Chromatic cues for the sign of defocus in the peripheral retina

Abstract

Detecting optical defocus at the retina is crucial for accurate accommodation and emmetropization. However, the optical characteristics of ocular defocus are not fully understood. To bridge this knowledge gap, we simulated polychromatic retinal image quality by considering both the monochromatic wavefront aberrations and chromatic aberrations of the eye, both in the fovea and the periphery (nasal visual field). Our study revealed two main findings: (1) chromatic and monochromatic aberrations interact to provide a signal to the retina (chromatic optical anisotropy) to discern positive from negative defocus and (2) that chromatic optical anisotropy exhibited notable differences among refractive error groups (myopes, emmetropes and hyperopes). These findings could enhance our understanding of the underlying mechanisms of defocus detection and their subsequent implications for myopia control therapies. Further research is needed to explore the retinal architecture’s ability to utilize the optical signals identified in this study.

Full text

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5098
Chromatic cues for the sign of defocus in the
peripheral retina
LEN ZHELEZNYAK,1,2,* CHANG LI U,3AND SIMON WINTER4
1Clerio Vision, Inc., Rochester NY, USA
2Center for Visual Science, University of Rochester, Rochester, New York, USA
3The Institute of Optics, University of Rochester, Rochester, New York, USA
4
Department of Biomedical Engineering, Wroclaw University of Science and Technology, Wroclaw, Poland
*lzheleznyak@cleriovision.com
Abstract:
Detecting optical defocus at the retina is crucial for accurate accommodation and
emmetropization. However, the optical characteristics of ocular defocus are not fully understood.
To bridge this knowledge gap, we simulated polychromatic retinal image quality by considering
both the monochromatic wavefront aberrations and chromatic aberrations of the eye, both in
the fovea and the periphery (nasal visual field). Our study revealed two main findings: (1)
chromatic and monochromatic aberrations interact to provide a signal to the retina (chromatic
optical anisotropy) to discern positive from negative defocus and (2) that chromatic optical
anisotropy exhibited notable differences among refractive error groups (myopes, emmetropes and
hyperopes). These findings could enhance our understanding of the underlying mechanisms of
defocus detection and their subsequent implications for myopia control therapies. Further research
is needed to explore the retinal architecture’s ability to utilize the optical signals identified in this
study.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Prompted by the global upsurge in myopia prevalence, peripheral optical quality has become an
increasingly important topic of research. The peripheral retina has been hypothesized to play an
important role in regulating emmetropization [1], containing many of the neurons necessary for
retina-to-sclera biochemical signaling [2–4], and is the target of optical therapies for combating
myopia progression [5], such as multifocal soft contact lenses, contrast-reducing spectacles, and
orthokeratology. While many studies have investigated peripheral optical quality, they have been
limited to monochromatic analyses. To gain a more complete understanding of peripheral optical
quality, this study examines the combined effects of the eye’s monochromatic and polychromatic
aberrations across the horizontal visual field.
Previous studies have shown that the eye’s peripheral optics are dominated by defocus,
astigmatism, coma, and trefoil [6–10]. These monochromatic wavefront aberrations are caused
by the shape of the eye’s refracting surfaces and the refractive index distribution of the crystalline
lens. Alternatively, polychromatic aberrations result from dispersion, the wavelength-dependent
variation of refractive index of the ocular media [11].
Polychromatic aberrations are classified as either longitudinal or transverse. Longitudinal
chromatic aberration (LCA) refers to wavelength-dependent defocus. An emmetropic eye
(typically corrected for distance at 555nm) is relatively myopic in the blue and relatively
hyperopic in the red. LCA is relatively constant across the retina, varying by 10 to 20% within
the central
±
30 deg of visual field [12]. Transverse chromatic aberration (TCA) refers to
wavelength-dependent magnification and increases linearly as a function of visual field angle
within the central
±
15 deg of visual field [13], and is small but non-zero in central vision due to
misalignment between the optical and visual axes.
#537268 https://doi.org/10.1364/BOE.537268
Journal © 2024 Received 25 Jul 2024; accepted 28 Jul 2024; published 8 Aug 2024

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5099
While monochromatic [14,15] and polychromatic [16,17] aberrations reduce retinal image
quality, they also provide functional utility: they help discern the sign of defocus and extend
depth of focus (see review by Del Aguila-Carrasco et al. [18]). Monochromatic aberrations
have been implicated in accommodation as providing a cue for the sign of defocus [19–21].
For instance, Wilson et al., found that the sign of defocus influenced the appearance of the
point spread function (PSF) resulting from even-order Zernike aberrations (e.g., astigmatism,
spherical aberration and quadrafoil) [20] but not odd-order aberrations (e.g., coma and trefoil)
[22]. However, a study by Bernal-Molina et al. demonstrated that wavefront aberrations are not
required for accommodation to track monochromatic dynamic accommodative stimuli, indicating
that another mechanism must be considered [23]. Polychromatic aberrations (i.e., LCA) also
provide a cue for the sign of defocus and affect accommodative response [24,25]. A unifying
feature of these previous works is that they have focused on foveal vision and did not consider the
influence of the peripheral retina.
The peripheral PSF, dominated by even-order monochromatic wavefront aberrations [20]
unlike the well-corrected foveal PSF, is anisotropic. Its orientation depends on the sign and
magnitude of defocus [26–28]. Due to the interaction of monochromatic aberrations and LCA, we
hypothesized that the shape and orientation of the predominantly astigmatic blur in the peripheral
retina is wavelength dependent. Furthermore, the peripheral TCA is expected to cause a lateral
displacement between PSFs of varying wavelength. Ultimately, the visual experience guiding
accommodation and eye growth is influenced by these factors, but the effects of peripheral
monochromatic and the polychromatic aberrations together remain unexplored.
This paper aims to bridge this gap in knowledge by investigating the underexamined relationship
between the eye’s peripheral monochromatic and chromatic aberrations. To achieve this goal, we
used previously published data of peripheral monochromatic wavefront aberrations, LCA and
TCA to model through-focus retinal image quality across the visible spectrum. We compared
three refractive error groups – emmetropes, myopes and hyperopes – to clarify the role of
peripheral image quality. Additionally, we examined both small and large pupil sizes to assess
the impact of ambient brightness. By quantifying peripheral image quality across the visible
spectrum, we aim to better understand physiological mechanisms which utilize the peripheral
retina, such as emmetropization, myopia progression, and optical therapies for myopia control.
2. Methods
2.1. Subject demographics
This study is the polychromatic extension of a previously published monochromatic analysis
[26]. The monochromatic aberrations data were taken from those reported in a population study
[6] which compiled the wavefront aberrations of 2,492 subjects from 16 studies carried out in
Europe, North America, and Australia.
Emmetropes represented 60% of the subjects (defined as a refractive error
>
-0.5 D and
<+
0.5
D), myopes 20% (
≤
-0.5 D; average spherical equivalent of -3.17
±
0.98 D), and hyperopes
20% (
≥+
0.5 D; average spherical equivalent
+
1.25
±
0.49 D). The subjects were both male and
female, phakic, and age ranged in age from 5 to 58 years. Complete details regarding subject
demographics and aberrometry techniques are described in Romashchenko et al [6].
2.2. Monochromatic aberrations
As shown previously [6–10,12], monochromatic wavefront aberrations such as astigmatism, coma
and trefoil increase significantly with retinal eccentricity. Relative peripheral refraction (RPR)
data for emmetropes, myopes and hyperopes was taken from Fig. 1of Romashchenko et al [6].
Equation (1) was used to compute Zernike defocus (C
20
) according to OSA standard, where r
pupil

