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INVITED REVIEW
Eye shape and retinal shape, and their relation to
peripheral refraction
Pavan K Verkicharla
1
, Ankit Mathur
1
, Edward AH Mallen
2
, James M Pope
3
and David A Atchison
1
1
School of Optometry and Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia,
2
Bradford
School of Optometry and Vision Science, University of Bradford, Bradford, UK, and
3
Faculty of Science and Technology and Institute of Health and
Biomedical Innovation, Queensland University of Technology, Brisbane, Australia
Citation information: Verkicharla PK, Mathur A, Mallen EAH, Pope JM & Atchison DA. Eye shape and retinal shape, and their relation to peripheral
refraction. Ophthalmic Physiol Opt 2012, 32, 184–199. doi: 10.1111/j.1475-1313.2012.00906.x
Keywords: conic sections, eye shape,
peripheral refraction, retinal shape
Correspondence: David Atchison
E-mail address: d.atchison@qut.edu.au
Received: 6 February 2012; Accepted: 14
March 2012
Abstract
Purpose: We provide an account of the relationships between eye shape, retinal
shape and peripheral refraction.
Recent findings: We discuss how eye and retinal shapes may be described as
conicoids, and we describe an axis and section reference system for determin-
ing shapes. Explanations are given of how patterns of retinal expansion during
the development of myopia may contribute to changing patterns of peripheral
refraction, and how pre-existing retinal shape might contribute to the develop-
ment of myopia. Direct and indirect techniques for determining eye and retinal
shape are described, and results are discussed. There is reasonable consistency
in the literature of eye length increasing at a greater rate than height and width
as the degree of myopia increases, so that eyes may be described as changing
from oblate/spherical shapes to prolate shapes. However, one study indicates
that the retina itself, while showing the same trend, remains oblate in shape for
most eyes (discounting high myopia). Eye shape and retinal shape are not the
same and merely describing an eye shape as being prolate or oblate is insuffi-
cient without some understanding of the parameters contributing to this; in
myopia a prolate eye shape is likely to involve both a steepening retina near
the posterior pole combined with a flattening (or a reduction in steepening
compared with an emmetrope) away from the pole.
Summary: In the recent literature, eye and/or retinal shape have often been
inferred from peripheral refraction, and, to a lesser extent, vice versa. Because
both the eye’s optics and the retinal shape contribute to the peripheral refraction,
and there is large variation in the latter, this inference should be made cautiously.
Recently retinal shape has been measured independent of optical methods using
magnetic resonance imaging. For further work on retinal shape, determining the
validity of cheaper alternatives to magnetic resonance techniques is required.
Introduction
With the recent interest in the possible roles of the shape
of the eye and peripheral refraction in refractive develop-
ment, it is timely to give a better explanation of eye and
retinal shapes. It is likely that the eye shape will be related
to the peripheral refraction as well as the latter depending
on the optics of the eye, but the picture is often simpli-
fied by unwarranted linking of the two, e.g. a particular
shape of the eye is taken to infer a particular pattern of
refraction such as a prolate shape causes relative periph-
eral hyperopia or vice versa. Retinal shape may be con-
fused with the more nebulous concept of eye shape, and
in this paper we set out to explain the relative quantities.
Ophthalmic & Physiological Optics ISSN 0275-5408
184 Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists
Retinal shape has been determined in different ways, and
a review of this will be presented.
Most theories and investigations of myopia develop-
ment have been concerned with the growth response to
defocus signals corresponding to foveal vision, but Wall-
man and Winawer
1
indicated that the defocus signal at
the periphery should be stronger than at the centre
because of the presence of more neurons in the periphery
than at centre, and that relative peripheral hyperopia
might stimulate the eye to grow, dominating the central
myopic refraction. This is supported by Ho et al.
2
who
found that the electrical response of the human retina is
sensitive to defocus, with the paracentral retina reacting
more vigorously to optical defocus than the central retina.
The mechanisms by which the retina might respond to a
blurred signal in the periphery to produce axial elonga-
tion are beyond the scope of this paper (see Charman
and Radhakrishnan,
3
; Charman,
4
for recent reviews). Also
beyond the scope of this paper is an assessment of
peripheral refraction treatments of myopia.
Shapes, axes and sections used to describe eye
and retinal shape
Ocular surfaces are typically described by conic sections.
A conic section rotated about one of its principal meridi-
ans becomes a rotationally symmetric conicoid. This can
be described by the equation
X2þY2þð1þQÞZ22ZRv¼0ð1Þ
where Zis measured along the optical axis, Xand Yare
measured along axes perpendicular to the Z-axis and to
each other, R
v
is the vertex radius of curvature, and Q
describes the asphericity (Figure 1). Q> 0 represents an
oblate ellipse (steepening away from the vertex), Q= 0 rep-
resents a sphere, )1<Q< 0 represents a prolate ellipse
(flattening away from the vertex), Q=)1 represents a
paraboloid and Q<)1 represents a hyperboloid. Alterna-
tive terms for oblate ellipsoid and prolate ellipsoid are
oblate spheroid and prolate spheroid, respectively. Some-
times asphericity is represented by the quantity pwhere
p¼1þQð2Þ
and sometimes it is represented by the eccentricity e,
where
e2¼Qð3Þ
An alternate equation to Equation (1) that can be applied
to ellipsoids is
ðX2þY2Þ=R2
xy þðZRzÞ2=R2
z¼1ð4Þ
where R
xy
,R
xy
and R
z
are the semi-axis lengths along the
X, Y and Zdirections, respectively (Figure 1). For an
oblate ellipsoid R
xy
>R
z
and for a prolate ellipsoid R
z
>
R
xy
. The vertex radius of curvature R
v
and the asphericity
Qare related to R
z
and R
xy
by
Rv¼R2
xy=Rzð5Þ
Q¼R2
xy=R2
z1ð6Þ
Non-rotationally symmetrical ellipsoids can be described
by
X2=R2
xþY2=R2
yþðZR2
zÞ=R2
z¼1
where R
x
,R
y
, and R
z
are the semi-axis lengths along the
X, Y and Zaxes. For the X-Z section, the vertex radius of
curvature R
xv
and asphericity Q
x
are given by
Rxv¼R2
x=Rzð7Þ
Qx¼R2
x=R2
z1ð8Þ
Similarly for the Y-Z section,
Ryv¼R2
y=Rzð9Þ
Qy¼R2
y=R2
z1ð10Þ
Further levels of sophistication would be to rotate and
decentre the surfaces, and to have more complex surfaces,
but we will not deal with these here.
