Calculation of retinal image quality for polychromatic light

Fabrication and performance evaluation of a design for an extended depth-of-focus intraocular lens based on an improved sinusoidal profile

This study presents the fabrication and evaluation of a sinusoidal extended depth-of-focus (EDoF) intraocular lens (IOL) based on our previously proposed design approach. The power, through-focus MTF, and surface profile were measured using commercial instruments. Through-focus images of a United States Air Force (USAF) 1951 resolution target formed by the fabricated IOL were compared with Symfony and AR40E under monochromatic and polychromatic light using optical bench testing. Simulations assessed visual acuity (VA) of a pseudophakic model eye with the EDoF IOL, including evaluation of tilt and decentration effects. Results indicate that the base power, add power, and the through-focus MTF@50 lp/mm of the fabricated IOL at a 3 mm pupil size align with the design specifications. The extended-depth-of-focus and imaging performance for the far vision of the fabricated IOL under both monochromatic and polychromatic light conditions at a 3.0 mm pupil diameter is comparable to that of Symfony. In addition, the fabricated IOL exhibits a similar extended-depth-of-focus for three discrete wavelengths. The pseudophakic model eye with the designed EDoF IOL demonstrates a VA exceeding 0.1 logMAR within a defocus range of 2.44 D. The VA is tolerant to both IOL tilt and decentration. These findings demonstrate the promising potential of the sinusoidal EDoF IOL design for future applications in cataract surgery.

Modulation transfer function formula for different age ranges

The modulation transfer function (MTF) is one of the most complete tools to study the optical performance of the eye. We present the average radial MTF profiles measured in 68 subjects grouped in six age ranges (from 20 to 80 years) and a general formula to estimate the radial profile of human MTF as a function of pupil size and age. The mean MTF for each age group was fitted to an analytical expression to compute two parameters related to aging. The proposed formula fitted reasonably well to experimental data available in previous works and predicted the average changes with aging of different optical quality parameters obtained from MTF.

Approach to the design of different types of intraocular lenses based on an improved sinusoidal profile

An approach is presented to design different types of Intraocular lenses (IOLs) with a uniform optimization algorithm. An improved sinusoidal phase function is proposed to realize adjustable energy allocations in different diffractive orders according to the design aims. By setting specific optimization goals, different types of IOLs can be designed using the same optimization algorithm. With this method, bifocal, trifocal, extended-depth-of-focus (EDoF), and mono-EDoF IOLs are successfully designed and their optical performance under monochromatic and polychromatic light is evaluated and compared with their commercial counterparts. The result shows that most of the designed IOLs, even though they don't have any multi-zones or combination of diffractive profiles, have superior or comparable performance to their commercial counterparts in terms of optical performance under monochromatic light. The result demonstrates the validity and reliability of the approach proposed in this paper. With this method, the development time of different types of IOLs could be reduced considerably.

Optical bench evaluation of the effect of pupil size in new generation monofocal intraocular lenses

BACKGROUND

A new generation of enhanced monofocal IOLs has been introduced to slightly increase the depth of focus as compared to standard monofocal IOLs. The purpose of this study is to evaluate the effect of pupil size on the through-focus optical performance of three new enhanced monofocal IOLs, designed to improve the range of vision as compared to standard monofocal IOLs.

METHODS

Optical bench testing in white light was performed for different pupils, using an average cornea eye. Distance image quality was evaluated using Modulation Transfer Function (MTF) measurements. Through-focus Visual Acuity (VA) was simulated from these measurements (sVA). Three enhanced monofocal IOLs (ICB00, ISOPure, and RayOne-EMV) and three standard monofocal IOLs: two aspheric (ZCB00 and SN60WF) and one spherical (AAB00) were included.

RESULTS

The enhanced monofocal IOLs provided an improvement in the intermediate sVA as compared to standard monofocal IOLs. For ICB00, the improvement was independent of the pupil size, while for the ISOPure and RayOne-EMV, the intermediate sVA improved with increased pupil size. Similar to the spherical monofocal IOL, the ISOPure and RayOne-EMV showed a strong correlation between improvement in intermediate sVA and reduction of distance sVA and MTF, and increasing pupil size. ICB00 provided the same distance sVA as the aspheric monofocal IOLs and the lowest variability in MTF with pupil size.

