Nonoptical Determinants of Aniseikonia - Investigative ...

Nonoptical Determinants of Aniseikonia
Arthur Bradley, Jeff Rabin,* and R. D. Freeman
Interocular differences in apparent size (aniseikonia) are typically associated with interocular differences
in refractive error (anisometropia). Aniseikonia is generally thought to reflect disparities in
retinal image size that often accompany anisometropia. This assumption was examined with seven
highly anisometropic subjects who were tested under conditions in which no substantial retinal image
size differences were present. Using a dichoptic size matching task, consistent and large (mean = 22%)
aniseikonias were found. Myopic anisometropes exhibit perceptual minification, while hyperopes
demonstrate perceptual magnification when using their more ametropic eye. Both ultrasonic and
fundus examinations of these subjects indicate that differential retinal growth or stretching is responsible
for these findings. Invest Ophthalmol Vis Sci 24:507-512, 1983
Substantial interocular differences in apparent size
(aniseikonia) 1 are typically associated with interocular
differences in refractive error (anisometropia), 2
although small amounts can occur in isometropic
subjects. 3 It has been suggested that both optical and
anatomical or physiologic differences between the
eyes may be responsible for aniseikonia. 1 However,
the critical factor is generally assumed to be the difference
in retinal image size produced by the anisometropia
or its correction. 24 " 7
Most anisometropias of greater than 2 diopters result
from interocular differences in axial length rather
than optical power. 8 Therefore, regardless of the magnitude
of the anisometropia, refractive errors can be
corrected and retinal image sizes equated in the two
eyes by a simple spectacle correction placed at the
anterior focal plane of the eyes. This relationship is
described by Knapp's Law, 9 which often serves as a
rule of thumb for correcting anisometropia and eliminating
aniseikonia. 10 However, several recent studies
report substantial amounts of aniseikonia present in
anisometropes corrected with spectacle lenses."" 13
These apparent failures of Knapp's Law could result
from one or more of several reasons. The spectacle
lens positions may have differed substantially from
that of the anterior focal plane of the eye, or the
anisometropias may have originated from optical and
not axial length differences. In addition, it is possible
that 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 Development
Award EY00092 from the US National Eye Institute.
Submitted for publication March 22, 1982.
Reprint requests: R. D. Freeman, School of Optometry, University
of California, Berkeley, CA 94720.
ferences were responsible. However, because complete
information about lens position, corneal powers,
and ocular dimensions was not provided it is impossible
to discriminate between these alternatives.
In the present study we have attempted to examine
the origins of aniseikonia in highly anisometropic
subjects and tried to evaluate the relative importance
of optical and neural factors. Under conditions of
approximate equality of retinal image size in the two
eyes we find large amounts of aniseikonia, which is
most likely the result of differential growth of the two
eyes.
Subjects
Materials and Methods
Seven highly anisometropic subjects (five myopes
and two hyperopes) were chosen for this study. All
were examined carefully in the university eye clinic,
and the resulting refractive information is presented
in Table 1. The anisometropias in our sample varied
from 5 to 20 diopters, and they were therefore at the
very edge of the normal distribution of interocular
refractive error differences. 6 However, very little interocular
difference in corneal power was found
(mean = 0.5 diopters). Also, the average corneal
power of our sample was 43 diopters, which is at the
center of the normal distribution. 14 Therefore, to a
first approximation, it was reasonable to assume that
we had a sample of axial anisometropes who had
approximately equal and typical optical powers in
their eyes. Consequently, using the calculations of
Gullstrand 15 for the typical eye, we estimated the anterior
focal plane to lie 15 mm anterior to the cornea.
Large deviations from this value are unlikely in our
sample because of the homogeneity of the corneal
powers (standard deviation = 1.4 diopters).