Figure 2 shows sections and axes of the eye. Transverse
axial sections are parallel to the XZ plane, and taking the
visual axis as the Zaxis, one is usually selected to match
the XZ plane as well as possible. Sagittal sections are par-
allel to the YZ plane, and one is usually selected to match
the YZ plane as well as possible. Coronal sections are
Figure 1. A family of conicoids, all with the same vertex curvature
R
v
. Semi-axis lengths R
xy
and R
z
are shown for the prolate ellipsoid.
PK Verkicharla et al. Eye shape and retinal shape
Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists 185
parallel to the XY plane, and one is usually selected where
the Xand Ydimensions are judged to be maximums.
The antero-posterior length is usually measured from
the anterior corneal surface to the posterior pole at the
inner retina, generally understood as the axial length,
although in some studies it has been measured from the
posterior cornea to the posterior pole and in others it has
been measured from the anterior cornea to the outer
sclera. This distance can be measured through either
transverse axial or sagittal sections.
The vertical length, or height, is the widest distance
between the top and bottom of the eye and can be
obtained from either sagittal or coronal sections. The hor-
izontal length, or width, is the widest distance between
temporal and nasal sides of the eye and can be obtained
from either transverse axial or coronal sections. The
height and width can be measured from inner retina to
inner retina or from outer sclera to outer sclera.
Eye shape can be quantified using the axial length,
height and width, with a number of studies using the
ratios of axial length to height and/or axial length to
width as additional descriptors. Clearly this is an oversim-
plification as it ignores the rapid change in shape that
occurs at the corneal-scleral intersection. Retinal shape
can be similarly described by fitting ellipsoids to its posterior
part, the functional part as far as imaging is concerned.
The eye shape and retinal shape components will have
similar heights and widths, but the lengths of the ellip-
soids used to fit the retina are shorter than the axial
length by about 3.1 mm.
5
Models of retinal shape and their relation to
peripheral refraction
Variations of retinal shape in myopic eyes can be related
to models of the retinal stretching that accompanies the
increase in axial length as shown in Figure 3. These
include a global expansion model (a), a model where the
stretching occurs parallel to the optical axis at the equato-
rial region (b), and a model where the stretching takes
place only at the posterior pole (c). A hybrid model,
called the axial expansion model is the combination of
equatorial and posterior pole expansion models (d). The
first three models are shown with spherical surfaces and
the hybrid model is shown with a prolate ellipsoid
surface.
A thin beam (pencil) of light from an off-axis object
point on a plane surface, passing through a symmetrical
optical system, will be focused as lines at two positions,
one corresponding to light refracted in the (tangential)
plane containing the object point and the optical axis and
the other in the (sagittal) plane perpendicular to this
plane. For a range of object points across the surface there
will be two image shells as shown in Figure 4a. Taking the
optical system as an emmetropic eye, we will assume that
its normal retinal shape is a sphere with radius of curva-
ture of about 12 mm and that the shell corresponding to
the average of the tangential and sagittal shells coincides
approximately with this sphere. Figure 4b shows this reti-
nal shape (solid line) along with changes in retinal curva-
ture that make the retina flatter or steeper. Light from a
distant off-axis point converges to a point that coincides
with the normal retina, is in front of the flatter retina
causing peripheral myopia, and is behind the steeper retina
Figure 2. Scanning sections and axes of the eye. The sagittal section
(solid line) is a vertical section containing the visual axis, the transverse
axial section (dashed line) is a horizontal section containing the visual
axis, and the coronal section (dotted line) is a vertical section perpen-
dicular to the visual axis.
(a) (b) (c) (d)
Figure 3. Models of retinal stretching in myopia: a) global b) equatorial c) posterior polar and d) axial expansion. The solid circles represent the
shape of the retina of an emmetropic eye, the dashed shapes represent the myopic retinas, and the arrows indicate the regions of stretching. The
first three models were presented by Strang et al.
6
Eye shape and retinal shape PK Verkicharla et al.
186 Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists
causing peripheral hyperopia. The eye with the steeper ret-
ina might respond to the peripheral hyperopic defocus by
elongating and thus causing myopia.
This description can be extended to a myopic eye.
Assuming the optics of the eye are the same as those of
the emmetropic eye described above apart from an
increase in length, for the flatter retina an off-axis light
beam’s ‘mean’ focus will be further in front of the retina
than for the ‘normal’ retina. The peripheral refraction
corresponding to this is referred to as relative peripheral
myopic refraction because a more negative correction is
needed than for the normal retina. For the steeper retina,
the off-axis light beam’s ‘mean’ focus will be closer to the
retina than for the normal retina, resulting in a relative
peripheral hyperopia. Similar to the emmetropic eye with
a steep retina, the eye might respond to the relative
hyperopic defocus by becoming yet more myopic.
The situation described above leading to myopia devel-
opment might be turned around – ‘excessive’ relative
peripheral myopia in the young emmetropic or hyperopic
eye might result in a ‘stop’ signal to normal emmetrop-
ization and lead to an adult hyperopic eye.
