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

A focusing method on refraction topography measurement

This paper introduces a novel focusing method Refraction Topography (RT) for wide-angle refraction measurement. The agreement of the test results obtained using RT is evaluated against simulation results and expected refraction. RT develops a refraction algorithm on fundus images at various focusing statuses. Unlike conventional techniques for peripheral refraction measurement, RT requires the subject to stare at a stationary fixation target. The refraction algorithm calculates the focus measure for multiple images at the Point of Interest and formulates them into a focus profile. The maximum focus measure correlates with the optimal focus position. Refraction Characterization Function (RCF) is proposed to translate the focus position into refraction determination, thus forming the refraction topography. The refraction characterization of RT optical system is performed using Isabel schematic eye. Three test eyes of - 15 D, 0 D, and + 15 D are defined, and expected refraction is obtained through simulation on an independent test schematic eye. Both simulation results and experimental results are obtained by combining the test eyes and RT system. Test results are compared with simulation results and expected refraction. The study demonstrates agreement among the test results, simulation results, and expected refraction on three test eyes.

Central and Peripheral Ocular High-Order Aberrations and Their Relationship with Accommodation and Refractive Error: A Review

High-order aberrations (HOAs) are optical defects that degrade the image quality. They change with factors such as pupil diameter, age, and accommodation. The changes in optical aberrations during accommodation are mainly due to lens shape and position changes. Primary spherical aberration (Z(4.0)) is closely related to accommodation and some studies suggested that it plays an important role in the control of accommodation. Furthermore, central and peripheral HOAs vary with refractive error and seem to influence eye growth and the onset and progression of myopia. The variations of central and peripheral HOAs during accommodation also appear to be different depending on the refractive error. Central and peripheral high-order aberrations are closely related to accommodation and influence the accuracy of the accommodative response and the progression of refractive errors, especially myopia.

Comparison of wavefront aberrations in the object and image spaces using wide-field individual eye models

Wavefront aberrations in the image space are critical for visual perception, though the clinical available instruments usually give the wavefront aberrations in the object space. This study aims to compare the aberrations in the object and image spaces. With the measured wavefront aberrations over the horizontal and vertical ±15° visual fields, the in-going and out-going wide-field individual myopic eye models were constructed to obtain the wavefront aberrations in the object and image spaces of the same eye over ±45° horizontal and vertical visual fields. The average differences in the mean sphere and astigmatism were below 0.25 D between the object and image spaces over the horizontal and vertical ±45° visual fields under 3 mm and 6 mm pupil diameter. The wavefront aberrations in the object space are a proper representation of the aberrations in the image space at least for horizontal visual fields ranging from -35°to +35° and vertical visual fields ranging from -15°to +15°.

Meridional Anisotropy of Foveal and Peripheral Resolution Acuity in Adults With Emmetropia, Myopia, and Astigmatism

Purpose

To quantify astigmatism-related meridional anisotropy in visual resolution at central, nasal, and inferior visual fields.

Methods

Three groups of young adults (range, 18–30 years) with corrected-to-normal visual acuity (logMAR 0) were recruited: (1) myopic astigmats (MA): spherical-equivalent error (SE) < −0.75D, with-the-rule astigmatism ≥ 2.00D, n = 19; (2) simple myopes (SM): SE < −0.75D, astigmatism ≤ 0.50D, n = 20; and (3) emmetropes (EM): SE ± 0.50D, astigmatism ≤ 0.50D, n = 14. Resolution acuity was measured for the horizontal and vertical gratings at central and peripheral visual fields (eccentricity: 15°) using a 3-down 1-up staircase paradigm. On- and off-axis refractive errors were corrected by ophthalmic lenses.

Results

The MA group exhibited meridional anisotropy preferring vertical gratings. At the central field, the MA group had better resolution acuity for vertical than horizontal gratings, and their resolution acuity for horizontal gratings was significantly worse than the SM and EM groups. At peripheral visual fields, both the SM and EM groups showed better resolution acuity for the radial (i.e., nasal field: horizontal gratings; inferior field: vertical gratings) than tangential orientation. However, the MA group tended to have better resolution acuity for the tangential orientation (i.e., vertical gratings), and their resolution acuity for horizontal gratings was significantly lower than the SM and EM groups at the nasal field. No significant differences were found in the inferior field among the three groups.

Conclusions

This study provided evidence of astigmatism-related meridional anisotropy at the fovea and nasal visual fields, underscoring the significant impact of astigmatism on orientation-dependent visual functions.

