The effect of accommodation on oblique astigmatism and field curvature of the human eye

Simultaneous measurements of foveal and peripheral aberrations with accommodation in myopic and emmetropic eyes

The difference in peripheral retinal image quality between myopic and emmetropic eyes plays a major role in the design of the optical myopia interventions. Knowing this difference under accommodation can help to understand the limitations of the currently available optical solutions for myopia control. A newly developed dual-angle open-field sensor was used to assess the simultaneous foveal and peripheral ( 20 ∘ nasal visual field) wavefront aberrations for five target vergences from -0.31 D to -4.0 D in six myopic and five emmetropic participants. With accommodation, the myopic eyes showed myopic shifts, and the emmetropic eyes showed no change in RPR. Furthermore, RPR calculated from simultaneous measurements showed lower intra-subject variability compared to the RPR calculated from peripheral measurements and target vergence. Other aberrations, as well as modulation transfer functions for natural pupils, were similar between the groups and the accommodation levels, foveally and peripherally. Results from viewing the same nearby target with and without spectacles by myopic participants suggest that the accommodative response is not the leading factor controlling the amplitude of accommodation microfluctuations.

Retinal defocus in myopes wearing dual-focus zonal contact lenses

Purpose

To evaluate the refractive impact of dual‐focus (DF) myopia control contact lenses (CLs) on accommodating young myopic adults.

Methods

Phase 1: accommodative accuracy was assessed in 40 myopic participants. Phase 2: a subset of four subjects who demonstrated accurate accommodation and six who chronically underaccommodated were fitted with single vision (SV, Proclear 1 day) and centre‐distance DF myopia control CLs (MiSight 1 day) with approximately +2.00 D of additional power in two surrounding annular zones. While binocularly viewing high contrast characters at 4.00, 1.00, 0.50, 0.33, 0.25 and 0.20 m, aberrometry data were captured across the central ±30° of the horizontal retina. Local refractive errors were pooled for each area of the pupil covered by the central distance or first annular defocus zone of the DF CLs.

Results

In the “good” accommodator group fitted with SV CLs, accommodative lags were generally absent except at the closest viewing distance (mean errors: −0.09 ± 0.22 D, −0.12 ± 0.26 D, −0.05 ± 0.37 D and +0.38 ± 0.54 D for −2.00, −3.00, −4.00 and −5.00 D target vergences, respectively) but significantly larger in the “poor” accommodating participants (+0.81 ± 0.21 D, +0.97 ± 0.27 D, +1.18 ± 0.39 D, +1.47 ± 0.55 D). For most viewing distances, hyperopic defocus observed in the region of the pupil covered by the first annular zone was replaced with myopic defocus when fitted with the DF CLs. Myopic defocus created by the first annular region was present across the central 30° of the retina.

Conclusions

Some young adult myopes chronically experience high levels of hyperopic defocus when viewing near targets, which was replaced by myopic defocus in the annular part of the pupil covered by the treatment zones when fitted with a centre‐distance myopia control DF CL.

Recent advances in measurement of monochromatic aberrations of human eyes

The field of aberrations of the human eye is moving rapidly, being driven by the desire to monitor and optimise vision following refractive surgery. It is important for ophthalmologists and optometrists to have an understanding of the magnitude of various aberrations and how these are likely to be affected by refractive surgery and other corrections. In this paper, I consider methods used to measure aberrations, the magnitude of aberrations in general populations and how these are affected by various factors (for example, age, refractive error, accommodation and refractive surgery) and how aberrations and their correction affect spatial visual performance.

Dual-angle open field wavefront sensor for simultaneous measurements of the central and peripheral human eye

We have developed a novel dual-angle open field wavefront sensor. This device captures real-time foveal and peripheral Zernike aberrations, while providing natural binocular viewing conditions for the subjects. The simultaneous data recording enables accurate analysis of changes in ocular optics with accommodation overcoming any uncertainties caused by accommodative lag or lead. The instrument will be used in myopia research to study central and peripheral ocular optics during near work and to investigate the effects of optical myopia control interventions. Proof of concept measurements, performed on an artificial eye model and on 3 volunteers, showed good repeatability with foveal-peripheral data synchronization of 65 msec or better. The deviations from subjective cycloplegic refractions were not more than 0.31 D. Furthermore, we tested the dual-angle wavefront sensor in two novel measurement schemes: (1) focusing on a close target, and (2) accommodation step change.