0146-0404/83/0400/507/$ 1.10 © Association for Research in Vision and Ophthalmology
507

508 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / April 1983 Vol. 24
Table 1. Clinical data from anisometropic subjects
Aniseikonia ('%)
Corneal power (D)
Subject
Refractive error
Visual acuity
SL
CL
H
V
JR
AN
-3.25
-10-3 X 180
-19-2.5 X 10
piano
+ 1
-8 -2 X 180
-0.5
+5 -.5 X 50
-7.5 -1X2
-3 -2.25 X 10
+2
+7.5 -1.25 X 90
-9.5 -2.5 X 180
-1.5 -3X2
20/20
20/200
20/180
20/15
-10.2
-34.1
-1.3
-6.5
42.25
42.25
41.75
42.67
43.25
43.75
44.00
43.12
42.00
41.5
44.25
44.25
44.50
44.50
44.20
41.70
CP
20/20
20/400
-27.6
41.50
42.50
44.00
44.00
DH
BP
20/15
20/400
20/15
20/400
+24.5
-11.3
46.50
46.50
CD
20/20
20/40
+26.2
R 42.60
L 42.20
42.25
41.75
DG
20/400
20/15
-20.5
44.00
44.25
R = right eye, L = left eye, H = horizontal, V = vertical, SL = spectacle lens, CL = contact lens.
Procedure
A Moller-Wedell phase differences haploscope was
used to measure aniseikonia. This instrument provides
a dichoptic view by phase-coupling projection
and exposure of alternate images to each eye. The left
eye viewed a 3° X 20 min luminous bar, while the
right eye viewed a similar bar of adjustable size. Both
bars were viewed in a large empty field, which helped
minimize the effects of size constancy by providing
very little distance information. Direct comparison
eikonometry 1 was used to evaluate the aniseikonia.
All subjects were instructed to vary the size of the
adjustable bar until both appeared equal. The experimenter
randomly adjusted the length of the variable
bar between each setting, and the mean and standard
deviation of a minimum of eight settings were obtained.
Aniseikonia (%) was calculated in the following
way: Aniseikonia (%) = ([E - A]/E) X 100%.
Where E and A represent the actual lengths of the
bars seen as equally long by the least and most ametropic
eyes respectively. Positive values indicate perceptual
magnification and negative values minification
for the more ametropic eye.
All subjects were tested with their refractive errors
neutralized with trial lenses placed at a vertex distance
of approximately 15 mm from the cornea. This distance
was carefully obtained by adjusting variable
head and chin rests until the subject's closed eyelid
just touched a 15-mm protrusion from a lens blank
mounted in the haploscope lens carrier. The trial
lenses were chosen to have a small and constant shape
factor of less than 1%, and therefore they magnified
primarily on the basis of power. Two subjects were
also tested with their contact lens corrections instead
of with trial lenses.
Additional examinations were conducted with several
subjects to obtain fundus photographs and also
A- and B-scan ultrasonographs in order to assess relative
sizes and differential growths of the two eyes.
A Zeiss fundus camera was used to photograph the
horizontal meridian from the nasal to temporal ora
serrata. Both axial lengths and overall shapes of the
eyes were measured with A- and B-scans, respectively.
A Sonometrics System was used, and the B-scans
were 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 correcting
lenses are placed at the anterior focal plane
of the eyes. Consequently, if aniseikonia is dependent
primarily on retinal image size differences, it should
be negligible in our sample when corrected at a vertex
distance of 15 mm. This prediction can be examined
directly in Figure 1, which shows aniseikonia in percent
as a function of anisometropia in diopters. Contrary
to the prediction, all of our sample exhibit large
amounts of aniseikonia when corrected at or around
the anterior focal plane (filled circles). In fact, there
is a systematic relationship between anisometropia
and aniseikonia. All of the myopic anisometropes
observed the 3° bar to be smaller with their more
ametropic eye (perceptual minification), while the
converse was true for the hyperopes.