The above situation is over-simplified: real eyes do not
generally exhibit rotational symmetry and so peripheral
refraction varies according to visual field meridian. Most
emmetropic eyes have low levels of peripheral myopia, as
will be discussed later. Most emmetropic retinas are
oblate in shape rather than spherical,
5
but for the present
we will ignore this.
Figure 5 shows how models of retinal stretching relate
to image position and relative peripheral refraction. For
all models, the image surface is closer to the retina in the
periphery than in the centre, resulting in less myopia in
the periphery than in the centre, that is, there is relative
peripheral hyperopia. This effect is greatest for posterior
polar expansion, followed by axial, equatorial and global
expansion.
Peripheral refraction
Peripheral refraction studies date back to Thomas Young
7
who determined the tangential and sagittal image shells,
for a 25 cm diameter circular object surface, for a
schematic eye based on measurements of his left eye. This
was followed by several studies in the late nineteenth and
early twentieth centuries as reported by Ames and
Proctor.
8
Ferree et al.
9–12
conducted a well-known study
of peripheral refraction along the horizontal meridian out
to 60from fixation in 21 subjects using an objective
refractometer. They identified three different patterns of
peripheral refraction. The type A pattern had ‘mixed’
astigmatism in which the tangential refraction (refraction
along the horizontal direction) became more myopic and
sagittal refraction (refraction along the vertical direction)
became more hyperopic, the type B pattern had relative
hyperopic astigmatism in which both tangential and
sagittal refraction became more hyperopic into the periph-
ery, and the type C pattern had asymmetrical astigmatism
(a) (b)
Figure 4. (a) Formation of tangential (T-dotted line) and sagittal (S-dashed line) images either side of retina (R-bold line). (b) Formation of the
mean of the image shells, and its location relative to the retina for three different retinal shapes. Should the shape of the retina influence growth,
this will be on the basis of summation of signals across the retina, not merely at a single position.
Figure 5. Positions of images relative to the myopic retina for the
global, equatorial, posterior pole, and axial expansion models. It is
assumed that the retinal surfaces remain spherical in the elongated
regions for the first three models, while the surface for the axial
expansion model is a prolate ellipsoid.
PK Verkicharla et al. Eye shape and retinal shape
Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists 187
with the peripheral refraction differing between nasal and
temporal sides of the horizontal peripheral field.
Ferree and Rand
11
related the peripheral refraction pat-
terns to the likely shapes of eyes. They did not use the
terms ‘relative peripheral myopia’ or ‘relative peripheral
hyperopia’ as are now used, but their assertions were
equivalent to suggesting that a prolate ellipsoid shape
would increase the relative peripheral hyperopia or
decrease the relative peripheral myopia. As should be
apparent from Figure 1, changing from a spherical shape
to oblate elliptical and prolate elliptical shapes, but with-
out changing the vertex curvature, will result in shifts
towards relative peripheral hyperopia and relative periph-
eral myopia, respectively. These are in the opposite direc-
tions to Ferree and Rand’s suggestions, as they assumed
that accompanying the change in asphericities would be a
change in vertex curvature. This is made clear at one
point only in the paper, when referring to an eye with a
pattern of relative peripheral myopia, or ‘myopic astigma-
tism’ because the nearly emmetropic eye has peripheral
myopia in both principal meridians, they refer to ‘‘an
eyeball flattened at the back, with a shape tending
towards that of an oblate spheroid’’ (page 930). It is likely
that Ferree and Rand did not consider that, accompany-
ing differences in axial length and eye shape, eyes might
have different equatorial dimensions as in the develop-
ment of myopia according to the global model of myopia
expansion. Figure 6 shows the effect of different shaped
ellipsoids on peripheral refraction in which the equatorial
diameter does not vary: both vertex curvature and asphe-
ricity differ between the ellipsoids.
By considering the amount of peripheral astigmatism
(the difference in refraction between the two principal
meridians), Ferree and Rand inferred the power and
length of the eye, considering that eyes with small degrees
of peripheral astigmatism were likely to be longer and less
powerful, and vice versa for eyes with higher degrees of
peripheral astigmatism.
While others since them involved in peripheral refrac-
tion have been vague about eye shape, e.g. is it the retinal
shape or an overall shape of the eye, Ferree and Rand
11
seemed to have in mind the shape of the retina: ‘‘Atten-
tion may be called to the following points... the possibility
of determining roughly the conformation of the retina
and the shape of the posterior half of the eyeball’’ (pages
937–938).
Rempt et al.
13
investigated peripheral refraction in 442
young adults undergoing pilot training out to 60along
the horizontal visual field using retinoscopy. They
described five patterns of peripheral refraction (types
I–V), shown in stylistic pattern in Figure 7. There is a
progression in pattern from type I, which is the same as
type B identified by Ferree et al., to type II, type IV and
type V, in which both horizontal meridian and vertical
meridian refractions move in the myopic direction. Type
III is an asymmetric pattern similar to Ferree et al.’s type
C. The frequency of the patterns was related to the cen-
tral refraction with 91/141 myopes having the type I pat-
tern, 135/217 emmetropes and 61/84 hyperopes having
the type IV pattern, and 17/34 cases of type V occurring
for hyperopes.
The findings of Rempt et al.
13
regarding the way in
which peripheral refraction patterns change with central
refraction have been supported and elaborated by numer-
ous studies. Since this time, results have been shown as
the mean refraction combined with a measure, or mea-
sures, of astigmatism. A summary of findings along the
horizontal visual field is as follows:
1There is considerable intersubject variation within
members of the same group (e.g within emmetropes),
as occurs for the higher order aberrations.
2Several studies have found emmetropic groups to have
a weak relative peripheral myopia
14–17
although some
have found a weak tendency in the hypermetropic
direction on one or both sides of the visual field.
18
Myopic groups show relative peripheral hyperopia,
14–19
which to some extent increases with increase in myo-
pia,
15
and hypermetropic groups show relative peri-
pheral myopia.