Customized models of ocular aberrations across the visual field during accommodation

We aimed to create individual eye models that accurately reproduce the empirical measurements of wave-front aberrations across the visual field at different accommodative states, thus providing a mechanistic explanation for the changes in the eye's aberration structure due to accommodation. Structural parameters of a generic eye model were optimized using optical design software to account for published measurements of wave-front aberrations measured for 19 individuals at 37 test locations over the central 30°-diameter visual field at eight levels of accommodative demand. Biometric data for individual eyes were used as starting values and normative data were used to constrain optimizations to anatomically reasonable values. Customizations of the accommodating eye model accurately accounted for ocular aberrations over the central 30° of visual field with an averaged root mean square fitting error typically below 0.2 μm at any given field location. Optimized structural parameters of the eye models were anatomically reasonable and changed in the expected way when accommodating. Accuracy for representing spherical aberration was significantly improved by relaxing anatomical constraints on the anterior surface of the lens to compensate for not including gradient-index media. Use of the model to compute pan-retinal image quality revealed large penalties of accommodative lag for activating photoreceptor responses to the retinal image.

Compensation of corneal oblique astigmatism by internal optics: a theoretical analysis

PURPOSE

Oblique astigmatism is a prominent optical aberration of peripheral vision caused by oblique incidence of rays striking the refracting surfaces of the cornea and crystalline lens. We inquired whether oblique astigmatism from these two sources should be expected, theoretically, to have the same or opposite signs across the visual field at various states of accommodation.

METHODS

Oblique astigmatism was computed across the central visual field for a rotationally-symmetric schematic-eye using optical design software. Accommodative state was varied by altering the apical radius of curvature and separation of the biconvex lens's two aspheric surfaces in a manner consistent with published biometry. Oblique astigmatism was evaluated separately for the whole eye, the cornea, and the isolated lens over a wide range of surface curvatures and asphericity values associated with the accommodating lens. We also computed internal oblique astigmatism by subtracting corneal oblique astigmatism from whole-eye oblique astigmatism.

RESULTS

A visual field map of oblique astigmatism for the cornea in the Navarro model follows the classic, textbook description of radially-oriented axes everywhere in the field. Despite large changes in surface properties during accommodation, intrinsic astigmatism of the isolated human lens for collimated light is also radially oriented and nearly independent of accommodation both in theory and in real eyes. However, the magnitude of ocular oblique astigmatism is smaller than that of the cornea alone, indicating partial compensation by the internal optics. This implies internal oblique astigmatism (which includes wavefront propagation from the posterior surface of the cornea to the anterior surface of the lens and intrinsic lens astigmatism) must have tangentially-oriented axes. This non-classical pattern of tangential axes for internal astigmatism was traced to the influence of corneal power on the angles of incidence of rays striking the internal lens.

CONCLUSIONS

Partial compensation of corneal astigmatism by internal optics is due mainly to the highly converging nature of wavefronts incident upon the lens resulting from corneal refraction. The degree of compensation is quadratically dependent on eccentricity but is expected to diminish as the eye accommodates. Neutralising the cornea by index-matching defeats internal compensation, revealing classical, radially-oriented oblique astigmatism in the isolated lens.

Interaction of axial and oblique astigmatism in theoretical and physical eye models

The interaction between oblique and axial astigmatism was investigated analytically (generalized Coddington's equations) and numerically (ray tracing) for a theoretical eye model with a single refracting surface. A linear vector-summation rule for power vector descriptions of axial and oblique astigmatism was found to account for their interaction over the central 90° diameter of the visual field. This linear summation rule was further validated experimentally using a physical eye model measured with a laboratory scanning aberrometer. We then used the linear summation rule to evaluate the relative contributions of axial and oblique astigmatism to the total astigmatism measured across the central visual field. In the central visual field, axial astigmatism dominates because the oblique astigmatism is negligible near the optical axis. At intermediate eccentricities, axial and oblique astigmatism may have equal magnitude but orthogonal axes, which nullifies total astigmatism at two locations in the visual field. At more peripheral locations, oblique astigmatism dominates axial astigmatism, and the axes of total astigmatism become radially oriented, which is a trait of oblique astigmatism. When eccentricity is specified relative to a foveal line-of-sight that is displaced from the eye's optical axis, asymmetries in the visual field map of total astigmatism can be used to locate the optical axis empirically and to estimate the relative contributions of axial and oblique astigmatism at any retinal location, including the fovea. We anticipate the linear summation rule will benefit many topics in vision science (e.g., peripheral correction, emmetropization, meridional amblyopia) by providing improved understanding of how axial and oblique astigmatism interact to produce net astigmatism.