CONCLUSION

Optical bench results showed that the ISOPure and RayOne-EMV provide similar performance to a spherical monofocal IOL, with a strong pupil dependency for distance and intermediate vision. The other enhanced monofocal IOL, ICB00, provided a sustained improvement in simulated intermediate VA and maintained distance image quality comparable to that of the standard aspheric monofocal IOLs, even for larger pupils.

Impact of temporal fluctuations in optical defocus on visual acuity: Empirical results and modeling outcomes

Optical defocus in human eyes is seldom steady during naturalistic steady-state viewing. It fluctuates by 0.3 to 0.5 diopters (D) from accommodative microfluctuations and by 1.5 to 2.5 D in dysfunctions such as spasm of near reflex, both with ≤2 Hz low-pass frequency spectra. This study observed losses in monocular visual acuity of cyclopleged adults who encountered varying amplitude (0.25-2.0 D) and temporal frequency (0.25-2.0 Hz) combinations of sinusoidal defoci induced using an electrically tunable lens. Visual acuity, recorded for 300-ms flashes of Sloan optotype presentation using the method of constant stimuli, deteriorated with defocus amplitude at a rate steeper for lower than higher temporal frequencies. A template matching model of acuity, incorporating optical and neural low-pass filters, neural noise, and a cross-correlated decision operator, showed the best match with empirical data when acuity was governed by the minimum defocus available during optotype display. This criterion minimized acuity loss for higher temporal frequencies due to the increased probability of zero-defocus encounters within the presentation duration. Other decision criteria such as defocus averaging across the entire or parts of the presentation duration yielded less satisfactory results. These results imply that vision loss in humans encountering broadband time-varying defocus is dictated by the dominant low frequencies, with higher frequencies largely compensated using the least defocus decision strategy.

The visual benefits of correcting longitudinal and transverse chromatic aberration

We describe a system-the Binocular Varichrome and Accommodation Measurement System-that can be used to measure and correct the eye's longitudinal and transverse chromatic aberration (LCA and TCA) and to perform vision tests with custom corrections. We used the system to investigate how LCA and TCA affect visual performance. Specifically, we studied the effects of LCA and TCA on visual acuity, contrast sensitivity, and chromostereopsis. LCA exhibited inter subject variability but followed expected trends compared with previous reports. TCA at the fovea was variable between individuals but with a tendency for the shift at shorter wavelengths to be more temporalward in the visual field in each eye. We found that TCA was generally greater when LCA was corrected. For visual acuity, we found that a measurable benefit was realized only with both LCA and TCA correction unless the TCA was low. For contrast sensitivity, we found that the best sensitivity to a 10-cycle/degree polychromatic grating was attained when LCA and TCA were corrected. Finally, we found that the primary cause of chromostereopsis is the TCA of the eyes.

Optical modelling of an accommodative light field display system and prediction of human eye responses

The spatio-angular resolution of a light field (LF) display is a crucial factor for delivering adequate spatial image quality and eliciting an accommodation response. Previous studies have modelled retinal image formation with an LF display and evaluated whether accommodation would be evoked correctly. The models were mostly based on ray-tracing and a schematic eye model, which pose computational complexity and inaccurately represent the human eye population's behaviour. We propose an efficient wave-optics-based framework to model the human eye and a general LF display. With the model, we simulated the retinal point spread function (PSF) of a point rendered by an LF display at various depths to characterise the retinal image quality. Additionally, accommodation responses to the rendered point were estimated by computing the visual Strehl ratio based on the optical transfer function (VSOTF) from the PSFs. We assumed an ideal LF display that had an infinite spatial resolution and was free from optical aberrations in the simulation. We tested points rendered at 0-4 dioptres of depths having angular resolutions of up to 4x4 viewpoints within a pupil. The simulation predicted small and constant accommodation errors, which contradict the findings of previous studies. An evaluation of the optical resolution on the retina suggested a trade-off between the maximum achievable resolution and the depth range of a rendered point where in-focus resolution is kept high. The proposed framework can be used to evaluate the upper bound of the optical performance of an LF display for realistically aberrated eyes, which may help to find an optimal spatio-angular resolution required to render a high quality 3D scene.