18,20
As noted by Charman and
Radhakrishnan,
3
there is a tendency for the peripheral
refractions of the different refraction groups to con-
verge as field angles get larger and this will occur for
the axial expansion model eye of Figure 3.
21,22
3Some subjects shift from a relative peripheral myopic
pattern to a relative peripheral hyperopic pattern at
large angles e.g >45.
23
4Peripheral astigmatism decreases with increase in myo-
pia;
15
possibly because of small numbers this has not
been noted in many studies.
Figure 6. Effect of different shaped ellipsoids with constant equato-
rial diameter on peripheral refraction.
Eye shape and retinal shape PK Verkicharla et al.
188 Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists
5The turning point (minimum or maximum) of mean
refraction or of regular (J
180
or 90/180) astigmatism
is usually a few degrees into the temporal visual field
24–26
and decreases slowly with increase in myopia.
15
This is
usually attributed to the angle alpha, the angle between
the visual axis and the best fit optical axis at the nodal
point; Atchison et al.,
15
but not Dunne et al.,
26
found a
significant relationship between the turning point of
astigmatism and angle alpha.
6The oblique component of astigmatism (J
45
or 45/135
astigmatism), which was not investigated in most stud-
ies before 1981, is much smaller in the periphery than
the J
180
component and is linearly related to peripheral
angle.
15
7Effects of age
17,20
and ethnicity are small.
16
8The effects of accommodation are unclear: Walker and
Mutti
27
found a hyperopic shift in relative peripheral
hyperopia upon accommodation,
28
Davies and Mallen
29
found no effect of accommodation on relative periph-
eral refraction for either emmetropic or myopic groups,
and Whatham et al.
30
found a myopic shift in relative
peripheral refraction in a group of myopic children
(e.g. 0.74D and 0.59D at 40temporal and nasal fields,
respectively, with nearly 3 D increase in accommoda-
tion demand).
9Manipulating refractive correction in the form of
refractive surgery,
31
orthokeratology,
32–34
special con-
tact lenses
35
and special spectacle lenses
36
has consider-
able and largely predictable effects on peripheral
refraction.
Studies of peripheral refraction have been restricted
mainly to the horizontal visual field, while some two
dimensional studies have only gone to small angles, e.g.
20–25from fixation.
37,38
Atchison et al.
15
measured
along the vertical visual field to ±35from fixation in a
subset of 43 of their 116 subjects and found different pat-
terns than along the horizontal visual field. For emme-
tropes the relative peripheral myopia was greater along
the vertical than along the horizontal visual field. With
increase in myopia, there was little change in relative
peripheral refraction. These findings have since been
supported.
17,19
Atchison et al. found that the regular
astigmatism was similar in vertical and horizontal fields,
apart from a change in sign. In the vertical visual field
the turning point of regular astigmatism was ())3in
the inferior field, without any dependence on central
refraction. The oblique astigmatism changed at three
times the rate with increasing angle along the vertical field
than along the horizontal field, and this was attributed to
angle alpha along the horizontal visual field.
Without any changes in the optics of the eye apart
from the shape and position of the retinal surface, all
models of retinal stretching predict, to various degrees,
the trend of increasing relative peripheral hyperopia along
the horizontal visual field with increase in myopia (Fig-
ure 5), but only the global stretching model comes close
to predicting the relative lack of change of relative
peripheral refraction along the vertical visual field.
Atchison
39
modelled peripheral optics according to bio-
metric measurements in 121 emmetropic and myopic
young adults. The models showed increase in corneal cur-
vature, increase in vitreous length, and change in retinal
shape with increase in myopia. The retinal vertex radii of
curvature and the retinal asphericities in XZ and YZ
sections were given by
RxvðmmÞ¼12:91 0:094SR
Qx¼þ0:27 þ0:0026SR
RyvðmmÞ¼12:72 þ0:004SR
Qy¼þ0:25 þ0:0017SR
where SR is the spectacle refraction
5
[see Measurements
of retinal shape]. The modelling predicted relative periph-
eral myopia in emmetropic eyes in both horizontal and
vertical visual fields. Along the horizontal visual field, the
modelling predicted slight increases in relative peripheral
hyperopia with increase in myopia that were less than
those of the experimental results of Atchison et al.
20
Along the vertical visual field, the modelling predicted little
Figure 7. Five types (I–V) of skiagrams (peripheral refraction plots) described by Rempt et al.
13
. Types I, III and IV are similar to types B, C, and A,
respectively, identified by Ferree et al. The curves are shown as parabolas, but real plots are seldom as regular.
PK Verkicharla et al. Eye shape and retinal shape
Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists 189
change in refraction, compared with the relative periph-
eral myopia of the experimental results for a range of
refractions (Figure 8).
Relative peripheral refraction and progression of
myopia
Hoogerheide et al.
40
followed the refraction of 214 trainee
pilots over an unspecified time interval (‘during the fol-
lowing years’), most of whom were in the Rempt et al.
13
study. The emmetropes and hyperopes who developed
myopia were disproportionately represented by those with
the type I refractive profile. The proportions of each type
that went on to develop myopia were 17/36 of type I
(47%), 3/43 type II (7%), 3/14 type III (21%), 3/112
(3%) type IV, and 0/9 (0%) type V. Stone and Flitcroft
41
and Wallman and Winawer
1
drew attention to this work,
beginning a period of interest that peripheral optics might
influence development of myopia either through the
peripheral refraction pattern or through the retinal shape.
Mutti et al.