The blur horopter: Retinal conjugate surface in binocular viewing

From measurements of wavefront aberrations in 16 emmetropic eyes, we calculated where objects in the world create best-focused images across the central 27∘ (diameter) of the retina. This is the retinal conjugate surface. We calculated how the surface changes as the eye accommodates from near to far and found that it mostly maintains its shape. The conjugate surface is pitched top-back, meaning that the upper visual field is relatively hyperopic compared to the lower field. We extended the measurements of best image quality into the binocular domain by considering how the retinal conjugate surfaces for the two eyes overlap in binocular viewing. We call this binocular extension the blur horopter. We show that in combining the two images with possibly different sharpness, the visual system creates a larger depth of field of apparently sharp images than occurs with monocular viewing. We examined similarities between the blur horopter and its analog in binocular vision: the binocular horopter. We compared these horopters to the statistics of the natural visual environment. The binocular horopter and scene statistics are strikingly similar. The blur horopter and natural statistics are qualitatively, but not quantitatively, similar. Finally, we used the measurements to refine what is commonly referred to as the zone of clear single binocular vision.

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.

Optimal allocation of quantized human eye depth perception for multi-focal 3D display design

Creating immersive 3D stereoscopic, autostereoscopic, and lightfield experiences are becoming the center point of optical design of future head mounted displays and lightfield displays. However, despite the advancement in 3D and light field displays, there is no consensus on what are the necessary quantized depth levels for such emerging displays at stereoscopic or monocular modalities. Here we start from psychophysical theories and work toward defining and prioritizing quantized levels of depth that would saturate the human depth perception. We propose a general optimization framework, which locates the depth levels in a globally optimal way for band limited displays. While the original problem is computationally intractable, we manage to find a tractable reformulation as maximally covering a region of interest with a selection of hypographs corresponding to the monocular depth of field profiles. The results indicate that on average 1731 stereoscopic and 7 monocular depth levels (distributed optimally from 25 cm to infinity) would saturate the visual depth perception. Such that adding further depth levels adds negligible improvement. Also the first 3 depth levels should be allocated at (148), then (83, 170), then (53, 90, 170) distances respectively from the face plane to minimize the monocular error in the entire population. The study further discusses the 3D spatial profile of the quantized stereoscopic and monocular depth levels. The study provides fundamental guidelines for designing optimal near eye displays, light-field monitors, and 3D screens.

2-D Peripheral image quality metrics with different types of multifocal contact lenses

To evaluate the impact of multifocal contact lens wear on the image quality metrics across the visual field in the context of eye growth and myopia control. Two-dimensional cross-correlation coefficients were estimated by comparing a reference image against the computed retinal images for every location. Retinal images were simulated based on the measured optical aberrations of the naked eye and a set of multifocal contact lenses (centre-near and centre-distance designs), and images were spatially filtered to match the resolution limit at each eccentricity. Value maps showing the reduction in the quality of the image through each optical condition were obtained by subtracting the optical image quality from the theoretical physiological limits. Results indicate that multifocal contact lenses degrade the image quality independently from their optical design, though this result depends on the type of analysis conducted. Analysis of the image quality across the visual field should not be oversimplified to a single number but split into regional and groups because it provides more insightful information and can avoid misinterpretation of the results. The decay of the image quality caused by the multifocal contacts alone, cannot explain the translation of peripheral defocus towards protection on myopia progression, and a different explanation needs to be found.

Off-axis optical coherence tomography imaging of the crystalline lens to reconstruct the gradient refractive index using optical methods

Earlier studies have shown that the gradient index of refraction (GRIN) of the crystalline lens can be reconstructed in vitro using Optical Coherence Tomography (OCT) images. However, the methodology cannot be extended in vivo because it requires accurate measurements of the external geometry of the lens. Specifically, the posterior surface is measured by flipping the lens so that the posterior lens surface faces the OCT beam, a method that cannot be implemented in vivo. When the posterior surface is imaged through the lens in its natural position, it appears distorted by the unknown GRIN. In this study, we demonstrate a method to reconstruct both the GRIN and the posterior surface shape without the need to flip the lens by applying optimization routines using both on-axis and off-axis OCT images of cynomolgous monkey crystalline lenses, obtained by rotating the OCT delivery probe from -45 to +45 degrees in 5 degree steps. We found that the GRIN profile parameters can be reconstructed with precisions up to 0.009, 0.004, 1.7 and 1.1 (nucleus and surface refractive indices, and axial and meridional power law, respectively), the radius of curvature within 0.089 mm and the conic constant within 0.3. While the method was applied on isolated crystalline lenses, it paves the way to in vivo lens GRIN and posterior lens surface reconstruction.

Differences in the Relation Between Perimetric Sensitivity and Variability Between Locations Across the Visual Field

Purpose

Perimetric sensitivities become more variable with glaucomatous functional loss. This study examines the extent to which this relation varies between locations, and whether this can be predicted by eccentricity-related differences in spatial summation.

Methods

Longitudinal series of visual fields from standard automated perimetry were obtained from participants with suspected or extant glaucoma. For each location in the 24-2 visual field, heterogeneous fixed-effects models were fit to the data, assuming that variability increased exponentially as sensitivity decreased. The predicted variability at each location was calculated when sensitivity was either 30 dB or 25 dB.