The BHVI-EyeMapper: peripheral refraction and aberration profiles

PURPOSE

The aim of this article was to present the optical design of a new instrument (BHVI-EyeMapper, EM), which is dedicated to rapid peripheral wavefront measurements across the visual field for distance and near, and to compare the peripheral refraction and higher-order aberration profiles obtained in myopic eyes with and without accommodation.

METHODS

Central and peripheral refractive errors (M, J180, and J45) and higher-order aberrations (C[3, 1], C[3, 3], and C[4, 0]) were measured in 26 myopic participants (mean [±SD] age, 20.9 [±2.0] years; mean [±SD] spherical equivalent, -3.00 [±0.90] diopters [D]) corrected for distance. Measurements were performed along the horizontal visual field with (-2.00 to -5.00 D) and without (+1.00 D fogging) accommodation. Changes as a function of accommodation were compared using tilt and curvature coefficients of peripheral refraction and aberration profiles.

RESULTS

As accommodation increased, the relative peripheral refraction profiles of M and J180 became significantly (p < 0.05) more negative and the profile of M became significantly (p < 0.05) more asymmetric. No significant differences were found for the J45 profiles (p > 0.05). The peripheral aberration profiles of C[3, 1], C[3, 3], and C[4, 0] became significantly (p < 0.05) less asymmetric as accommodation increased, but no differences were found in the curvature.

CONCLUSIONS

The current study showed that significant changes in peripheral refraction and higher-order aberration profiles occurred during accommodation in myopic eyes. With its extended measurement capabilities, that is, permitting rapid peripheral refraction and higher-order aberration measurements up to visual field angles of ±50 degrees for distance and near (up to -5.00 D), the EM is a new advanced instrument that may provide additional insights in the ongoing quest to understand and monitor myopia development.

The effect of multifocal soft contact lenses on peripheral refraction

PURPOSE

To compare changes in peripheral refraction with single-vision (SV) and multifocal (MF) correction of distance central refraction with commercially available SV and MF soft contact lenses (SCLs) in young myopic adults.

METHODS

Thirty-four myopic adult subjects were fitted with Proclear Sphere and Proclear Multifocal SCLs to correct their manifest central refractive error. Central and peripheral refraction were measured with no lens wear and subsequently with the two different types of SCL correction.

RESULTS

At baseline, refraction was myopic at all locations along the horizontal meridian. Peripheral refraction was relatively hyperopic compared with center at 30 and 35 degrees in the temporal visual field (VF) in low myopes, and at 30 and 35 degrees in the temporal VF, and 10, 30, and 35 degrees in the nasal VF in moderate myopes. Single-vision and MF distance correction with Proclear Sphere and Proclear Multifocal SCLs, respectively, caused a hyperopic shift in refraction at all locations in the horizontal VF. Compared with SV correction, MF SCL correction caused a significant relative myopic shift at all locations in the nasal VF in both low and moderate myopes and also at 35 degrees in the temporal VF in moderate myopes.

CONCLUSIONS

Correction of central refractive error with SV and MF SCLs caused a hyperopic shift in both central and peripheral refraction at all positions in the horizontal meridian. Single-vision SCL correction caused the peripheral retina, which initially experienced absolute myopic defocus at baseline with no correction to experience an absolute hyperopic defocus. Multifocal SCL correction resulted in a relative myopic shift in peripheral refraction compared with SV SCL correction. This myopic shift may explain recent reports of reduced myopia progression rates with MF SCL correction.

Peripheral defocus with spherical and multifocal soft contact lenses

PURPOSE

To describe peripheral defocus when myopic eyes are corrected with spherical and center-distance multifocal soft contact lenses while looking at distance and near.

METHODS

Twenty-five young adults with spherical contact lens-corrected refractive error of -0.50 to -6.00 D participated. Refractive error of each participant's right eye was measured while it wore a spherical soft contact lens (Biofinity) and again while it wore a center-distance multifocal soft contact lens with a +2.50-D add (Biofinity Multifocal "D"). Measurements were made centrally and along the horizontal meridian at ±20, ±30, and ±40 degrees from the line of sight at distance and near (3.33-D demand).