14
measured peripheral refraction at 30in
the nasal visual field in 820 children aged between 5 and
15 years. Following Ferree et al., they described ocular
shapes on the basis of relative peripheral refraction at this
position. Relative peripheral hyperopia of +0.80 ± 1.29D
was measured in myopic children and interpreted as indi-
cating prolate eye shapes. Relative peripheral myopia of
)0.41 ± 0.75D was measured in emmetropic children and
interpreted as indicating near spherical or oblate eye
shapes, and relative peripheral myopia of )1.09 ± 1.02D
was measured for hyperopic children and interpreted as
indicating oblate shapes. These inferences of shape based
on peripheral refraction have appeared in many papers
since.
Mutti’s group has followed its cohort for a decade.
Mutti et al.
42
reported rapid changes in relative peripheral
refraction in the hyperopic direction before the onset of
myopia, although as noted by Charman and Radhakrish-
nan
3
progression towards myopia began before relative
peripheral refraction became markedly hypermetropic. In
their latest paper Mutti et al.
43
were less enthusiastic,
reporting that relative peripheral hyperopia had little con-
sistent influence on the risk of myopia onset, with a mean
annual progresion of myopia of only )0.024D per diopter
of relative peripheral hyperopia.
Sng et al.
44
performed a 1 year longitudinal study on
central and peripheral refraction along the horizontal
visual field at ±15and ±30in Chinese Singaporean
children aged 7 ± 3 years. At baseline, the peripheral
refraction patterns in children who became or did not
become myopic were similar. The children who were
myopic at baseline or who became myopic had relative
peripheral hyperopia at the follow up, while children who
did not become myopic retained relative peripheral myo-
pia. Shifts in spherical equivalent refraction after 1 year in
the ‘became myopic group’ were )1.51 ± 0.63D at centre
and )1.08 ± 0.70D and )1.06 ± 0.64D at temporal and
nasal 30º visual field, respectively. These results indicate
that relative peripheral hyperopia might not be an essen-
tial factor in development of myopia.
Studies with rhesus monkeys by Earl Smith’s group
provide compelling evidence for the role of peripheral
retina in the development of myopia.
45–49
Smith and col-
leagues suggested that, for the monkey model, there are
similarities in the ocular shape changes that occur due to
form deprivation and imposed refractive blur, perhaps
indicating a common mechanism relating these different
visual interventions.
47
However, the recent findings
Horizontal
(a) (b) Vertical
Figure 8. Mean refraction in (a) horizontal and (b) vertical visual fields, as a function of angle for measured data fits
15
and theoretical data
39
for
emmetropia, 4.00 D myopia and 8.00 D myopia. For the experimental results, quadratic fitting coefficients are used and asymmetry about the
fixation point is ignored. The quadratic fitting co-efficient is given by H)0.000206x)0.000270, V)0.000551, where xis central refraction in
dioptres, with units of D per degrees
2
.
Eye shape and retinal shape PK Verkicharla et al.
190 Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists
mentioned above lead to the view, that in humans, the
peripheral refraction pattern is largely a consequence of,
rather than a determinant of central refraction. It remains
possible that the retinal shape, possibly through biome-
chanical factors, might be a determinant for the develop-
ment of myopia.
50–52
Measurements of eye shape
Eye shape can be investigated by imaging techniques such
as X-rays and computerized tomography,
53–55
ultrasonog-
raphy
56,57
and magnetic resonance imaging.
5,58–65
The
results from several studies of eye shape are given in
Table 1. The mean increases in axial length with increase
in myopia for adult eyes are 0.33 mm D
)1
and 0.35 mm
D
)1
according to Deller et al.
53
and Atchison et al.
61
which are in good agreement with studies of axial length
in adults using other methods. Eye shape in these studies
was mainly a comparison of one or both of height Hand
width of the eye Wwith the length L. The dimensions
were not measured consistently across studies, for exam-
ple some studies used the outer eye while others used the
inner retina, but this does not affect the rate at which
dimensions change with alteration in refraction. The
results are expressed in different ways, but apart from
Cheng et al.
59
the studies found greater increase in length
than in height and/or width with increase in myopia. Del-
ler
53
found changes in L,H,Wwith changes in refraction
in the approximate ratio 2:1:1, while Atchison et al.
61
obtained the ratio 3:2:1 (in the midst of considerable
intersubject variation). Two studies found no significant
differences in eye shapes between emmetropia and hyper-
opia, but hyperopia was small in one study
53
and its
range was not specified in the other.
54
Some studies referred to the eye shape in terms of
ellipsoids, using prolate and oblate to describe the situ-
ation where the ratio L/H(and/or L/W) is greater than
and less than one, respectively,
62–64
while Zhou et al
54
used the terms ‘long oval-shaped’ and ‘cross oval-
shaped’ and Moriyama et al.
63
used the terms ‘cylindri-
cal’ and ‘barrel’. Ishii et al.
65
considered that the use of
a single metric was insufficient to describe eye shape
and proposed the use of ‘elliptic Fourier’ descriptors.
Two of these, ‘width expansion’ and ‘posterior length’
terms, were strongly correlated with the L/H ratio and
seemed to give useful information, although it is
doubtful that these are any more suitable than provid-
ing the lengths.
Atchison et al.
61
considered that approximately a quar-
ter of their myopes fitted each of the global and axial
expansion models, described in Figure 3, exclusively.
When considering height the proportions shifted slightly
in favour of the global expansion model (30% vs 26%),
and while considering width the proportions shifted in
favour of the axial expansion model (18% vs 47%).
Measurements of retinal shape
Retinal shape can be determined by the methods men-
tioned in the previous section, e.g. magnetic resonance
imaging.
5,58,66
It can be determined also by indirect opti-
cal methods that are based on peripheral refraction
22,67,68
and partial coherence interferometry.
69–73
Results using
these techniques are summarised in Table 1.
Following their magnetic resonance imaging study of
eye shape,
61
Atchison et al.