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5100
is the pupil radius in mm and C40is the Zernike coefficient for primary spherical aberration.
RPR =−4√3
r2
pupil
C0
2+12√5
r2
pupil
C0
4(1)
Here, TCA is given in arcminutes and eccentricity
𝜃
in deg. For the calculated TCA, a
positive sign of horizontal TCA means that the direction of TCA is the same as a base-in
prism would cause (i.e., short wavelengths will end up at the retina more toward the nasal
retina than the longer wavelengths).
Fig 1. (a) Longitudinal and (b) transverse chromatic aberration across the visible spectrum (405-695 nm).
2.5 Reliability and Robustness of the TCA Data Extrapolation Approach
For checking the reliability and robustness of the TCA data extrapolation approach, visual
inspection of the TCA measurement data did not point to a significant difference in precision
of the data between center and periphery of the visual field. The simplest extrapolation model
possible, linear regression was chosen. Supposed the values beyond 15 deg eccentricity would
be more correlated to the measured values near 15 deg eccentricity than at the center, the data
was also fitted using firstly an unweighted least square method, and secondly, a weighted
least square method, where the weights were chosen to linearly increase from 1 at 0 deg
eccentricity to 3 at 15 deg eccentricity. However, the difference of extrapolated TCA between
the different extrapolation methods were in all cases smaller than 0.07 arcminutes of TCA for
eccentricities up to 30 deg. The impact of this difference on vision is negligible, considering
that peripheral grating detection acuity, in the 20 deg nasal visual field, is reduced by
approximately 0.05 to 0.06 logMAR∕arcmin of TCA induced to the eye[34]. Additionally, it
has been assumed in the extrapolation, that there is symmetry in the slope of the TCA data of
the nasal and temporal visual field, and it has not been the aim to prove or disprove this
symmetry.
2.6 Quantifying Retinal Image Quality
Overall image quality, defined as the volume under the MTF (MTFvol) for all spatial
frequencies, was normalized to an aberration-free wavefront at 555nm wavelength with a 4
mm circular pupil. Thus, a diffraction-limited wavefront with no aberrations would yield an
MTFvol value of 1.0 and would decrease as aberrations increase. Peripheral refractive error
(PRE) was defined as the difference in defocus values (in diopters) required to maximize
MTFvol between a peripheral retinal eccentricity and the fovea.
2.7 Quantifying Optical Anisotropy
Fig. 1.
(a) Longitudinal and (b) transverse chromatic aberration across the visible spectrum
(405-695 nm).
Monochromatic aberrations were defined using Zernike polynomials for a 4 mm pupil, at
eccentricities of 0, 10, 20 and 30 deg across the horizontal nasal visual field. An elliptical pupil
was used to account for iris tilt as a function of retinal eccentricity [29] using the cosine function
(Eq. (2)), where θis the visual field angle.
Minor Axis Pupil Diameter =Major Axis Pupil Diameter ∗cosθ(2)
In the horizontal visual field, the pupil became vertically elongated, with an ellipticity of 100%
(circular), 98.4%, 94.0% and 86.6% at 0, 10, 20 and 30 deg, respectively. For all calculations,
the pupil function was defined within a 400
×
400 pixel array, corresponding to a width of 8 mm
and a resolution of 20
µ
m per pixel. The image plane (i.e., at the retina) had a resolution of 0.24
arcminutes per pixel. The resolution of the PSF images was increased to 0.16 arcminutes per
pixel for illustration purposes.
A Matlab program was used to compute the monochromatic PSF and two-dimensional
modulation transfer function (MTF) at each eccentricity and through-focus (from -3.0 to
+
3.0
D in 0.1 D steps). As described by Chen et al [30] (see their Eqs. (3), (4 and (8)), the PSF
was calculated via the modulus-squared of the Fourier transform of the pupil function, where
the wavefront aberrations comprised the phase of the pupil function. Polychromatic PSFs were
depicted by superimposing monochromatic PSFs calculated at 405, 555 and 695 nm wavelengths
at equal intensities. While this does not accurately represent “white” light with a continuous
spectrum, this approach was selected to clearly demonstrate the effect of wavelength.
The two-dimensional modulation transfer function (MTF) was calculated via the modulus of
the Fourier transform of the PSF. A defocus value of 0 D indicates an image in focus on the retina
with no refractive error. Negative diopters refer to myopic defocus (i.e., axial planes anterior to,
or in front of, the retina), whereas positive diopters refer to hyperopic defocus (i.e., axial planes
posterior to, or behind, the retina). The simulations in this study assumed all refractive error
groups are foveally corrected for distance (0 D) at 555nm.
2.3. Longitudinal chromatic aberration
To address polychromatic aberrations, both longitudinal and transverse chromatic aberrations
were considered. LCA is the difference in refractive power of the eye for different wavelengths