RESULTS

The mean (±SD) age and spherical equivalent refractive error were 23.8 ± 1.3 years and -3.62 ± 1.56 D, respectively. At distance, the multifocal contact lens resulted in significantly more myopic defocus than the spherical contact lens at the 40- and 30-degree locations on the nasal retina and at the 20- and 30-degree locations on the temporal retina (p < 0.0001). When accommodating to a near target, peripheral defocus was more myopic with the multifocal lens than with the spherical lens (p < 0.0001). When viewing the near target with the spherical lens, participants experienced foveal hyperopic defocus and peripheral hyperopic defocus at all but one peripheral location. While participants also experienced foveal hyperopic defocus with the multifocal when looking at near, peripheral defocus was minimal (not significantly different than zero) at several locations (i.e., peripheral emmetropia).

CONCLUSIONS

The center-distance multifocal lens created peripheral myopic defocus when looking at distance. When looking at near, the multifocal lens resulted in relatively more myopic (less hyperopic) peripheral defocus than the spherical lens. The defocus profiles experienced with the multifocal contact lens in this study make it a good candidate for studies seeking to examine the effect of peripheral myopic defocus on myopia progression in children.

Peripheral refraction in myopic children wearing orthokeratology and gas-permeable lenses

PURPOSE

To investigate changes in peripheral refraction after orthokeratology (OK) and rigid gas-permeable (GP) lens wear in progressing myopic children and to compare these peripheral defocus changes with reported changes in adults wearing OK.

METHODS

Sixteen myopic children subjects were fitted with an OK lens in one eye for overnight wear and a GP lens in the other eye for daily wear. Central and peripheral refraction were measured at baseline and then after 3 mo of lens wear.

RESULTS

At baseline, myopic children showed relative peripheral hyperopia compared with central refraction at and beyond 20° in the temporal visual field (VF) and 30° in the nasal VF. Three months of OK lens wear produced hyperopic shifts in refraction between 30° in the temporal VF and 20° in the nasal VF. Peripheral refraction was similar to center at all positions in the temporal VF while remaining significantly myopic at all locations in the nasal VF. No change in either central or peripheral refraction was found after 3 mo in the eye assigned for GP lens wear.

CONCLUSIONS

OK significantly reduced myopia in the central 20° VF in myopic children, converting relative peripheral hyperopia measured at baseline to relative peripheral myopia. These changes in children are similar to changes reported in myopic adults wearing OK lenses. No change in either central or peripheral refraction was found after 3 mo of daily GP lens wear. OK lenses can be used to induce myopic defocus in the periphery in myopic children and may thus provide a potential mechanism for myopia control.

Accommodative response to peripheral stimuli in myopes and emmetropes

PURPOSE

It has been suggested that peripheral refractive error may influence eye growth and the development of axial refractive error, implying that the peripheral retina is sensitive to defocus. This study aimed to evaluate the steady-state accommodative response to peripheral stimuli in 10 young, adult myopes (mean spherical equivalent error -2.10 ± 1.72 D, median -1.63 D, range -0.83 to -6.00 D) and 10 emmetropes (mean spherical equivalent error -0.02 ± 0.35 D, median +0.08 D, range -0.50 to +0.50 D).

METHODS

The subjects were asked to view monocularly the centre of a screen displaying each of a series of eccentric accommodative targets placed at 5, 10 and 15°. An axial target was viewed for comparison purposes. Accommodation was measured using an open-field autorefractor, each stimulus being varied between about 0 and 4 D with spherical trial lenses placed in front of the viewing eye.

RESULTS

The results confirm that the peripheral retina is sensitive to optical focus, up to field angles of at least 15°, with accommodative responses weakening as the peripheral angle increases. There is some evidence that peripheral accommodation may be less effective in myopes than emmetropes.

CONCLUSIONS

Although peripheral accommodation can be demonstrated in the absence of a central stimulus, the accommodation response is normally dominated by the central stimulus and it seems unlikely that peripheral accommodation effects play an important role in refractive development.

Fast scanning photoretinoscope for measuring peripheral refraction as a function of accommodation

A new device was designed to provide fast measurements (4 s) of the peripheral refraction (90 degrees central horizontal field). Almost-continuous traces are obtained with high angular resolution (0.4 degrees) while the subject is fixating a central stimulus. Three-dimensional profiles can also be measured. The peripheral refractions in 10 emmetropic subjects were studied as a function of accommodation (200 cm, 50 cm, and 25 cm viewing distances). Peripheral refraction profiles were largely preserved during accommodation but were different in each individual. Apparently, the accommodating lens changes its focal length evenly over the central 90 degrees of the visual field.