Differences in Image Quality after Three Laser Keratorefractive Procedures for Myopia

SIGNIFICANCE

Psychophysical estimates of spatial and depth vision have been shown to be better after bilateral ReLEx small-incision lenticule extraction (SMILE) refractive surgery for myopia, relative to photorefractive keratectomy (PRK) and femtosecond laser-assisted in situ keratomileusis (FS-LASIK). The present study provides the optical basis for these findings using computational image quality analysis.

PURPOSE

This study aimed to compare longitudinal changes in higher-order wavefront aberrations and image quality before and after bilateral PRK, FS-LASIK, and SMILE refractive procedures for correcting myopia.

METHODS

Wavefront aberrations and image quality of both the eyes of 106 subjects (n = 40 for FS-LASIK and SMILE and n = 26 for PRK) were determined pre-operatively and at 1-week, 1-month, 3-month, and 6-month post-operative intervals using computational through-focus analysis for a 6-mm pupil diameter. Image quality was quantified in terms of its peak value and its interocular difference, residual defocus that was needed to achieve peak image quality (best focus), and the depth of focus.

RESULTS

The increase in root mean squared deviations of higher-order aberrations post-operatively was lesser after SMILE (1-month visit median [25th to 75th interquartile range], 0.34 μm (0.28 to 0.39 μm]) than after PRK (0.80 μm [0.74 to 0.87 μm]) and FS-LASIK (0.74 μm [0.59 to 0.83 μm]; P ≤ .001), all relative to pre-operative values (0.20 μm [0.15 to 0.30 μm]). The peak image quality dropped and its interocular difference increased, best focus shifted myopically by 0.5 to 0.75 D, and depth of focus widened significantly after PRK and FS-LASIK surgeries, all relative to pre-operative values (P < .001). All these changes were negligible but statistically significant in a minority of instances after SMILE surgery (P ≥ .01).

CONCLUSIONS

Although all three refractive surgeries correct myopia, the image quality and its similarity between eyes are better and closer to pre-operative values after SMILE, compared with FS-LASIK and PRK. These results can be explained from the underlying increase in higher-order wavefront aberrations experienced by the eye post-operatively.

Matching convolved images to optically blurred images on the retina

Convolved images are often used to simulate the effect of ocular aberrations on image quality, where the retinal image is simulated by convolving the stimulus with the point spread function derived from the subject's aberrations. However, some studies have shown that convolved images are perceived far more degraded than the same image blurred with optical defocus. We hypothesized that the positive interactions between the monochromatic and chromatic aberrations in the eye are lost in the convolution process. To test this hypothesis, we evaluated optical and visual quality with natural optics and with convolved images (on-bench, computer simulations, and visual acuity [VA] in subjects) using a polychromatic adaptive optics system with monochromatic (555 nm) and polychromatic light (WL) illumination. The subject's aberrations were measured using a Hartmann Shack system and were used to convolve the visual stimuli, using Fourier optics. The convolved images were seen through corrected optics. VA with convolved stimuli was lower than VA through natural aberrations, particularly in WL (by 26% in WL). Our results suggest that the systematic decrease in visual performance with visual acuity and retinal image quality by simulation with convolved stimuli appears to be primarily associated with a lack of favorable interaction between chromatic and monochromatic aberrations in the eye.

Correlation between Contrast Sensitivity and Modulation Transfer Functions

SIGNIFICANCE

Previous studies found no correlation between visual acuity and optical quality in a population of young subjects with good vision. Using sinusoidal gratings, we systematically investigate the correlation between contrast sensitivity and optical quality as a function of spatial frequency.

PURPOSE

This study describes the correlation between the contrast sensitivity function (CSF) and the modulation transfer function (MTF) in a sample of young and informed subjects. Our results are compared with prior studies on the correlation between visual acuity and metrics of image quality. We also compare our results with previous studies that compare the CSF, the MTF, and the neural contrast sensitivity function (NCSF).