5
analysed posterior retinal
shapes as asymmetric, decentred and tilted ellipsoids. An
example of this analysis is given in Figure 9. The mean
ellipsoid of emmetropes had an oblate retinal shape with
the dimensions R
z
= 10.04 ± 0.49 mm,R
x
= 11.40 ± 0.47
mm, R
y
= 11.18 ± 0.50 mm,). With increase in myopia,
the retinas became less oblate with more elongation in
length (0.16 mm D
)1
) than in height (0.09 mm D
)1
) and
width (0.04 mm D
)1
), the latter not being significantly
different from zero, but few myopes had retinal shapes
that were prolate. There was significant increase in vertex
curvature c
xv
with myopia (0.64 m
)1
D
)1
) along the hori-
zontal plane, but not along the vertical plane. Fitting
equations were:
Cxvðmm1Þ¼77:639 þ0:636SR
Qx¼þ0:279 þ0:028SR
Cyvðmm1Þ¼78:691 0:019SR
Qy¼þ0:258 þ0:018SR
where SR is the spectacle refraction. Also of note is that
the mean retinal ellipsoid was tilted by 11.5about the
vertical axis towards the nose, the retina vertex was de-
centred relative to the visual axis by x=)2.28 + 0.055SR
(to the nasal side) and there was a space, or ‘anterior seg-
ment’, from the anterior cornea to the front of the retinal
ellipsoids of approximately 3.0 mm that was not affected
by refraction.
Dunne
67
developed an algorithm to determine retinal
shape. Model eyes were generated, using a method
devised by Bennett
74
and modified by Royston et al.,
75
comprising a corneal surface, two lens surfaces and the
retina, using measurements of corneal curvature, lens
thickness, anterior chamber depth, vitreous depth, and
peripheral refraction. In this method, the curvatures of
the lens surfaces are selected so that the ratio of the sur-
face curvatures matches those of the lens in the Gull-
strand-Emsley model eye. Dunne determined theoretical
peripheral refractions at each field angle using sagittal and
PK Verkicharla et al. Eye shape and retinal shape
Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists 191
Table 1. Summary of studies of eye shape and retinal shape.
Authors Technique Procedure Subjects Results
Comments
about
distances
a
Deller et al.
53b
Radiography from
X-rays – subjective
responses
Slit beam transversed
the eye
perpendicular to the
dimension
measured. Exposure
marked on film
11 Hyp, 19 E, 15 My
Adults
E: similar L, H, W; Hyp similar
L, H, W
As My›, increase in L, H,
W in approx ratio 2:1:1
Vohra &
Good
56b
B-scan
ultrasonography
Transverse axial 100 eyes per 50
patients classified by
axial length. Most
high My
DL:DW>3
Fledelius &
Goldschmidt
57b
B-scan
ultrasonography
Transverse axial 61 eyes/31 unilateral
and bilateral high
My > 50 years
‘Regular’ and ‘irregular’
shapes
Mean L/W 1.07 – range
0.92–1.36
Irregular shaped eyes had
highest My and high L/W
Zhou et al.
54b
Computerized
X-Ray tomography
Transverse axial
section
33 Hyp, 76 E, 141 My
(255 eyes/131 adults)
L/W for My > L/W for E, Hyp
L/W›as My›
Not clear. L
measured
through optic
nerve
Song et al.
55b
Computerized
X-Ray tomography
Transverse axial and
coronal sections
406 eyes/354
children <20 years
Emmetropes similar L, H, W
Myopia AL > H, W
L from
posterior
cornea
Cheng et al.
59b
Magnetic resonance
imaging
Eye coil, transverse
axial and coronal
sections
8 Hyp, 6 E, 7 My W > L, H
Little change in shape with
refraction
Outer
dimensions
Chen et al.
58c
Magnetic resonance
imaging
Eye coil, transverse
axial and coronal
sections
3 Hyp, 4 E, 4 My Posterior retina more prolate
in shape for My than E and
Hyp in transverse axial
section
Miller et al.
60b
Magnetic resonance
imaging
Transverse axial
section
9 Hyp, 32 E, 37 My As My›,DL>DW
Atchison et al.
61b
Magnetic resonance
imaging
Eye coil, transverse
axial and sagittal
sections
22 E, 66 My young
adults
As My›, increase in L, H,
W in approx ratio 3: 2: 1
Atchison et al.
5c
Magnetic resonance
imaging
Per Atchison
et al. 2004
Retina shape
determined from
posterior 240.3D
shapes obtained
from sections, with
rotations,
decentration and
asymmetry
Per Atchison et al.
2004
As My›, increase in L, H,
W of posterior retina in
approx ratio 3: 2: 1
Oblate shape retinas in most
eyes, but less so as My›
Steepening of vertex
curvature in transverse axial
section, but not sagittal
section
Singh et al.
62b
Magnetic resonance
imaging
Head coil
3D images
determined from 2D
transverse axial slices
Ocular shape
described
qualitatively by
colour coding
7 young adults with a
range of refractions
Considerable variations in eye
shape between subjects of
similar refractive errors
Outer
dimensions
Eye shape and retinal shape PK Verkicharla et al.
192 Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists
Table 1. Continued
Authors Technique Procedure Subjects Results
Comments
about
distances
a
Moriyama
et al.
63b
Magnetic resonance
imaging
Head coil
Section not stated
3D images
determined from
series of 2D slices
20 E, 8 unilateral high
myopes, 36 bilateral
high myopes
Posterior staphyloma in
several high myopic subjects
Some had exaggerated
posterior retinal oblate
shapes (termed ‘barrel’) and
others had pronounced
prolate shapes (termed
‘cylindrical’)
Outer
dimensions
Lim
et al.
64b
Magnetic resonance
imaging
Head coil
3D images
determined from
series of 2D
transverse axial slices
134 eyes/67 6 year
old Singaporean
Chinese boys
For non-My, as refraction less
hyperopic: L›,H›,W›
(unadjusted for height)
For My, as My›:L›but no
change H, W (unadjusted
for height)
Conclusion: My eyes axially
elongated
Outer
dimensions
Ishii et al.