There are several alternative explanations for the
results. First, it is possible that large errors were made

VINO)
No. 4 NONOPTICAL DETERMINANTS OF ANISEIKONIA / Bradley er ol.' : 509
in placing the trial lenses. Although conceivable this
is unlikely, because errors of more than 15 mm would
be required to account for these data. 1 The consistancy
of the measurements make such large errors
unlikely. However, we have tested the possibility of
such a positioning error directly by repeating the
measurements with two of our sample (AN and JR)
while they wore their contact lens corrections (Fig.
1, open circles). Large position errors could not occur
with a contact lens correction. Therefore, assuming
the refracting surface of the contact lens to lie about
3 mm anterior to the entrance pupil of the eye, 15 the
formula for spectacle magnification (M = 1/1 - zF,
where M = % magnification, z = distance of lens
from entrance pupil, and F = power of correcting lens
in diopters) allows the trial lens position to be estimated
based on the measured aniseikonia differences
under these two conditions. For example, subject AN
exhibited a 28% increase in minification with her
myopic eye when the trial lens was used. This places
the trial lens at approximately 16 mm anterior to the
entrance pupil of the eye. The corresponding prediction
for subject JR was approximately 14 mm, indicating
spectacle lens positions slightly closer to the
eye than expected. Therefore, it is very unlikely that
the observed aniseikonias were produced by significant
lens positioning errors. In fact, to produce such
large minification for the myopic eyes of these subjects
(34% for AN and 10% for JR) the lenses would
need to be much farther, rather than a little nearer
to the eye than the anterior focal plane.
The results shown in Figure 1 are only surprising
if the ametropias are axial. However, these data are
entirely consistant with those expected from refractive
anisometropia, 1 where there should be very small
differences in retinal image size with contact lens correction
but much larger ones with spectacle corrections.
Because most anisometropias greater than 2
diopters are axially produced, 8 it is improbable that
all seven of our sample have refractive anisometropias.
The similarity in the keratometric measurements
for each eye (see Table 1) also makes this unlikely.
However, it is possible, for example, that differences
in anterior chamber depth, or lens thickness
are responsible. Therefore, in an attempt to evaluate
the relative roles of both optical and axial length differences,
we examined two of our sample with A-scan
ultrasonography (Fig. 2). The data from each eye of
subjects AN and JR are given in Table 2. The anterior
chamber depths and lens thicknesses are essentially
identical in both eyes of each subject. However, the
differences in axial length are very close to those expected
if the anisometropias were axial. Subject AN
has 20 diopters of myopic anisometropia and an axial
length difference of 7.7 mm, which could account for
2
ISEIH
z
<
CP
o
E
min
30 ~
10
0
10
20
30
40 "~
-20
ANISOMETROPIA
Fig. 1. The amount of aniseikonia in percent is plotted as a
function of anisometropia in diopters for each subject. All subjects
were tested with trial lens corrections (filled circles), and two were
also tested with their contact lens corrections (open circles). Vertical
bars indicate ±1SE.
over 90% of her anisometropia. The axial length difference
for subject JR can account for at least 95%
of his anisometropia. In conclusion, then, it is very
likely that the anisometropias in our sample result
primarily from axial length differences between the
two eyes.
The accurate lens positioning and confirmed axial
nature of the anisometropia emphasize that the aniseikonias
reported by our subjects did, in fact, occur
with approximately congruous retinal images. Therefore,
some very significant nonoptical interocular differences
must be responsible. The large amount of
neural processing that intervenes between the retinal
image and the appreciation of size (the "ocular image"
1 ) provides many possible locations for the source
of the aniseikonia. It is certainly possible that central
differences between the inputs from the two eyes
could exist in visual cortex, but the eye itself is a more
likely candidate because differences in size already
exist here.