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5101
and is shown in Fig. 1(a). Across the visible spectrum (400 to 700 nm), LCA is roughly 2 D
[11,31]. LCA was computed using the Cauchy equation [32]:
Rx(λ)=A+B
λ2+C
λ4+D
λ6(3)
Where R
x
is defocus in diopters,
λ
is the wavelength in nanometers and the coefficients were
A
=
1.7845, B
=
-6.7094
×
10
5
, C
=
5.5533
×
10
10
and D
=
-5.6000
×
10
15
. Coefficients B, C and
D were taken from Atchison and Smith [11], and coefficient A was optimized for 0 D at 555nm,
the peak of retinal spectral sensitivity [33]. LCA was assumed to be constant across the visual
field [12].
2.4. Transverse chromatic aberration
Ocular TCA data was based on the study by Winter et al., objectively measuring TCA between
543 nm and 842 nm of four emmetropic subjects over horizontal and vertical meridians using
an adaptive optics scanning laser ophthalmoscope [13]. For the linear extrapolation of the
measured ocular TCA data from
±
15 deg of the visual field, to
±
30 deg, the average rate in the
change of TCA with changing eccentricity was taken. In the horizontal meridian, a negative
eccentricity denotes the nasal visual field and positive eccentricity denotes the temporal visual
field. Additionally, there is an offset due to foveal TCA.
For the conversion of the extrapolated TCA data to the different wavelength range of this
study (405-695 nm), the same refractive index distribution as published by Thibos et al. [31] was
applied, and is shown in Eq. (4) (with wavelength, λ, in micrometers):
n(λ)=1.320535 +0.004685
λ−0.214102 (4)
Furthermore, it was assumed for simplicity in Eq. (5), as in the study by Winter et al. [13],
that TCA alters proportionally to the change in refractive index. The TCA in the new wavelength
band (TC
Anew)
in 10 nm intervals was then calculated from the TCA in the original wavelength
band (TCA543−842) by:
TCAnew =TCA543−842 1
nnew−upper −1
nnew−lower 
1
n842 −1
n543 (5)
Here, the indices refer to the corresponding wavelengths, i.e.,
nnew−upper
is the refractive index
at the upper limit of the wavelength interval, and
nnew−lower
is the refractive index at the lower
limit of the wavelength interval. TCA from 405 to 695nm, and over
±
30 deg of visual field is
shown in Eq. (6) and is plotted in Fig. 1(b).
TCA =−0.4097 θ+4.6109 (6)
Here, TCA is given in arcminutes and eccentricity
θ
in deg. For the calculated TCA, a positive
sign of horizontal TCA means that the direction of TCA is the same as a base-in prism would
cause (i.e., short wavelengths will end up at the retina more toward the nasal retina than the
longer wavelengths).
2.5. Reliability and robustness of the TCA data extrapolation approach
For checking the reliability and robustness of the TCA data extrapolation approach, visual
inspection of the TCA measurement data did not point to a significant difference in precision
of the data between center and periphery of the visual field. The simplest extrapolation model

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5102
possible, linear regression was chosen. Supposed the values beyond 15 deg eccentricity would
be more correlated to the measured values near 15 deg eccentricity than at the center, the data
was also fitted using firstly an unweighted least square method, and secondly, a weighted least
square method, where the weights were chosen to linearly increase from 1 at 0 deg eccentricity
to 3 at 15 deg eccentricity. However, the difference of extrapolated TCA between the different
extrapolation methods were in all cases smaller than 0.07 arcminutes of TCA for eccentricities
up to 30 deg. The impact of this difference on vision is negligible, considering that peripheral
grating detection acuity, in the 20 deg nasal visual field, is reduced by approximately 0.05 to
0.06 logMAR/arcmin of TCA induced to the eye [34]. Additionally, it has been assumed in the
extrapolation, that there is symmetry in the slope of the TCA data of the nasal and temporal
visual field, and it has not been the aim to prove or disprove this symmetry.
2.6. Quantifying retinal image quality
Overall image quality, defined as the volume under the MTF (MTF
vol
) for all spatial frequencies,
was normalized to an aberration-free wavefront at 555nm wavelength with a 4 mm circular pupil.
Thus, a diffraction-limited wavefront with no aberrations would yield an MTF
vol
value of 1.0
and would decrease as aberrations increase. Peripheral refractive error (PRE) was defined as the
difference in defocus values (in diopters) required to maximize MTF
vol
between a peripheral
retinal eccentricity and the fovea.
2.7. Quantifying optical anisotropy
Because the peripheral wavefront is dominated by non-rotationally symmetric aberrations (e.g.,
astigmatism and coma), a new metric was defined to quantify the optical anisotropy (OA) of
retinal blur. The OA metric was defined as the ratio of the horizontal to vertical meridians of the
area under the two-dimensional MTF over all spatial frequencies. OA of 1.0 corresponds to a
circularly symmetric two-dimensional MTF, and thus a circularly symmetric PSF. This can occur
with either an aberration-free pupil, or with circularly symmetric aberrations such as defocus or
spherical aberration. A vertically elongated blur has OA
>
1.0, and a horizontally elongated blur
has OA
<
1.0. For more details and an illustrative example of optical anisotropy, see Fig. 2(b) of
Zheleznyak [26].
2.8.
Illustration of the interaction of monochromatic aberrations and longitudinal chro-
matic aberration
Figure 2illustrates the interaction between monochromatic aberrations and LCA. Through-
focus PSFs are shown for monochromatic (at 405, 555 and 695nm) and polychromatic (as the
superposition of these PSFs) light using physiological levels of LCA for a 4 mm pupil. Figure 2(a)
represents the diffraction-limited eye, while Fig. 2(b) represents an eye with 2.0 D of astigmatism,
similar to what is observed in the peripheral retina at 30 deg. Finally, we also include the
polychromatic PSFs in gray-scale format. It is evident that the astigmatism of Fig. 2(b) produces
an optical anisotropy which varies with defocus and wavelength. TCA was not included in this
illustration.
The bottom rows of Figs. 2(a) and 2(b) serve as an illustrative example of applying a spectral
weighting to the polychromatic PSF. In this case, the cone spectral sensitivity (photopic luminous
efficiency function V(
λ
)) is applied, for which the relative sensitivities of 405, 555 and 695 nm
are 0.0006, 1.0 and 0.0057, respectively [33]. The V(
λ
) weighting in Fig. 2is just one example of
spectral weighting and is originally intended only for “on-axis visual tasks” within the central 4
deg (see section 5.2 of ISO/CIE 23539:2023) [35] [. Other possibly relevant weightings would be
the spectral sensitivities of the rod photoreceptors and intrinsically photosensitive retinal ganglion
cells (ipRGCs). Applying spectral weighting presumes knowledge of which retinal cell-type is