65b
Magnetic resonance
imaging
Head coil
3D images
determined from 2D
transverse axial slices
Analysis of horizontal
section
Shape given by
‘Elliptic Fourier’
descriptors
105 children,
1 month to 19 years
old
‘width expansion’ term PC1
strongly positively correlated
with ‘oblateness’ given by
1)L/(2*W) and also with
spherical equivalent
refraction
‘posterior length term’ PC2
negatively correlated with
oblateness
Summary: Hard to made firm
conclusion with regards eye
shape and refraction as
confounding effect of age
L measured
from post
corneal
Gilmartin
et al.
66bc
Magnetic resonance
imaging
Head coil
3D images
Determined
semi-distances from
visual axis at 17.%,
52.5% and 72.50%
of axial length
31 E, 35 My
young adults
Most retinas have oblate
shapes, but less so for My
than for E
At half axial length, (H for
My)/(H for E) = 1.02 and
(W for My)/(W for E)
= 1.01
Above results suggest
predominately axial
expansion in both horizontal
and vertical meridians
Logan et al
68c
Dunne’s approach
67
Transverse axial section
Peripheral refraction
to ±35
Transverse chord
diameter TCD (width
at maximum angles)
compared with L
56 isometropes and
anisomyopes (>2 D),
white and
Taiwanese-Chinese
TCD/Lsmaller in the more
My eye
TCD/Lflas My›in Chinese
eyes only
Smaller TCD/Linterpreted as
more prolate shape
Schmid
69,70c
Partial coherence
interferometry
Retinal steepness
based on comparing
lengths along
different meridians
to ±20.RPEL = peripheral
L– central L, steeper as
more negative
23 Hyp, 23 E, 17 My
7-15 years
RPEL steeper in My than E,
Hyp
RPEL significantly related to
refractive error group at 15
nasal and superior visual
fields
PK Verkicharla et al. Eye shape and retinal shape
Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists 193
tangential ray-tracing. The corneal surface was treated as
an ellipse and its asphericity was adjusted so that the
calculated peripheral astigmatism matched the measured
peripheral astigmatism at any field angle. The retinal cur-
vature was altered until the theoretical sagittal refraction
matched the measured sagittal refraction. When this pro-
cedure was completed for a number of positions, the reti-
nal shape was estimated by fitting an ellipse. Testing with
model eyes gave good results.
Logan et al.
68
used Dunne’s method to estimate retinal
shape in the transverse axial section for white and Chi-
nese isomyopes and anisomyopes. Their measure was the
ratio of the transverse chord diameter of the retina, at the
maximum angles tested, to the axial length. This was
found to be smaller in the more myopic eye of anisomyo-
pes, and become smaller as myopia increased in the Chi-
nese eyes only. Reduction in the ratio was interpreted as
a more prolate shape of the retina, but this parameter
requires further investigation.
Partial coherence interferometry compares the optical
path lengths of two beams, one of which is reflected from
the cornea and the other which travels into the eye and is
reflected at one of the surfaces. Because the source (diode
laser or super luminescent diode) has a wide bandwidth
of wavelengths compared with a laser, and consequen-
tially a short coherence length, a strong interference signal
occurs only when the optical path lengths are similar
rather than when optical path lengths differ by multiples
of wavelengths. One commercial instrument, the Carl
Zeiss IOLMaster, provides only the total axial length
(anterior chamber depth is provided by an optical
method), while the newer Haag-Streit Lenstar provides
internal lengths also. The IOLMaster uses a single index
within the eye (1.3549), but Haag-Streit does not indicate
what is used for the Lenstar.
Schmid
69–71
developed his own partial coherence inter-
ferometer. He measured corneal to retinal lengths both
axially and in the periphery at a maximum of 20from
fixation and gave a measure of retinal steepness by sub-
tracting the central length from the peripheral length (rel-
ative peripheral eye length, RPEL). Because of the small
angles used, this is probably a measure of foveal radius of
curvature and surface tilt. RPEL was more negative (‘stee-
per’) for myopic than for emmetropic and hypermetropic
children,
69,70
and myopic shifts over 2 years correlated
significantly with RPEL at 20nasal field (steeper retinas
giving more myopic shift).
71
Mallen and Kashyap
72
used the IOLMaster with an
external attachment containing a beam splitter, goniome-
ter and a Maltese cross target that allowed the measure-
ments of peripheral eye lengths. Figure 10 shows
measurements with this type of system. This method
could be extended to giving estimates of vertex radius of
curvature and asphericity.
Table 1. Continued
Authors Technique Procedure Subjects Results
Comments
about
distances
a
Schmid
71c
Partial coherence
interferometry
Retinal steepness per
Schmid 2003a,b
140 7-11 year
children, 92 available
at 2 year follow-up
Myopic shifts over 2 years
correlated significantly with
RPEL at 20nasal field
(steeper retinas give more
myopic shift)
Mallen &
Kashyap
72c
Partial coherence
interferometry
Modification of
commercial
instrument,
horizontal and
vertical fields
to ±40
One emmetrope and
two myopes
Retinal asymmetry
Evidence of temporal-nasal
retinal asymmetry
Atchison &
Charman
73c
Partial coherence
interference
Theoretical In model eyes, reasonably
accurate measure of retinal
contour when incident
beam normal to cornea
without taking into account
light bending within eye.
Most technical details omitted. It is understood that L for Myp > L for E > L for H, as is found for all relevant studies and this is not covered.
a
Information included if length is not anterior cornea to inner retina or height and width are not measured between inner retinas.
b
Eye shape.
c
Retinal shape.
E, emmetropes; My, myopes; Hyp, hyperopes; L, length; H, height; W, width; ›increases; fldecreases.