In order to evaluate what ocular variables were responsible
for the aniseikonias, we made a detailed
examination of the globe and retinae of some of our
sample. First, to assess how differences in axial length
affected the shape of the eye, we obtained B-scan ultrasonographs
from subjects AN and JR. Complete
scans of both eyes are shown in Figure 3A for one
subject (AN). To facilitate interocular comparison the
right and left halves of the sonographs of the right
and left eyes respectively have been placed side by

INVE5TIGATIVE OPHTHALMOLOGY b VISUAL SCIENCE / April 1983 Vol. 24
SUBJECT
AN
LE piano RE -20.25
AL = 23.56mm
mmm
1 SUBJECT JR
AL = 31.22 mm
LE -12.50 RE -3.25
AL = 29.13mm
AL = 25.51 mm
Fig. 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, from
left to right, are produced by the following sources: First, on the
far left, is the emitter artifact. The second peak indicates the position
of the cornea. Then comes the peaks from the front and
back surface of the lens. Finally, a large peak can be seen from the
retina, choroid, sclera, and orbital tissue. AL = axial length. The
quantitative details of these scans are tabulated in Table 2.
side (Fig. 3B). Several aspects of globe shape can be
evaluated by simple inspection of these figures.First,
from the symmetry of the anterior segments it is evident
that the ocular length differences are restricted
to the posterior section of the eye. Also, the more
myopic eye does not exhibit much shape distortion.
These pictures indicate that the area of the globe covered
by the retina has grown considerably larger in
the more myopic eye. Therefore, when retinal image
sizes have been equated in the two eyes, the image
in the larger more myopic eye covers a smaller proportion
of the retina. It is these subjects who report
minification in their more myopic eye when the retinal
images are matched in size. Therefore, it seems
likely that the proportion of the retina covered by an
image, and not its absolute size may determine its
apparent size.
Although these pictures show conclusive evidence
of differential eye growth in anisometropia, it is not
clear where the extra (in the case of myopes) growth
occurs. Are these differences in growth spread out
uniformly over the globe posterior to the ora serata,
or are they concentrated at the posterior pole of the
eye? The interpretation of our size matching data
depends on the answer to this question, because we
sampled only a very small and select region of the
retina (1.5° on either side of the fovea). Therefore,
to examine differential growth, or stretching across
the retina we took a series of fundus shots across the
horizontal meridian of the eyes from several subjects.
Sample data are shown in Figure 4. A fundus comparison
of an emmetropic (left) eye and highly myopic
(right) eye of subject AN can be made from Figure
4A. The fundus of the left emmetropic eye is
ophthalmoscopically normal. The uniform coloring
of the retina is typical. However, the fundus of the
right myopic eye exhibits many features commonly
found in highly myopic eyes that have undergone
excessive growth or stretching. First, the separation
of the retina, pigment epithelium, and choroid from
around the optic disc is typical. Second, the pale and
nonuniform fundus is indicative of stretching and
thinning. Third, the thin retinal vessels, and the visible
choroidal vessels also indicate stretching. It is
clear from these two pictures that the area of retina
that manifested perceptual minification has undergone
excessive stretching. Therefore, in our experiment,
where retinal image size was held constant in
the two eyes of this subject (AN), the image in the
myopic right eye fell on a retina containing fewer
Table 2. A-scan ultrasonography data: ocular
dimensions in millimeters for two myopic
anisometropes whose ultrasonographs
are shown in figures 2 and 3.
Ocular dimention
Anterior cornea/
anterior lens
Lens thickness
Vitreous chamber
depth
Axial length
LE
3.7
3.4
16.4
23.6
LE = left eye, RE = right eye.
AN
RE
3.6
3.7
23.8
31.2
Subject
LE
4.0
4.1
20.9
29.1
JR
RE
3.8
3.8
18.0
25.5

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 for
subjects AN and JR.
photoreceptors per unit area than the emmetropic left
eye. This deduction is not unreasonable considering
that there is no evidence of additonal retinal .growth
to compensate for the extra size of the eye. Consequently,
it seems likely that apparent size is determined
by the number of retinal elements stimulated
and not the absolute size of the retinal image.