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5103
Fig 2. Theoretical simulation of through-focus point spread functions for 2 conditions: (a) monochromatic aberration-
free and (b) astigmatism of 2 D, both for a 4 mm pupil. PSFs are shown monochromatically at 405, 555 and 695 nm,
and polychromatically in color and in grayscale (with and without V(λ) weighting[33, 35]).
3. Results
Fig. 2.
Theoretical simulation of through-focus point spread functions for 2 conditions: (a)
monochromatic aberration-free and (b) astigmatism of 2 D, both for a 4 mm pupil. PSFs are
shown monochromatically at 405, 555 and 695nm, and polychromatically in color and in
grayscale (with and without V(λ) weighting [33,35]).

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5104
responsible for detecting defocus via anisotropy, but this information is currently unknown (for
further details, see Discussion subsection Retinal Mechanisms of Defocus Detection).
3. Results
Simulated through-focus monochromatic optical quality for wavelengths across the visible
spectrum is shown in Fig. 3for myopes, emmetropes and hyperopes (rows) at 0, 10, 20 and 30
deg eccentricities in the nasal visual field (columns). As eccentricity increased, peak optical
quality reduced due to the rise in wavefront aberrations. For example, at 555nm, peak MTF
vol
at 0 deg was 0.74, and reduced to 0.54, 0.29 and 0.14 at 10, 20 and 30 deg, respectively. The
effect of LCA can be seen in Fig. 3by the lateral (dioptric) shift in the curves for individual
wavelengths. While all refractive error groups were best-corrected at 555nm foveally (0 deg),
the model predicted for myopes optimal optical quality for short wavelengths in the periphery.
Alternatively, in the periphery, the model showed for emmetropes relatively little shift in optimal
wavelength and predicted for hyperopes highest optical quality for longer wavelengths.
Simulated through-focus monochromatic optical quality for wavelengths across the visible
spectrum is shown in Fig. 3 for myopes, emmetropes and hyperopes (rows) at 0, 10, 20 and 30
deg eccentricities in the nasal visual field (columns). As eccentricity increased, peak optical
quality reduced due to the rise in wavefront aberrations. For example, at 555 nm, peak MTFvol
at 0 deg was 0.74, and reduced to 0.54, 0.29 and 0.14 at 10, 20 and 30 deg, respectively. The
effect of LCA can be seen in Fig. 3 by the lateral (dioptric) shift in the curves for individual
wavelengths. While all refractive error groups were best-corrected at 555 nm foveally (0 deg),
the model predicted for myopes optimal optical quality for short wavelengths in the periphery.
Alternatively, in the periphery, the model showed for emmetropes relatively little shift in
optimal wavelength and predicted for hyperopes highest optical quality for longer
wavelengths.
Fig 3. Through-focus monochromatic optical quality (MTFvol) for myopes, emmetropes and hyperopes across the
visible spectrum and retinal eccentricities (nasal visual field) for a 4 mm pupil.
Fig. 4 shows simulated through-focus monochromatic OA across the visible spectrum for
myopes, emmetropes and hyperopes (rows) at 0, 10, 20 and 30 deg eccentricities in the nasal
visual field (columns). Due to increasing odd-error wavefront aberrations, such as
astigmatism, the through-focus variation in OA increased with eccentricity. Similarly to
optical quality of Fig. 3, the effect of LCA can be seen in Fig. 4 by the lateral (dioptric) shift
in the curves for individual wavelengths.
Fig. 3.
Through-focus monochromatic optical quality (MTF
vol
) for myopes, emmetropes
and hyperopes across the visible spectrum and retinal eccentricities (nasal visual field) for a
4 mm pupil.
Figure 4shows simulated through-focus monochromatic OA across the visible spectrum for
myopes, emmetropes and hyperopes (rows) at 0, 10, 20 and 30 deg eccentricities in the nasal
visual field (columns). Due to increasing odd-error wavefront aberrations, such as astigmatism,
the through-focus variation in OA increased with eccentricity. Similarly to optical quality of
Fig. 3, the effect of LCA can be seen in Fig. 4by the lateral (dioptric) shift in the curves for
individual wavelengths.