Results

Variability significantly increased with damage at all 52 locations. When sensitivity was 30 dB, variability increased with eccentricity, with P = 0.0003. The average SD was 1.54 dB at the four most central locations, versus 1.74 dB at the most peripheral locations. When sensitivity was 25 dB, variability did not vary predictably with eccentricity, with P = 0.340. The average SD was 2.36 dB at the four central locations, versus 2.24 dB at the most peripheral locations.

Conclusions

The relation between sensitivity and variability differed by eccentricity. Among healthy locations, variability was lower centrally, where the stimulus size is larger than Ricco's area, than peripherally. Among damaged locations, variability did not systematically vary with eccentricity. This could be because Ricco's area expands in glaucoma, such that stimuli were now smaller than this area at all locations.

Profile of off-axis higher order aberrations and its variation with time among various refractive error groups

Peripheral higher order aberrations (HOA) of 646 children at 30° temporal, nasal and inferior visual field were measured under cycloplegia (5 mm pupil diameter) using a commercially available Shack-Hartmann aberrometer in the Sydney Myopia Study [age, 12.7 ± 0.4 years (mean ± standard deviation)] and five years later in the Sydney Adolescent Vascular and Eye Study. At baseline, 176 eyes were emmetropic, 95 were myopic and 375 were hyperopic. Coma, 3rd order and RMS of coma increased with eccentricity for all eyes and no difference was observed for 4th order and RMS of C(4,0) among refractive error groups. More positive C(4,0) was observed for hyperopic eyes at periphery. At follow up, 26% had 'myopic change' and 70% had 'no change' in refractive error. At follow-up, horizontal coma became more negative at nasal field and more positive at temporal field for all eyes. More positive C(4,0) for hyperopic eyes at baseline may indicate variation in optical characteristics of peripheral cornea and crystalline lens. An increase in horizontal coma with time, irrespective of refractive error change, may be attributed to variation in the shape factor of peripheral cornea and crystalline lens and/or misalignment of optical surfaces/components relative to the visual axis (angle kappa) as the eye grows in axial length.

Role of parafovea in blur perception

The blur experienced by our visual system is not uniform across the visual field. Additionally, lens designs with variable power profile such as contact lenses used in presbyopia correction and to control myopia progression create variable blur from the fovea to the periphery. The perceptual changes associated with varying blur profile across the visual field are unclear. We therefore measured the perceived neutral focus with images of different angular subtense (from 4° to 20°) and found that the amount of blur, for which focus is perceived as neutral, increases when the stimulus was extended to cover the parafovea. We also studied the changes in central perceived neutral focus after adaptation to images with similar magnitude of optical blur across the image or varying blur from center to the periphery. Altering the blur in the periphery had little or no effect on the shift of perceived neutral focus following adaptation to normal/blurred central images. These perceptual outcomes should be considered while designing bifocal optical solutions for myopia or presbyopia.

Reconstruction of the optical system of personalized eye models by using magnetic resonance imaging

This study presents a practical method for reconstructing the optical system of personalized eye models by using magnetic resonance imaging (MRI). Monocular images were obtained from a young (20-year-old) healthy subject viewing at a near point (10 cm). Each magnetic resonance image was first analyzed using several commercial software to capture the profile of each optical element of the human eye except for the anterior lens surface, which could not be determined because it overlapped the ciliary muscle. The missing profile was substituted with a modified profile from a generic eye model. After the data-including the refractive indices from a generic model-were input in ZEMAX, we obtained a reasonable initial layout. By further considering the resolution of the MRI, the model was optimized to match the optical performance of a healthy eye. The main benefit of having a personalized eye model is the ability to quantitatively identify wide-angle ocular aberrations, which were corrected by the designed free-form spectacle lens.

Optical and neural anisotropy in peripheral vision

Optical blur in the peripheral retina is known to be highly anisotropic due to nonrotationally symmetric wavefront aberrations such as astigmatism and coma. At the neural level, the visual system exhibits anisotropies in orientation sensitivity across the visual field. In the fovea, the visual system shows higher sensitivity for cardinal over diagonal orientations, which is referred to as the oblique effect. However, in the peripheral retina, the neural visual system becomes more sensitive to radially-oriented signals, a phenomenon known as the meridional effect. Here, we examined the relative contributions of optics and neural processing to the meridional effect in 10 participants at 0°, 10°, and 20° in the temporal retina. Optical anisotropy was quantified by measuring the eye's habitual wavefront aberrations. Alternatively, neural anisotropy was evaluated by measuring contrast sensitivity (at 2 and 4 cyc/deg) while correcting the eye's aberrations with an adaptive optics vision simulator, thus bypassing any optical factors. As eccentricity increased, optical and neural anisotropy increased in magnitude. The average ratio of horizontal to vertical optical MTF (at 2 and 4 cyc/deg) at 0°, 10°, and 20° was 0.96 ± 0.14, 1.41 ± 0.54 and 2.15 ± 1.38, respectively. Similarly, the average ratio of horizontal to vertical contrast sensitivity with full optical correction at 0°, 10°, and 20° was 0.99 ± 0.15, 1.28 ± 0.28 and 1.75 ± 0.80, respectively. These results indicate that the neural system's orientation sensitivity coincides with habitual blur orientation. These findings support the neural origin of the meridional effect and raise important questions regarding the role of peripheral anisotropic optical quality in developing the meridional effect and emmetropization.