Peripheral refraction in orthokeratology patients

PURPOSE

The purpose of this study is to measure refraction across the horizontal central visual field in orthokeratology patients before and during treatment.

METHODS

Refractions were measured out to 34 degrees eccentricity in both temporal and nasal visual fields using a free-space autorefractor (Shin-Nippon SRW5000) for the right eyes of four consecutively presenting myopic adult patients. Measurements were made before orthokeratology treatment and during the course of treatment (usually 1 week and 2 weeks into treatment). Refractions were converted into mean sphere (M), 90 degrees to 180 degrees astigmatism (J180), and 45 degrees to 135 degrees astigmatism (J45) components.

RESULTS

Before treatment, subjects had either a relatively constant mean sphere refraction across the field or a relative hypermetropia in the periphery as compared with the central refraction. As a result of treatment, myopia decreased but at reduced rate out into the periphery. Most patients had little change in mean sphere at 30 degrees to 34 degrees . In all patients, the refraction pattern altered little after the first week.

CONCLUSION

Orthokeratology can correct myopia over the central +/- 10 degrees of the visual field but produces only minor changes at field angles larger than 30 degrees . If converting relative peripheral hypermetropia to relative peripheral myopia is a good way of limiting the axial elongation that leads to myopia, orthokeratology is an excellent option for achieving this.

Longitudinal changes in peripheral refraction with age

The changes in the patterns of refraction (skiagrams) over the central +/-35 degrees of the horizontal field of 3 originally near-emmetropic eyes of 2 subjects were determined over a time interval of 26 years. The subjects were aged 32 and 40 years at the time of the first measurements. The central refractions shifted in the expected hyperopic direction, while the radial and tangential image fields in the periphery became more myopic. These longitudinal results agree with recent transverse studies, provided that allowance is made for the change in central refraction: the reported loss with age in peripheral visual performance does not seem to be attributable to markedly increased peripheral astigmatism.

Refraction and aberration across the horizontal central 10 degrees of the visual field

PURPOSE

The purpose of this study was to measure refraction and aberrations across the horizontal central visual field.

METHODS

Cycloplegic refraction was measured on eight subjects at 13 points across the horizontal central 10 degrees of the retina using a Hartmann-Shack wavefront sensor. Refractions were converted into mean sphere (M), 90 degrees to 180 degrees astigmatism (J180), and 45 degrees to 135 degrees astigmatism (J45) components. For five subjects, higher-order aberrations were determined at the center and edges of the field.

RESULTS

Subtle changes in refraction were found to exist across the central 10 degrees of the retina, with changes in mean best sphere varying by up to half a diopter across this region and with smaller changes in astigmatism. Horizontal coma, but no other higher-order aberrations, varied systemically across the visual field; it varied linearly with angle but at different rates for the different subjects.

CONCLUSION

Subtle changes in cycloplegic refraction exist across the horizontal central 10 degrees of the retina. The results indicate the need for correct alignment when measuring objective refraction.

Peripheral refraction along the horizontal and vertical visual fields in myopia

Peripheral refractions were measured to 35 degrees eccentricity using a free-space autorefractor in young adult emmetropic and myopic subjects. Refractions were measured along horizontal and vertical visual fields for 116 subjects and a 43 subject subset, respectively. Along the horizontal visual field, peripheral myopic shifts in spherical equivalent M of emmetropes changed to relative hypermetropic shifts in the myopes, there were temporal-nasal asymmetries of 90 degrees to 180 degrees astigmatism J(180) which decreased as myopia increased, and 45 degrees to 135 degrees astigmatism J(45) was linearly related to field angle. Along the vertical visual field, both peripheral myopic shifts in peripheral M and J(180) asymmetry were unaffected by magnitude of myopia, and J(45) changed at three times the rate as for the horizontal visual field. Myopia has more effect on peripheral refraction of adult eyes along the horizontal than along the vertical visual field. The peripheral variations in refraction match well what is known about the shapes of emmetropic and myopic eyes.