Eye shape and retinal shape PK Verkicharla et al.
194 Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists
As it has been applied to determining retinal shape,
partial coherence interferometry suffers from optical
distortions. Firstly, little account has been taken of the
different refractive indices in the eye’s media; as men-
tioned earlier the IOLMaster uses a constant refractive
index to convert from optical path lengths to distances,
and it is not clear what procedure is used by the Haag-
Streit Lenstar. Secondly, no allowance has been made for
deviation of beams inside the eye.
A theoretical investigation of the partial coherence
interferometry technique indicated that it can give reason-
ably accurate results for retinal shape.
73
An improved
method would make allowance for deviation of beams
inside the eye using other biometric parameters (e.g. corneal
Figure 9. Processing of sagittal (right) and transverse axial magnetic resonance images for one subject with a )2.50 D refraction. Note that this
subject has negative retinal asphericities, unlike most participants in the Atchison et al.
5
study.
Horizontal
(a) (b)
Run 1
Run 2
Run 1
Run 2
Vertical
Figure 10. Off-axis length measurements for one participant using partial coherence interferometry (Haag-Streit Lenstar) along the horizontal (a)
and vertical (b) visual fields. Results are shown for two runs and error bar show intra-run standard deviations of five measurements.
PK Verkicharla et al. Eye shape and retinal shape
Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists 195
topography, internal distances, lens surfaces from Sche-
impflug photography or phakometry and lens gradient
index from magnetic resonance imaging) and should be
verified by a direct technique such as magnetic resonance
imaging. Figure 11 shows the conversion of the off-axis
length measurements of Figure 10 to retinal shapes using
a simple eye model. The match between the partial coher-
ence method and MRI is excellent apart from at the tem-
poral retina for which the partial coherence technique
overestimates the steepness of the retina and more sophis-
ticated modelling is required.
If measuring retinal shape is considered to be impor-
tant and potentially diagnostic concerning the value of
treatment for myopia, it will be useful to validate meth-
ods such as Dunne’s method and partial coherence inter-
ferometry, as these provide cheaper and quicker
alternatives to magnetic resonance imaging.
Conclusions
This paper has shown how eye and retinal shapes may be
described in terms of conicoids, and in it we have
described an axis and section reference system for deter-
mining shapes. We have described how patterns of retinal
expansion during the development of myopia contribute
to changing patterns of peripheral refraction, and how
the pre-existing retinal shape might be a contributor to
the development of myopia. We have described tech-
niques, both direct and indirect, for determining eye and
retinal shape, and results using these techniques.
To conclude this review, we make the following points:
1Eye shape and retinal shape are not the same; as an exam-
ple an eye shape may be described as prolate because the
length is longer than the width and/or height, but the
corresponding retinal shape might be oblate.
2Merely describing an eye shape as being prolate or
oblate is insufficient without some understanding of
the parameters contributing to this; in myopia a pro-
late eye shape is likely to involve a steepening retina
near the posterior pole with a flattening (or a reduc-
tion in steeping) away from the pole.
3In the recent literature, eye and/or retinal shape have
been inferred from peripheral refraction, and to a lesser
extent, vice versa. Given that both the eye’s optics and
the retinal shape contribute to the peripheral refraction,
and the large variation found in the latter, this infer-
ence should be made cautiously.
4For further work on retinal shape using cheaper alter-
natives to magnetic resonance techniques, determining
the validity of the techniques is essential.
Acknowledgements
This work was supported by an ARC Discovery grant
and an ARC Linkage grant to David Atchison. Edward
Mallen was supported by a QUT IHBI Visiting Research
Fellowship.
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For details of the authors of this review please see the next page.
Eye shape and retinal shape PK Verkicharla et al.
198 Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists
Pavan Kumar Verkicharla received a Bachelors degree in Optometry from the Bausch &
Lomb School of Optometry (BITS-Pilani), India in 2010 after one year of internship at
the L V Prasad Eye Institute. He has a higher degree research scholarship from the
Queensland University of Technology, Australia to work in the Ophthalmic and Visual
Optics Laboratory. His research interests are retinal shape and myopia optics.
Dr Ankit Mathur completed his PhD under the supervision of Prof. David Atchison in
2009 and is currently a Postdoctoral Fellow at the School of Optometry and Institute of
Health and Biomedical Innovation at the Queensland University of Technology, Australia.
He graduated with a Bachelor of Science (Optometry) from the Bausch & Lomb School
of Optometry (Hyderabad, India) in 2004. His current interests are aberrations in the
peripheral visual field and methods to improve peripheral image quality.
Dr Edward Mallen is Reader in Physiological Optics at the Bradford School of Optome-
try and Vision Science, West Yorkshire, UK. Ed’s principal research interests are accom-
modation control in the human visual system, neural adaptations to blur, ocular
biometry in refractive error, orthokeratology, ocular aberrations and adaptive optics. He
is particularly interested in the link between structural and functional correlates within
the myopic eye, and methods to reduce the progression of myopia in the juvenile and
young adult eye.
James Pope is an Adjunct Professor of Physics at Queensland University of Technology
in Australia. His research interests include novel applications of MRI. His recent work
has included the use of magnetic resonance micro-imaging to map refractive index distri-
bution in the crystalline eye lens and the application of diffusion tensor imaging to study
macromolecular architecture and transport properties in articular cartilage.
David Atchison is a Professor of Optometry at Queensland University of Technology in
Australia, where he have been involved in the teaching and research of visual optics for
twenty-seven years. His current interests are the influence of optics on peripheral visual
performance and biometry of the eye in diabetes and myopia. He was awarded the Glenn
A. Fry Award of the American Academy of Optometry in 2011.
PK Verkicharla et al. Eye shape and retinal shape
Ophthalmic & Physiological Optics 32 (2012) 184–199 ª2012 The College of Optometrists 199