Investigation of aberration characteristics of eyes at a peripheral visual field by individual eye model

We propose a method of constructing an individual eye model with a large visual field, and then investigate aberration characteristics of eyes in peripheral fields with constructed models. Twelve eyes of different aberrations are selected from 89 myopic eyes. It is shown that astigmatism increases as visual field in a quadratic manner. The variation tendency of defocus can be expressed by the cubic curve for 50% of eyes. For most of the eyes, the variation of spherical aberration shows a quadratic rule within ±24° visual field. Coma exhibits obvious individual differences. The impact of high-order aberrations on vision is mainly at a smaller visual field, and it becomes negligible beyond 24° visual field.

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.

Aberrometry in patients implanted with accommodative intraocular lenses

PURPOSE

To evaluate the objective accommodative response, change of aberrations, and depth of focus in eyes implanted with the Crystalens accommodative intraocular lens (IOL) at different accommodative demands.

DESIGN

Prospective, observational study.

METHODS

Eleven cataract patients (22 eyes) who underwent implantation of a Crystalens accommodative IOL, and control groups of 9 normal subjects (17 eyes) and 17 pseudophakic patients (17 eyes) implanted with monofocal IOLs were evaluated. A custom-developed laser ray tracing aberrometer was used to measure the optical aberrations. The monochromatic wave aberrations were described using a sixth-order Zernike polynomial expansion. Measurements were obtained under dilated and natural viewing conditions (for accommodative efforts ranging from 0 to 2.5 diopters [D]). The accommodative response was obtained by analyzing changes in paraxial defocus (associated to changes in defocus) and by evaluating the differences in the effective defocus (associated with defocus, spherical aberrations, and pupil diameter) with the accommodative demand. Depth of focus was estimated from through-focus objective optical quality.

RESULTS

Wave aberration measurements were highly reproducible. Vertical trefoil (Z3(-3)) was the predominant higher-order aberration in the Crystalens group and significantly higher (P < .0001) than in the young group, but similar to the monofocal IOL group. The coma root mean square also was higher (P < .005) in the Crystalens group than in the young group. On average, the defocus term (Z2(0)), astigmatism, or higher-order aberrations did not change systematically with accommodative demand in Crystalens eyes. As found for paraxial defocus, the effective defocus in Crystalens eyes did not show significant differences between conditions: 0.34 ± 0.48 D (far), 0.32 ± 0.50 D (intermediate), and 0.34 ± 0.44 D (near). Depth of focus was statistically significantly higher in the Crystalens eyes than in the control groups.

CONCLUSIONS

The accommodative response of eyes implanted with the Crystalens accommodative IOLs, measured objectively using laser ray tracing aberrometry, was lower than 0.4 D in all eyes. Several subjects showed changes in astigmatism, spherical aberration, trefoil, and coma with accommodation, which must arise from geometrical and alignment changes in the lens with accommodative demand. Pseudoaccommodation from increased depth of focus may contribute to near vision functionality in Crystalens-implanted patients.

The Glenn A. Fry Award Lecture 2011: Peripheral optics of the human eye

There has been a low level of interest in peripheral aberrations and corresponding image quality for over 200 years. Most work have been concerned with the second-order aberrations of defocus and astigmatism that can be corrected with conventional lenses. Studies have found high levels of aberration, often amounting to several dioptres, even in eyes with only small central defocus and astigmatism. My investigations have contributed to understanding shape changes in the eye with increases in myopia, changes in eye optics with ageing, and how surgical interventions intended to correct central refractive errors have unintended effects on peripheral optics.My research group has measured peripheral second- and higher-order aberrations over a 42° horizontal × 32° vertical diameter visual field. There is substantial variation in individual aberrations with age and pathology. While the higher-order aberrations in the periphery are usually small compared with second-order aberrations, they can be substantial and change considerably after refractive surgery.The thrust of my research in the next few years is to understand more about the peripheral aberrations of the human eye, to measure visual performance in the periphery and determine whether this can be improved by adaptive optics correction, to use measurements of peripheral aberrations to learn more about the optics of the eye and in particular the gradient index structure of the lens, and to investigate ways of increasing the size of the field of good retinal image quality.