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5105
Fig 4. Through-focus monochromatic optical anisotropy (OA) for myopes, emmetropes and hyperopes across the
visible spectrum and retinal eccentricities (nasal visual field) for a 4mm pupil.
OA experienced on the retina (at 0 D) across the visible spectrum is shown across
eccentricities for myopes, emmetropes and hyperopes in Fig. 5. At 0 and 10 deg, all groups
had OA less than 10% (i.e.,0.9 < OA < 1.1) for all wavelengths, except myopes at 555, 655
and 695 nm. However, as eccentricity increased, so did the difference in OA between
myopes and the other groups. At 20 deg, myopes had OA > 1.0, whereas both emmetropes
and hyperopes had OA < 1.0 for wavelengths longer than 555 nm. Strikingly, at 30 deg,
myopes had OA > 1.0 and emmetropes and hyperopes had OA < 1.0 for wavelengths longer
than 455 nm.
Fig 5. Optical anisotropy as a function of wavelength for hyperopes, emmetropes and myopes across the nasal
visual field for a 4 mm pupil.
Fig. 4.
Through-focus monochromatic optical anisotropy (OA) for myopes, emmetropes
and hyperopes across the visible spectrum and retinal eccentricities (nasal visual field) for a
4 mm pupil.
OA experienced on the retina (at 0 D) across the visible spectrum is shown across eccentricities
for myopes, emmetropes and hyperopes in Fig. 5. At 0 and 10 deg, all groups had OA less than
10% (i.e.,0.9
≤
OA
≤
1.1) for all wavelengths, except myopes at 555, 655 and 695 nm. However,
as eccentricity increased, so did the difference in OA between myopes and the other groups.
At 20 deg, myopes had OA
>
1.0, whereas both emmetropes and hyperopes had OA
<
1.0 for
wavelengths longer than 555 nm. Strikingly, at 30 deg, myopes had OA
>
1.0 and emmetropes
and hyperopes had OA <1.0 for wavelengths longer than 455nm.
Fig 4. Through-focus monochromatic optical anisotropy (OA) for myopes, emmetropes and hyperopes across the
visible spectrum and retinal eccentricities (nasal visual field) for a 4mm pupil.
OA experienced on the retina (at 0 D) across the visible spectrum is shown across
eccentricities for myopes, emmetropes and hyperopes in Fig. 5. At 0 and 10 deg, all groups
had OA less than 10% (i.e.,0.9 < OA < 1.1) for all wavelengths, except myopes at 555, 655
and 695 nm. However, as eccentricity increased, so did the difference in OA between
myopes and the other groups. At 20 deg, myopes had OA > 1.0, whereas both emmetropes
and hyperopes had OA < 1.0 for wavelengths longer than 555 nm. Strikingly, at 30 deg,
myopes had OA > 1.0 and emmetropes and hyperopes had OA < 1.0 for wavelengths longer
than 455 nm.
Fig 5. Optical anisotropy as a function of wavelength for hyperopes, emmetropes and myopes across the nasal
visual field for a 4 mm pupil.
Fig. 5.
Optical anisotropy as a function of wavelength for hyperopes, emmetropes and
myopes across the nasal visual field for a 4 mm pupil.
Figure 6demonstrates the combined effects of LCA and TCA on retinal image quality, as
shown by the superposition of three monochromatic PSFs across the visible spectrum. Across
the nasal visual field from 0 to 30 deg, the superimposed PSFs were calculated at 405, 555 and

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5106
695 nm wavelengths, and are plotted in blue, green and red, respectively. Note the orientation of
the green and red PSFs at 30 deg for different refractive error groups: myopes had a distinctly
vertical green and red PSFs, whereas for emmetropes and hyperopes they were horizontal.
Fig. 6 demonstrates the combined effects of LCA and TCA on retinal image quality, as shown
by the superposition of three monochromatic PSFs across the visible spectrum. Across the
nasal visual field from 0 to 30 deg, the superimposed PSFs were calculated at 405, 555 and
695 nm wavelengths, and are plotted in blue, green and red, respectively. Note the orientation
of the green and red PSFs at 30 deg for different refractive error groups: myopes had a
distinctly vertical green and red PSFs, whereas for emmetropes and hyperopes they were
horizontal.
Fig 6. Point spread functions across the nasal visual field for foveally distance corrected eyes of hyperopes (top row),
emmetropes (middle row) and myopes (bottom row). Within each frame, are superimposed monochromatic point
spread functions of wavelengths 405 nm (in blue), 555 nm (in green) and 695 nm (in red) which are defocused and
decentered from one another due to LCA and TCA, respectively.
4. Discussion
This study analyzed a population average of monochromatic wavefront aberrations across the
nasal visual field in combination with the eye’s polychromatic aberrations. Two major
findings may be concluded: (1) the chromatic spectrum of optical anisotropy in the peripheral
retina can indicate the sign of retinal defocus, and (2) different refractive error groups (i.e.,
myopes, emmetropes and hyperopes) have distinct patterns of chromatic peripheral optical
anisotropy due to their relative peripheral refraction. The following sections will explore these
findings in greater detail.
4.1 Chromatic Optical Anisotropy: A Cue for the Sign of Defocus in the Periphery
Fig. 6.
Point spread functions across the nasal visual field for foveally distance corrected
eyes of hyperopes (top row), emmetropes (middle row) and myopes (bottom row). Within
each frame, are superimposed monochromatic point spread functions of wavelengths 405 nm
(in blue), 555 nm (in green) and 695 nm (in red) which are defocused and decentered from
one another due to LCA and TCA, respectively.
4. Discussion
This study analyzed a population average of monochromatic wavefront aberrations across the
nasal visual field in combination with the eye’s polychromatic aberrations. Two major findings
may be concluded: (1) the chromatic spectrum of optical anisotropy in the peripheral retina
can indicate the sign of retinal defocus, and (2) different refractive error groups (i.e., myopes,
emmetropes and hyperopes) have distinct patterns of chromatic peripheral optical anisotropy
due to their relative peripheral refraction. The following sections will explore these findings in
greater detail.
4.1. Chromatic optical anisotropy: a cue for the sign of defocus in the periphery
In the fovea, LCA provides an effective cue for the sign of defocus in the form of relative
chromatic image quality. For example, a well-focused emmetropic eye (in green) is relatively
myopic in blue and hyperopic in red. While the impact of LCA on spatial tasks, such as visual
acuity and contrast sensitivity, is minimal [17,36,37], previous work has demonstrated LCA’s
substantial impact on accommodation [38], emmetropization in animals studies [39–41] and
short-term changes in axial length in humans [42,43]. For instance, Gawne et al. have proposed a

