pos-sible interocular differences in perceived size in theperiphery may be the best compromise.
Key words: Anisometropia, aniseikonia, magnification,myopia, hyperopia, neural development
Acknowledgments
The authors thank Drs. R. D. Stone and D. Sheets fortheir help in producing, respectively, the ultrasonographsand fundus photographs.
References
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4. Von Bahr G: An analysis of the change in perceptual size ofthe retinal image at correction of ametropia. Doc Ophthalmol20:530, 1966.
6. Rayner AW: Aniseikonia and magnification in ophthalmiclenses. Problems and solutions. Am J Optom 43:617, 1966.
7. Straatsma BR, Heckenlively JR, Foos RY, and Shahinian JK:Myelinated retinal nerve fibers associated with ipsilateral my-opia, amblyopia, and strabismus. Am J Ophthalmol 88:506,1979.
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9. Knapp H: The influence of spectacles on the optical constantsand visual acuteness of the eye. Arch Ophthalmol Otol 1:377,1869.
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11. Arner RS: Eikonometer measurements in anisometropes withspectacles and contact lenses. J Am Optom Assoc 40:712,1969.
12. Rose L and Levinson A: Anisometropia and aniseikonia. AmJ Optom 49:480, 1972.
13. Awaya S and von Noorden GK: Aniseikonia measurement byphase difference haploscope in myopic anisometropia and uni-lateral aphakia (with special reference to Knapp's law and com-parison between correction with spectacle lenses and contactlenses). J Jpn Contact Lens Soc 13:131, 1971.
14. Sorsby A, Benjamin B, Davey JB, Sheridan M, and TannerJM: Emmetropia and its abberations. Med Res Council SpecRep Ser No. 293. London, HMSO, 1957.
15. Gullstrand A: Appendix A. In Helmholtz's Treatise on Phys-iological Optics. Translated from the 3d German edition,Southall, J. P. G, editor. Rochester, The Optical Society ofAmerica, 1924.
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