Specifying peripheral aberrations in visual science

PURPOSE

Investigations of foveal aberrations assume circular pupils. However, the pupil becomes increasingly elliptical with increase in visual field eccentricity. We address this and other issues concerning peripheral aberration specification.

METHODS

One approach uses an elliptical pupil similar to the actual pupil shape, stretched along its minor axis to become a circle so that Zernike circular aberration polynomials may be used. Another approach uses a circular pupil whose diameter matches either the larger or smaller dimension of the elliptical pupil. Pictorial presentation of aberrations, influence of wavelength on aberrations, sign differences between aberrations for fellow eyes, and referencing position to either the visual field or the retina are considered.

RESULTS

Examples show differences between the two approaches. Each has its advantages and disadvantages, but there are ways to compensate for most disadvantages. Two representations of data are pupil aberration maps at each position in the visual field and maps showing the variation in individual aberration coefficients across the field.

CONCLUSIONS

Based on simplicity of use, adequacy of approximation, possible departures of off-axis pupils from ellipticity, and ease of understanding by clinicians, the circular pupil approach is preferable to the stretched elliptical approach for studies involving field angles up to 30 deg.

Peripheral aberrations and image quality for contact lens correction

PURPOSE

Contact lenses (CLs) reduced the degree of hyperopic field curvature present in myopic eyes and rigid CLs reduced spherocylindrical image blur on the peripheral retina, but their effect on higher order aberrations and overall optical quality of the eye in the peripheral visual field is still unknown. The purpose of our study was to evaluate peripheral wavefront aberrations and image quality across the visual field before and after CL correction.

METHODS

A commercial Hartmann-Shack aberrometer was used to measure ocular wavefront errors in 5° steps out to 30° of eccentricity along the horizontal meridian in uncorrected eyes and when the same eyes are corrected with soft or rigid CLs. Wavefront aberrations and image quality were determined for the full elliptical pupil encountered in off-axis measurements.

RESULTS

Ocular higher order aberrations (HOA) increase away from fovea in the uncorrected eye. Third-order aberrations are larger and increase faster with eccentricity compared with the other HOA. CLs increase all HOA except third-order Zernike terms. Nevertheless, a net increase in image quality across the horizontal visual field for objects located at the foveal far point is achieved with rigid lenses, whereas soft CLs reduce image quality.

CONCLUSIONS

Second-order aberrations limit image quality more than HOA in the periphery. Although second-order aberrations are reduced by CLs, the resulting gain in image quality is partially offset by increased amounts of HOA. To fully realize the benefits of correcting HOA in the peripheral field requires improved correction of second-order aberrations as well.

Peripheral aberration measurements: elliptical pupil transformation and variations in horizontal coma across the visual field

BACKGROUND

The aim was to determine the critical eccentricity at which two methods of elaborating peripheral wavefront measurements are significantly different and to characterise horizontal coma in healthy young adults.

METHODS

Peripheral aberrations were determined for 20 observers for central and eight peripheral gaze positions up to 20° using an IRX-3 aberrometer. In one subject, additional measurements up to 40° were obtained. Two definitions of stretching coefficients were compared. The raw empirical data were compared with theoretical modelling.

RESULTS

For both 3.5 mm and 6.0 mm pupils, no significant differences were observed between recalculated and non-recalculated elliptical pupils for both methods (p > 0.05) up to 20° eccentricity. For eccentricities greater than 20° and up to 40°, significant differences between circular and elliptical pupils at some eccentricities were apparent, which corresponded to theoretical models. Wide individual variations in horizontal coma across the peripheral field were observed.

CONCLUSIONS

The data suggest that for eyes with average levels of aberrations, the elliptical transformation is of no practical importance for eccentricities up to 20°. In some cases the slope of horizontal coma was reversed compared with previous findings in normal eyes.

Modeling the patterns of visual field loss in glaucoma

PURPOSE

A computer model was developed to test the assumption that diffuse neural loss can result in the field loss pattern characteristic of glaucoma.

METHODS

The anterior visual pathways comprised the retinal ganglion cells, and their axons up to the optic nerve head (ONH) were modeled in a computer program. Axon resistance to stress was accounted for depending on the location on the ONH, taking into consideration the presence or absence of vessels in the area. Damage patterns were applied to the axons at the ONH, and the corresponding dendritic fields were removed accordingly. A visual field was extracted and represented on a gray scale after a predetermined stage of damage was reached. Two patterns of damage were considered, a diffuse damage produced by randomly removing fibers and an ordered anteroposterior elimination.

RESULTS

Random damage never rendered a pattern loss. Ordered centrifugal fiber loss may produce a radial pattern more conspicuous when the vessels are endowed with a protective role. In both cases, scotomas tend to be detectable earlier in more peripheral locations, attributable to the increasing size of the receptive fields with eccentricity.