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5107
model by which the retina compares relative image sharpness of blue versus red light for guiding
eye growth [41].
In the periphery, however, the sign of defocus determines not only relative refractive error, but
also the orientation of blur (due to oblique astigmatism). For the well-focused emmetropic eye,
all wavelengths in the visible spectrum exhibited horizontally elongated blur in the horizontal
nasal visual field, with a maximal effect at 555 nm (Fig. 5, blue curve). The results of this study
are in agreement with previously published ray-tracing-based peripheral eye models, which
described similar values of Zernike coefficients as those used in this study, and subsequently also
predicted horizontal monochromatic blur in the nasal visual field [44,45].
4.2. Impact of accommodation
Myopia is associated with near-work and extended periods of accommodation [46,47]. Also,
myopes tend to have a larger lag of accommodation as compared to emmetropes. Therefore, it is of
interest to consider the ramifications of a near-rich environment on optical quality and anisotropy.
When a near object is introduced to an eye distance-focused, defocus is negative. Thus, the
eye brings the retinal image into focus by increasing its optical power, via accommodation or a
positive powered lens (e.g., reading glasses).
Regarding optical anisotropy, the defocus required to change the blur orientation from horizontal
to vertical elongation (i.e., from OA
<
1.0 to OA
>
1.0) is plotted in Fig. 7, a quantity we term
Critical Defocus. A distance-focused emmetropic eye encountering a near object will have
vertically elongated blur in the nasal visual field before accommodating. After accommodation,
the peripheral blur switches back to horizontal elongation, provided the accommodative lag is
less than the values shown in Fig. 7. In other words, accommodative lag introduces negative
defocus, thereby shifting the optical quality and anisotropy curves of Figs. 3and 4to the right
along the x-axis. Longer wavelengths require less defocus to increase OA above 1.0. The Critical
Defocus (averaged over 10, 20 and 30 deg) required to flip blur orientation from horizontal to
vertical in the emmetropic eye is -2.2
±
0.2 D at 405 nm, -0.7
±
0.2 D at 555 nm and -0.1
±
0.2 D
at 695 nm.
Fig 7. Critical Defocus required to flip blur orientation from horizontal (OA < 1.0) to vertical (OA > 1.0) in the
horizontal nasal visual field of the average emmetropic eye for a 4 mm pupil.
While the wavefront aberrations degrade visual performance[48], they may play a beneficial
role for encoding the sign of defocus by way of peripheral blur orientation. However, it
should be noted that not all functions of the eye correlate with spatial visual tasks. Although
the peripheral retina has notably lower visual acuity and contrast sensitivity[49] as compared
to the fovea, it displays heightened motion sensitivity and contains ipRGCs which contribute
to pupil size control and circadian rhythm entrainment. Stated differently, the peripheral retina
plays an important role in visual functions beyond the conventional notion of “spatial vision”.
It is plausible that detecting the sign of defocus for guiding eye growth may be another such
role of the peripheral retina.
4.3 Refractive Error Groups Differ in their Peripheral Chromatic Optical Anisotropy
Peripheral chromatic OA was significantly different between refractive error groups. As
shown in Fig. 5, for wavelengths longer than 500 nm, the model showed that myopes
exhibited vertically elongated blur, whereas emmetropes and hyperopes exhibited horizontally
elongated blur. This difference is likely be due to groups’ differences in globe shape which
affects relative peripheral defocus. For example, myopes’ axial elongation is coincident with a
prolate globe shape and relative peripheral hyperopia[50-52], whereas hyperopia is associated
with a more oblate globe shape and relative peripheral myopia.
While a clear difference in peripheral chromatic OA was found for myopes versus the
emmetropes and hyperopes (Fig. 5), it is likely that these differences are a consequence, rather
than a cause, of their different retinal shapes. Atchison and Rozema recently emphasized that
globe shape and relative peripheral refractive error do not predict refractive error
development[53], however, clinical studies have had mixed results. In Chinese children,
relative peripheral hyperopia exhibits after, not before foveal myopia onset[54-56], whereas
the opposite was true in a white population[57, 58]. Nevertheless, optical therapies[5, 59]
which induce relative peripheral myopia (e.g., orthokeratology and multifocal soft contact
lenses) have shown significant, albeit somewhat limited, success in slowing myopia
progression in children[60-63]. Paradoxically, therapies which reduce peripheral contrast via
Fig. 7.
Critical Defocus required to flip blur orientation from horizontal (OA
<
1.0) to
vertical (OA
>
1.0) in the horizontal nasal visual field of the average emmetropic eye for a 4
mm pupil.
While the wavefront aberrations degrade visual performance [48], they may play a beneficial
role for encoding the sign of defocus by way of peripheral blur orientation. However, it should be
noted that not all functions of the eye correlate with spatial visual tasks. Although the peripheral