Aberrations and myopia

It has been suggested that high levels of axial aberration or specific patterns of peripheral refraction could play a role in myopia development. Possible mechanisms involving high levels of retinal image blur caused by axial aberrations include form deprivation through poor retinal image quality in distance vision, enhanced accommodative lags favouring compensatory eye growth, and an absence of adequate directional cues to guide emmetropization. In addition, in initially emmetropic eyes, hyperopia in the retinal periphery may result in local compensatory eye growth, which induces axial myopia. Evidence in support of these ideas is reviewed and it is concluded that, for any fixed pupil diameter, evidence for higher levels of axial aberration in myopes in comparison with other refractive groups is weak, making involvement of axial aberrations in myopization through image degradation at the fovea unlikely. If, however, some potential myopes had unusually large pupil diameters, their effective aberration levels and associated retinal blur would be larger than those of the rest of the population. There is stronger evidence in favour of differences in patterns of peripheral refraction in both potential and existing myopes, with myopes tending to show relative hyperopia in the periphery. These differences appear to be related to a more prolate eyeball shape. Longitudinal studies are required to confirm whether the retinal defocus associated with the peripheral hyperopia can cause patterns of eyeball growth which lead to axial myopia.

Monochromatic aberrations of human eyes in the horizontal visual field

We measured the monochromatic aberrations of five subjects' right eyes both temporally and nasally out to 40 degrees from fixation. We used a Hartmann-Shack sensor with modifications to equipment and software to enable off-axis measurements. Results were standardized for 6-mm pupils. There was considerable variation among subjects in the pattern of aberrations. Aberrations were generally greater in the nasal visual field than in the temporal visual field; in the case of third-order aberrations, this was true for all subjects. The contribution of third-order Zernike aberrations to the root-mean-square aberration increased up to four times from the center to the edge of the field, but the contribution of fourth- to sixth-order Zernike aberrations varied little across the visual field. Results were similar to those of a previous investigation using laser ray tracing and were of the order of those predicted by Navarro's finite schematic eye.

Designing lenses to correct peripheral refractive errors of the eye

The purpose of this work was to design ophthalmic lenses that correct peripheral refractive errors of human eyes along a meridian. We designed lenses with the tangential section of one surface based on a figured spheroid but figured in the tangential section only. The curvature of the sagittal section of this surface was adjusted separately. A merit function was used to modify these surfaces until the lenses had power errors that corrected the eye. Examples are presented of lenses that correct a schematic eye. They do excellent jobs of correcting the peripheral power errors of the eye and are relatively insensitive to small changes in fitting distance. We conclude that it is theoretically feasible to design lenses to correct peripheral refractive errors.

Monochromatic aberrations and point-spread functions of the human eye across the visual field

The monochromatic aberrations of the human eye along the temporal meridian are studied by a novel laser ray-tracing method. It consists of delivering a narrow laser pencil into the eye through a given point on the pupil and recording the aerial image of the retinal spot with a CCD camera. The relative displacement of this image is proportional to the geometrical aberration of the ray (laser pencil) at the retina. We scanned the pupils of four observers in steps of 1 mm (effective diameter, 6.7 mm) and for five field angles (0 degree, 5 degrees, 10 degrees, 20 degrees, and 40 degrees). In addition, the aerial image for each chief ray is a low-pass-filtered version of the retinal point-spread function corresponding to a fully dilated pupil. The resulting spot diagrams, displaying the distribution of ray aberrations, are highly correlated with these point-spread functions. We have estimated the wave-front error by fitting Zernike polynomials (up to the fifth order). Despite the large variation found among observers, the overall rms wave-front error is relatively homogeneous. At the fovea, the average rms value was 1.49 microns when the second-order terms (defocus and astigmatism) were considered; this was reduced to 0.45 micron when the second-order terms were ignored. The rms values increase slowly, in a roughly linear fashion with eccentricity, such that at 40 degrees they are approximately double. These results are consistent with previous findings on the off-axis optical quality of the eye.

Analytic approximation of the off-axis modulation transfer function of the eye

Published experimental measurements of the ocular modulation transfer function (MTF) in the peripheral field are approximated by the expression T(f) = exp[-(f/fc)n], where T(f), f, fc, and n are modulation transfer, spatial frequency, spatial frequency constant and MTF index, respectively. It is shown that n (which describes the shape of the MTF) remains relatively constant at about 0.9 for field angles out to 40 deg but fc (which defines the spatial frequency scaling) declines steeply over this range, depending upon the pupil diameter and conditions of focus. The oblique astigmatism of the eye plays a major role in the off-axis changes in fc at field angles > or = 20 deg. The approximation may be useful in allowing the form of the degraded optical stimulus in studies of the peripheral retinal function to be evaluated.