CONCLUSIONS

The model shows that pattern loss typical of glaucoma cannot be solely the result of a random loss of fibers. Anteroposterior damage of the ONH can explain radial progression of scotomas if a protective role is introduced for the central vessels.

Design of isoplanatic aspheric monofocal intraocular lenses

A new and complete methodology of monofocal intraocular lens (IOL) design is presented aiming at isoplanatism, i.e. IOLs that provide the eye with optimized optical quality over a wide field of view (typically in a range of ten degrees). The methodology uses a merit function considering dimensional and biomechanical constraints, and a geometrical optical quality metric that is evaluated simultaneously at different field angles. As an example, we present new isoplanatic designs based on different commercial IOL platforms. Aspheric isoplanatic designs improve peripheral quality over current aspheric IOLs. Also, isoplanatic designs provide more stable optical quality across the field and across pupil diameter.

Peripheral refraction with and without contact lens correction

PURPOSE

Peripheral refractive error degrades the quality of retinal images and has been hypothesized to be a stimulus for the development of refractive error. The purpose of this study was to investigate the changes in refractive error across the horizontal visual field produced by contact lenses (CLs) and to quantify the effect of CLs on peripheral image blur.

METHODS

A commercial Shack-Hartmann aberrometer measured ocular wavefront aberrations in 5 degrees steps across the central 60 degrees of visual field along the horizontal meridian before and after CLs correction. Wavefront refractions for peripheral lines-of-sight were based on the full elliptical pupil encountered in peripheral measurements. Curvature of field is the change in peripheral spherical equivalent relative to the eye's optical axis.

RESULTS

Hyperopic curvature of field in the naked eye increases with increasing amounts central myopic refractive error as predicted by Atchison (2006). For an eccentricity of E degrees, field curvature is approximately E percent of foveal refractive error. Rigid gas permeable (RGP) lenses changed field curvature in the myopic direction twice as much as soft CLs (SCLs). Both of these effects varied with CLs power. For all lens powers, SCL cut the degree of hyperopic field curvature in half whereas RGP lenses nearly eliminated field curvature. The benefit of reduced field curvature was partly offset by increased oblique astigmatism. The net reduction of retinal blur because of CLs is approximately constant across the visual field.

CONCLUSIONS

Both SCL and RGP lenses reduced the degree of hyperopic field curvature present in myopic eyes, with RGP lenses having greater effect. The tradeoff between field curvature and off-axis astigmatism with RGP lenses may limit their effectiveness for control of myopia progression. These results suggest that axial growth mechanisms that depend on retinal image quality will be affected more by RGP than by SCL lenses.

Combining coma with astigmatism can improve retinal image over astigmatism alone

We demonstrate that certain combinations of non-rotationally symmetric aberrations (coma and astigmatism) can improve retinal image quality over the condition with the same amount of astigmatism alone. Simulations of the retinal image quality in terms of Strehl Ratio, and measurements of Visual Acuity under controlled aberrations with adaptive optics were performed, varying defocus, astigmatism and coma. Astigmatism ranged between 0 and 1.5D. Defocus ranged typically between -1 and 1D. The amount of coma producing best retinal image quality (for a given relative angle between astigmatism and coma) was computed and the amount was found to be different from zero in all cases (except for 0D of astigmatism). For example, for a 6mm pupil, in the presence of 0.5D of astigmatism, a value of coma of 0.23mum produced (for best focus) a peak improvement in Strehl Ratio by a factor of 1.7, over having 0.5D of astigmatism alone. The improvement holds over a range of >1.5D of defocus and peak improvements were found for amounts of coma ranging from 0.15mum to 0.35mum. We measured VA under corrected high order aberrations, astigmatism alone (0.5D) and astigmatism in combination with coma (0.23mum), with and without adaptive optics correction of all the other aberrations, in two subjects. We found that the combination of coma with astigmatism improved decimal VA by a factor of 1.28 (28%) and 1.47 (47%) in both subjects, over VA with astigmatism alone when all the rest of aberrations were corrected. Nevertheless, in the presence of typical normal levels of HOA the effect of the coma/astigmatism interaction is considerably diminished.

High-resolution retinal imaging through open-loop adaptive optics

Using the liquid crystal spatial light modulator (LC-SLM) as the wavefront corrector, an open-loop adaptive optics (AO) system for fundus imaging in vivo is constructed. Compared with the LC-SLM closed-loop AO system, the light energy efficiency is increased by a factor of 2, which is helpful for the safety of fundus illumination in vivo. In our experiment, the subjective accommodation method is used to precorrect the defocus aberration, and three subjects with different myopia 0, -3, and -5 D are tested. Although the residual wavefront error after correction cannot to detected, the fundus images adequately demonstrate that the imaging system reaches the resolution of a single photoreceptor cell through the open-loop correction. Without dilating and cyclopleging the eye, the continuous imaging for 8 s is recorded for one of the subjects.