This conclusion is supported further by the evidence
given in Figure 4B, showing the fundae of two
myopic eyes. The first is from the left eye of subject
JR who has slightly more anisometropia and myopia
than subject DG, whose right eye fundus is shown in
the lower picture. Although JR has more myopia, the
fundus of DG shows considerably more signs of
stretching. The significance of this difference can be
seen by comparing the amount of perceptual minification
exhibited by the myopic eyes of these two
subjects (Fig. 1). Subject DG exhibits twice as much
minification (20%) than JR (10%). Therefore, even
for subjects with similar amounts of anisometropia
the degree of aniseikonia correlates well with the
amount of retinal stretching. This emphasizes both
the importance of nonoptical factors in determining
aniseikonia, and also the weakness of any optically
based rule of thumb for correcting it.
Discussion
Although the possibility of nonoptical factors influencing
aniseikonia has been appreciated for some
time, 1 such influences are generally assumed to be
secondary, and most emphasis in the clinical literature
is placed on the role of retinal image size. 4 However,
our results show convincingly that very substantial
aniseikonias can be observed with congruous
retinal images. The findings also emphasize that previous
reports of large amounts of aniseikonia in anisometropes
corrected with spectacle lenses 1213 are
probably not due to retinal image size disparities.
A)
RE
B)
LE
RE
Fig. 4, Composite fundus photographs are shown here from three
subjects. A, Both the left (top and right (bottom) eyes of subject
AN. B, The more myopic left eye of subject JR (top) and more
myopic right eye of DG (bottom).

512 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / April 1983 Vol. 24
At the outset we posed the question: are optical or
nonoptical factors most important for producing aniseikonia?
It turns out that these two types of interocular
difference are always opposite in sign. Myopic
anisometropes have optical magnification and neural
minification. Conversely, hyperopic anisometropes
have optical minification, but nonoptical magnification.
Therefore, the relative importance of each factor
can be gauged by measuring the resultant aniseikonia
when both are present, that is, for the uncorrected
eye. Unfortunately this experiment is very
difficult to do because of the poor image quality.
However, we have already measured the neural magnification
differences, and it is simple to predict the
optical differences. The uncorrected retinal image size
differences (%) in axial anisometropia are approximately
1.7 X RX, where RX is the spectacle correction
necessary at the anterior focal plane. Only one
of our sample (JR) had a neural difference that is
smaller than the predicted retinal image size difference.
All other subjects exhibited larger neural than
optical differences. Therefore, we conclude that, in
general, there are likely to be larger neural than optical
magnification differences between the two eyes
in high anisometropia.
Although these findings are somewhat contrary to
those expected, the explanation seems straight-forward.
As the eye grows, it increases in length and
circumference. Consequently, the retinal image size
increases, but so does the area of retina receiving the
image. To a first approximation these opposite effects
cancel. However, our data indicate that the retinal
stretching around the fovea may increase by a greater
proportion than the axial length of the eye. Therefore,
although, for example, the retinal image in an uncorrected
myopic eye is very large, it may actually
stimulate a smaller number of retinal photoreceptors.
The clinical implications of these data are clear.
First, contrary to popular belief, Knapp's Law, although
an adequate approximation for equating retinal
image size, cannot be used as a rule of thumb
for eliminating aniseikonia in anisometropes. Second,
it may seem from our data (Fig. 1) that, a contact
lens correction would serve as a useful correction for
these patients. However, before accepting this conclusion
it is worth noting a major limitation of this
study. Our results only represent a very small region
of the retina, and it is clear from the fundus photographs
in Figure 4 that the retina is likely to be
stretched in a very nonuniform way. Consequently,
what may be the perfect correction for one part of
the retina may introduce large aniseikonias in another
part of the visual field. Indeed, it may be impossible
to correct for both the anisometropia and the aniseikonia
for any large region of the retina. Eliminating
aniseikonia in the central retina while ignoring possible
interocular differences in perceived size in the
periphery 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 for
their help in producing, respectively, the ultrasonographs
and fundus photographs.
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