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5108
retina has notably lower visual acuity and contrast sensitivity [49] as compared to the fovea, it
displays heightened motion sensitivity and contains ipRGCs which contribute to pupil size control
and circadian rhythm entrainment. Stated differently, the peripheral retina plays an important
role in visual functions beyond the conventional notion of “spatial vision”. It is plausible that
detecting the sign of defocus for guiding eye growth may be another such role of the peripheral
retina.
4.3. Refractive error groups differ in their peripheral chromatic optical anisotropy
Peripheral chromatic OA was significantly different between refractive error groups. As shown
in Fig. 5, for wavelengths longer than 500 nm, the model showed that myopes exhibited vertically
elongated blur, whereas emmetropes and hyperopes exhibited horizontally elongated blur. This
difference is likely be due to groups’ differences in globe shape which affects relative peripheral
defocus. For example, myopes’ axial elongation is coincident with a prolate globe shape and
relative peripheral hyperopia [50–52], whereas hyperopia is associated with a more oblate globe
shape and relative peripheral myopia.
While a clear difference in peripheral chromatic OA was found for myopes versus the
emmetropes and hyperopes (Fig. 5), it is likely that these differences are a consequence, rather
than a cause, of their different retinal shapes. Atchison and Rozema recently emphasized that
globe shape and relative peripheral refractive error do not predict refractive error development
[53], however, clinical studies have had mixed results. In Chinese children, relative peripheral
hyperopia exhibits after, not before foveal myopia onset [54–56], whereas the opposite was true in
a white population [57,58]. Nevertheless, optical therapies [5,59] which induce relative peripheral
myopia (e.g., orthokeratology and multifocal soft contact lenses) have shown significant, albeit
somewhat limited, success in slowing myopia progression in children [60–63]. Paradoxically,
therapies which reduce peripheral contrast via scatter, as for example with novel spectacles
(CooperVision/SightGlass DOT [64], HOYA MiyoSmart [65], Essilor Stellest [66]) share a level
of efficacy in myopia control similar to their peripheral-hyperopia-inducing counterparts [59].
4.4. Retinal mechanisms of defocus detection
Putting the two learnings of this study together: if a visual diet of myopigenic stimuli is optically
encoded in the retina, then for it to influence eye growth, a detection mechanism is required.
This raises several questions: What is the detectability of peripheral optical anisotropy? What
photosensitive retinal cell-type, if any, is responsible for detecting optical anisotropy?
While the mechanisms are not yet fully understood, recent evidence suggests that the peripheral
retina can detect the sign of defocus. The seminal work of Smith et al. showed that primate eyes
emmetropized at the correct rate even with a laser ablated fovea [67]. More recently, Pusti et al.
found that peripheral choroidal thickness responded bidirectionally to defocus [68], indicating
that the retina is capable of discerning positive from negative defocus. Interestingly, they found
that removing optical anisotropy by correcting monochromatic aberrations with adaptive optics
also eliminated the choroidal response to defocus, regardless of its sign.
To determine which photosensitive retinal cells (e.g., short, medium and long wavelength
cones, rods, ipRGCs) are involved in the detection of defocus, their spectral sensitivities should
be considered. Due to the eye’s chromatic aberration, photosensitive retinal cells encounter
distinct optical quality and anisotropy at various wavelengths. Table 1provides a summary
of the photosensitive retinal cells, including their peak sensitivity wavelengths [69–72] and
corresponding Critical Defocus values. Further research is required to determine if these
photosensitive cells and their associated receptive fields exhibit anatomical and functional
anisotropy. An instance of anatomical anisotropy would be a radially elongated ganglion
cell receptive field [73]. A case of functional anisotropy would be the meridional effect,

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5109
characterized by higher contrast sensitivity for radial as opposed to circumferential luminance
gratings [27,74,75].
Table 1. Photosensitive retinal cell types, their peak sensitivity wavelengths, and their
corresponding Critical Defocus values at 10, 20 and 30 deg in the average emmetropic eye.
Cell Type Peak Sensitivity
Wavelength [nm]
Critical Defocus [D]
10 deg 20 deg 30 deg
S Cones 420 -1.8 -2.0 -2.2
ipRGCs (melanopsin) 480 -1.1 -1.3 -1.5
Rods 500 -0.9 -1.1 -1.3
M Cones 530 -0.7 -0.9 -1.1
L Cones 560 -0.5 -0.7 -0.9
Regarding photoreceptors, at 30 deg in the temporal retina, rods make up approximately 95%
and cones the remaining and cones 5% [76,77]. At this eccentricity, the sampling frequencies of
rods and cones are approximately 62.5 cyc/deg and 8.9 cyc/deg, respectively [76]. Peripheral
rods and cones send electrochemical signals to the bipolar and amacrine cells, and finally to the
retinal ganglion cells (RGCs). As outlined previously [26], the peripheral retina is populated by
orientation sensitive ganglion cells [73,78–80] with radially elongated receptive fields, described
by Levick and Thibos as being “like the spokes of a wheel with the area centralis at the hub” [73].
If peripheral RGCs are sensitive to the orientation of optical blur, then optical anisotropy may
play a part in the biochemical cascade of neurotransmitter signaling (e.g., dopamine, retinoic
acid, etc.) associated with eye growth [2–4]. Furthermore, as shown in Fig. 8(OA as a function
of spatial frequency), the chromatic OA differences between refractive error groups persist for
spatial frequencies above approximately 2 cyc/deg.
Beyond rods and cones, 1-2% of RGCs contain light-absorbing photopigments, such as
melanopsin [81] and neuropsin [82], with peak absorption wavelengths of approximately 480 and
380 nm, respectively. There intrinsically-photosensitive RGCs are associated with many visual
functions: environmental intensity detection, pupil size [83], local contrast sensitivity [84], eye
growth [82,85] and entrainment of the circadian rhythm [86,87]. The sensitivity of ipRGCs to
optical anisotropy is still unknown, but this information could be crucial for both understanding
current therapies and optimizing future treatments for myopia control.
4.5. Impact of pupil size
Time spent outdoors is associated with protection against myopia development in children, higher
light levels and consequently smaller pupil sizes [46,88]. To determine whether pupil size (and
indirectly, light intensity) affects peripheral chromatic optical anisotropy, we repeated the analysis
for pupils smaller than 4 mm. Figure 9shows the through-focus monochromatic optical quality
and anisotropy in the emmetropic eye at 30 deg in the nasal visual field at 555 nm for pupils
ranging from 1.0 to 4.0 mm.
As expected, decreasing pupil size extended the depth of focus and improved optical quality
(Fig. 9(a)), characteristic of the pinhole effect. Surprisingly, little change in the through-focus
optical anisotropy was observed for pupil diameters above 1.5 mm (Fig. 9(b)). Peripheral optical
anisotropy cues persisted across a wide range of pupils and presumably, intensity levels. Because
the trend of through-focus anisotropy did not change for pupil sizes larger than 1.5 mm, we
hypothesize that the protective nature of time spent outdoors is not related to peripheral optical
anisotropy.