Population distribution of wavefront aberrations in the peripheral human eye

We present a population study of peripheral wavefront aberrations in large off-axis angles in terms of Zernike coefficients. A laboratory Hartmann-Shack sensor was used to assess the aberrations in 0 degrees, 20 degrees, and 30 degrees in the nasal visual field of 43 normal eyes. The elliptical pupil meant that the quantification could be done in different ways. The three approaches used were (1) over a circular aperture encircling the pupil, (2) over a stretched version of the elliptical pupil, and (3) over a circular aperture within the pupil (MATLAB conversion code given). Astigmatism (c(2)(2)) increased quadratically and coma (c(3)(1)) linearly with the horizontal viewing angle, whereas spherical aberration (c(4)(0)) decreased slightly toward the periphery. There was no correlation between defocus and angle, although some trends were found when the subjects were divided into groups depending on refractive error. When comparing results of different studies it has to be kept in mind that the coefficients differ depending on how the elliptical pupil is taken into consideration.

The Optical Design of the Human Eye: a Critical Review

Cornea, lens and eye models are analyzed and compared to experimental findings to assess properties and eventually unveil optical design principles involved in the structure and function of the optical system of the eye. Models and data often show good match but also some paradoxes. The optical design seems to correspond to a wide angle lens. Compared to conventional optical systems, the eye presents a poor optical quality on axis, but a relatively good quality off-axis, thus yielding higher homogeneity for a wide visual field. This seems the result of an intriguing combination of the symmetry design principle with a total lack of rotational symmetry, decentrations and misalignments of the optical surfaces.

Association between Offset of the Pupil Center from the Corneal Vertex and Wavefront Aberration

Purpose

To investigate the influence of offsets of the pupil center from the corneal vertex on wavefront aberrations in the anterior cornea and the whole eye.

Methods

Both right and left eyes of 103 subjects were measured for the wavefront aberrations in the anterior cornea, along with the offset of the pupil center relative to the corneal vertex, using a Humphrey corneal topographer, and for the wavefront aberration in the whole eye using a WASCA wavefront sensor. Correlations of the pupil center offsets with the Zernike aberrations were tested.

Results

X-axis shift of the pupil center from the corneal vertex was significantly correlated to horizontal coma for both the right (r = 0.54, P<0.0001) and left eyes (r=0.48, P<0.0001) in the cornea, but was weakly correlated to the coma in the whole eye (r=0.17, P=0.04 for OD; and r=0.17, P=0.05 for OS). Significant but weak correlations with the x-axis pupil center shift were also found for several other Zernike aberrations, including the oblique astigmatism, vertical trefoil and secondary astigmatism. Very few Zernike aberrations were significantly correlated to y-axis pupil center shift. Most Zernike aberrations were significantly correlated between the right and left eyes to produce bilateral symmetry in the cornea and the whole eye.

Conclusions

The results suggest that offset of the pupil center from the corneal vertex plays an important role in determining horizontal coma and few other Zernike aberrations. Factors controlling bilateral symmetry of the wavefront aberrations between the two eyes could make important contributions to wavefront aberrations in the human eye.

Wide-field schematic eye models with gradient-index lens

We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.

Potential Higher-Order Aberration Cues for Sphero-Cylindrical Refractive Error Development

PURPOSE

To investigate analytically whether higher-order wavefront errors comprising combinations of trefoil along 30 degrees (trefoil30), vertical coma, and spherical aberration could provide cues to sphero-cylindrical refractive error development.

METHODS

A total of 25 test wavefronts, subdivided into five different types and five levels of higher-order root mean square errors (HO-RMS), were created for the study. One type contained spherical aberration only, producing HO-RMS levels between 0.1 and 0.5 microm. Four wavefront types contained coma, trefoil, and spherical aberration of various sign combinations also producing HO-RMS levels between 0.1 and 0.5 microm. From the 25 wavefronts, refractive power maps were created and 2025 different sphero-cylindrical combinations were added to each refractive power map. For each sphero-cylinder combination, the visual Strehl ratio based on the modulation transfer function (VSMTF) was calculated. Retinal images and refractive power histograms were calculated for the refractive power maps corresponding to the peak of the VSMTF.

RESULTS

Spherical aberration affected the best focal plane thereby inducing spherical or defocus cues. The VSMTF produced by vertical coma and trefoil30, in combination with spherical aberration, could be improved with sphero-cylinders of various magnitudes and directions (i.e., with-the-rule, against-the rule, myopic astigmatism, or hyperopic astigmatism). Clinical significance of sphero-cylinders (i.e., >or=0.25 D) was reached at HO-RMS levels between 0.2 and 0.3 microm for a 5-mm pupil zone.

CONCLUSIONS

In the context of compensatory blur driven eye growth, commonly occurring combinations of the three considered higher-order aberrations have the potential to produce cues to eye growth resulting in myopia and with-the-rule astigmatism.

Neural and optical limits to visual performance in myopia

We investigated the relative importance of neural and optical limitations to visual performance in myopia. A number of visual performance measures were made on all or subsets of 121 eyes of emmetropic and myopic volunteers aged 17-35 years. These tests included visual measures that are mainly neurally limited (spatial summation out to +/-30 degrees in the horizontal visual field and resolution acuity out to +/-10 degrees in the horizontal visual field) and central ocular aberrations. We found that myopia affected the neurally limited tests, but had little effect on central higher order aberration. The critical area for spatial summation increased in the temporal visual field at 0.03 log units/dioptre of myopia. Resolution acuity decreased at approximately 0.012 log units/dioptre of myopia. Losses of visual function were slightly greater in the temporal than in the nasal visual field. The observed visual deficit in myopia can be explained by either global retinal expansion with some post-receptor loss (e.g. ganglion cell death) or a posterior polar expansion in which the point about which expansion occurs is near the centre of the previously emmetropic globe.

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.

On the prediction of optical aberrations by personalized eye models

PURPOSE

The purpose of this study is to develop and analyze a method to obtain optical schematic models of individual eyes. Each model should be able to reproduce the measured monochromatic wave aberration with high fidelity.

METHODS

First, we choose a generic eye model as the input guess and then apply a two-stage customization procedure. Stage 1 consists of replacing, in the initial generic model, those anatomic and optical parameters with experimental data measured on the eye under analysis. The set of experimental data was that provided by a standard clinical preoperative examination, namely lens topography, ultrasound biometry, and total wave aberration. Then, the second stage is to find the unknown lens structure that would reproduce the measured wave aberration through optical optimization. Two totally different initial eye models have been compared; one considers a simpler constant refractive index for the lens, whereas the second model has a gradient-index (GRIN) lens.

RESULTS

This automatic customization method has been applied to 19 eyes with different degrees of spherical ametropia (from +0.4 D to -8 D). Two models have been obtained for each eye (constant and gradient index lens). The results were highly satisfactory, with 100% convergence, and with average RMS prediction errors approximately lambda/100. This is one order of magnitude lower than typical measurement errors. The models with a constant refractive index lens tended to overestimate surface curvatures, whereas for the GRIN model, lens surfaces were too flat.

CONCLUSIONS

The proposed method is highly efficient and robust giving a high-fidelity reproduction of the wavefront in all cases attempted so far. Limitations found in reproducing the geometry of the lens seem to be associated with the use of inaccurate models of its refractive index.

Monochromatic ocular wave aberrations in young monkeys

High-order monochromatic aberrations could potentially influence vision-dependent refractive development in a variety of ways. As a first step in understanding the effects of wave aberration on refractive development, we characterized the maturational changes that take place in the high-order aberrations of infant rhesus monkey eyes. Specifically, we compared the monochromatic wave aberrations of infant and adolescent animals and measured the longitudinal changes in the high-order aberrations of infant monkeys during the early period when emmetropization takes place. Our main findings were that (1) adolescent monkey eyes have excellent optical quality, exhibiting total RMS errors that were slightly better than those for adult human eyes that have the same numerical aperture and (2) shortly after birth, infant rhesus monkeys exhibited relatively larger magnitudes of high-order aberrations predominately spherical aberration, coma, and trefoil, which decreased rapidly to assume adolescent values by about 200 days of age. The results demonstrate that rhesus monkey eyes are a good model for studying the contribution of individual ocular components to the eye's overall aberration structure, the mechanisms responsible for the improvements in optical quality that occur during early ocular development, and the effects of high-order aberrations on ocular growth and emmetropization.

Validation of the PowerRefractor for measuring human infant refraction

PURPOSE

Eccentric photorefraction provides an opportunity to gather rapid and remote estimates of refraction and gaze position from infants. The technique has the potential for extensive use in vision screenings and studies of visual development. The goal of this study was to assess the refraction calibration of the PowerRefractor (Multichannel Systems) for use with uncyclopleged infants.

METHODS

The defocus measurements from the instrument were compared with the results of simultaneous retinoscopy in one analysis and with known amounts of defocus induced with trial lenses in another. Data were collected from infants 1 to 6 months of age and adults.

RESULTS

The PowerRefractor typically read < 1 D of myopia when the retinoscopy reflex was judged to be neutral at the same working distance in both infants and adults. The slopes of both infant and adult validation functions (trial lens power vs. measurement of induced defocus) were close to 1 over a 4D range. The infant slopes were significantly greater than those of the adults, however.

CONCLUSIONS

The results suggest that the instrument is capable of detecting large amounts of defocus but needs individual calibration for detailed studies of accommodative accuracy and absolute levels of defocus, as has been recommended previously for adult subjects.

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.