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5110
Regarding photoreceptors, at 30 deg in the temporal retina, rods make up approximately 95%
and cones the remaining and cones 5%[76, 77]. At this eccentricity, the sampling frequencies
of rods and cones are approximately 62.5 cyc/deg and 8.9 cyc/deg, respectively[76].
Peripheral rods and cones send electrochemical signals to the bipolar and amacrine cells, and
finally to the retinal ganglion cells (RGCs). As outlined previously[26], the peripheral retina
is populated by orientation sensitive ganglion cells[73, 78-80] with radially elongated
receptive fields, described by Levick and Thibos as being “like the spokes of a wheel with the
area centralis at the hub”[73]. If peripheral RGCs are sensitive to the orientation of optical
blur, then optical anisotropy may play a part in the biochemical cascade of neurotransmitter
signaling (e.g., dopamine, retinoic acid, etc.) associated with eye growth[2-4]. Furthermore, as
shown in Fig. 8 (OA as a function of spatial frequency), the chromatic OA differences
between refractive error groups persist for spatial frequencies above approximately 2 cyc/deg.
Fig. 8.
Monochromatic OA as a function of spatial frequency for refractive error groups at
405, 555 and 695 nm wavelengths. All data in this figure pertains to the 30 deg nasal visual
field.
4.6. Limitations of the current study
A limitation of this study is that only the nasal visual field was analyzed. While the magnitude of
astigmatism is approximately constant at a given retinal eccentricity regardless of location in the
visual field [9], variations in defocus have been observed. For example, Lin et al. have recently
shown that the superior retina tends to be more myopic relative to the inferior retina [89]. Further
investigation is needed to expand the current analysis of chromatic optical anisotropy beyond the
nasal visual field to the entire visual field.
Another limitation was the assumption that peripheral astigmatism and higher order aberrations
were the same in all refractive error groups. Previous studies have shown subtle differences in the

Research Article Vol. 15, No. 9 / 1 Sep 2024 / Biomedical Optics Express 5111
Fig 8. Monochromatic OA as a function of spatial frequency for refractive error groups at 405, 555 and 695 nm
wavelengths. All data in this figure pertains to the 30 deg nasal visual field.
Beyond rods and cones, 1-2% of RGCs contain light-absorbing photopigments, such as
melanopsin[81] and neuropsin[82], with peak absorption wavelengths of approximately 480
and 380 nm, respectively. There intrinsically-photosensitive RGCs are associated with many
visual functions: environmental intensity detection, pupil size[83], local contrast
sensitivity[84], eye growth[82, 85] and entrainment of the circadian rhythm[86, 87]. The
sensitivity of ipRGCs to optical anisotropy is still unknown, but this information could be
crucial for both understanding current therapies and optimizing future treatments for myopia
control.
4.5 The Impact of Pupil Size
Time spent outdoors is associated with protection against myopia development in children,
higher light levels and consequently smaller pupil sizes[46, 88]. To determine whether pupil
size (and indirectly, light intensity) affects peripheral chromatic optical anisotropy, we
repeated the analysis for pupils smaller than 4 mm. Fig. 9 shows the through-focus
monochromatic optical quality and anisotropy in the emmetropic eye at 30 deg in the nasal
visual field at 555 nm for pupils ranging from 1.0 to 4.0 mm.
As expected, decreasing pupil size extended the depth of focus and improved optical quality
(Fig. 9a), characteristic of the pinhole effect. Surprisingly, little change in the through-focus
optical anisotropy was observed for pupil diameters above 1.5 mm (Fig. 9b). Peripheral
optical anisotropy cues persisted across a wide range of pupils and presumably, intensity
levels. Because the trend of through-focus anisotropy did not change for pupil sizes larger
than 1.5 mm, we hypothesize that the protective nature of time spent outdoors is not related to
peripheral optical anisotropy.
Fig 9. Through-focus (a) optical quality and (b) anisotropy for various pupil sizes at 30 deg in emmetropes at 555 nm.
4.6 Limitations of the Current Study
A limitation of this study is that only the nasal visual field was analyzed. While the magnitude
of astigmatism is approximately constant at a given retinal eccentricity regardless of location
in the visual field[9], variations in defocus have been observed. For example, Lin et al. have
recently shown that the superior retina tends to be more myopic relative to the inferior
Fig. 9.
Through-focus (a) optical quality and (b) anisotropy for various pupil sizes at 30
deg in emmetropes at 555 nm.
anterior segment (specifically corneal radius of curvature [90,91], and crystalline lens thickness
and power [92,93]) between emmetropes and myopes, however their impact on peripheral
aberrations is not known. As such, future work should examine chromatic optical anisotropy in
individuals rather than population averages.
Additionally, an important next step will be to repeat this analysis for various spectra associated
with natural and artificial light sources (e.g., sunlight, LEDs, digital screens, etc.) and for natural
scenes with rich spatial frequency composition. Future work should also assess chromatic optical
anisotropy across the retina for conventional corrections (e.g., monofocal spectacles and contact
lenses) and myopia control therapies (e.g., orthokeratology, multifocal soft contact lenses, and
novel spectacles) to better understand their underlying mechanisms of action. Finally, while the
current study investigated the presence and characteristics of chromatic optical anisotropy, future
work should investigate retinal mechanisms responsible for its detection.
5. Conclusion
In conclusion, this study revealed two significant findings through the evaluation of retinal image
quality across the nasal visual field, taking into account both monochromatic and polychromatic
wavefront aberrations. First, that the chromatic spectrum of optical anisotropy in the peripheral
retina contains information about the sign of defocus, and this cue persists over a wide range
of pupil sizes. Second, chromatic optical anisotropy was significantly different in myopes
versus both emmetropes and hyperopes. Specifically, the average myopic eye in the nasal visual
field exhibited vertically elongated blur for wavelengths longer than 455nm. Alternatively,
peripheral blur was horizontally elongated for emmetropes and hyperopes across most of the
visible spectrum. Future work should encompass the entire visual field and identify the retinal
mechanisms, if any, that may utilize chromatic optical anisotropy of the peripheral retinal image.
Funding. Clerio Vision, Inc.; National Science Foundation (1549700, 1738506).
Disclosures. LZ: Clerio Vision (E, P), CL: None, SW: Clerio Vision (C)
Data availability.
The data underlying the results presented in this paper are snot publicly available at this time but
may be obtained from the authors upon reasonable request.
Supplemental document. See Supplement 1 for supporting content.
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