METHODS

The CSF of 28 informed subjects is measured in photopic conditions. The polychromatic MTF is computed from the measurements of monochromatic aberrations. The (CSF, MTF) correlation is estimated as the Pearson correlation coefficient, at each spatial frequency. The NCSF of each subject is estimated as the ratio of CSF to MTF.

RESULTS

We obtain high correlation coefficients (0.8) in the range of spatial frequencies of 3 to 6 cycles per degree, which also corresponds to high NCSF. Correlation decreases with increasing spatial frequency in the range of 6 to 18 cycles per degree (down to 0.0 at 18 cycles per degree). In that range, optical and neural contrast sensitivities are both approximately reduced by factor 4.

CONCLUSIONS

In our sample of young subjects with good vision, the CSF with sinusoidal gratings better differentiates eyes of good optical quality at intermediate spatial frequencies (3 to 6 cycles per degree) than at higher spatial frequencies (12 to 18 cycles per degree). At the highest tested spatial frequency of sinusoidal gratings (18 cycles per degree), there is no significant correlation between optical quality and contrast sensitivity.

Vision is protected against blue defocus

Due to chromatic aberration, blue images are defocused when the eye is focused to the middle of the visible spectrum, yet we normally are not aware of chromatic blur. The eye suffers from monochromatic aberrations which degrade the optical quality of all images projected on the retina. The combination of monochromatic and chromatic aberrations is not additive and these aberrations may interact to improve image quality. Using Adaptive Optics, we investigated the optical and visual effects of correcting monochromatic aberrations when viewing polychromatic grayscale, green, and blue images. Correcting the eye’s monochromatic aberrations improved optical quality of the focused green images and degraded the optical quality of defocused blue images, particularly in eyes with higher amounts of monochromatic aberrations. Perceptual judgments of image quality tracked the optical findings, but the perceptual impact of the monochromatic aberrations correction was smaller than the optical predictions. The visual system appears to be adapted to the blur produced by the native monochromatic aberrations, and possibly to defocus in blue.

The Impact of IOL Abbe Number on Polychromatic Image Quality of Pseudophakic Eyes

Purpose

The human eye exhibits large amounts (2.5 diopters) of longitudinal chromatic aberration (LCA). Its impact on polychromatic image quality, however, has been shown experimentally and by computer modeling to be small or absent. We hypothesized that modest changes in pseudophakic LCA created by higher and lower Abbe number materials will have little or no impact on polychromatic image quality in pseudophakic eyes.

Materials and Methods

Using published chromatic and monochromatic aberration data from pseudophakic eyes and higher and lower Abbe number materials (37 and 55), we computed monochromatic point spread functions for 21 wavelengths across the visible spectrum. After weighting by either the RGB spectra of a liquid crystal display or by a flat white spectrum, they were weighted by the human spectral sensitivity function (V_λ) before being added to generate polychromatic PSFs.

Results

In the absence of monochromatic aberrations, the reduced LCA due to higher Abbe number intraocular lens (IOL) materials resulted in a reduction of 0.08 diopters in the mean defocus generated by LCA. At the retinal plane, the higher Abbe number pseudophakic model produced improvements in polychromatic modulation transfer functions (MTFs) similar to those generated by a 0.05 diopter reduction in spherical defocus. When monochromatic aberrations were added to make the model more representative of actual pseudophakic eyes, the differences in image quality became sub-threshold for human vision or disappeared completely.

Conclusion

The anticipated gains in polychromatic image quality from employing higher Abbe number IOL materials with reduced LCA do not materialize in plausible aberrated models of pseudophakic eyes.

Optical and imaging properties of a novel multi-segment spectacle lens designed to slow myopia progression

PURPOSE

High sampling density optical metrology combined with pupil- and image-plane numerical analyses were applied to evaluate a novel spectacle lens containing multiple small zones designed to slow myopia progression.

METHODS

High-resolution aberrometry (ClearWave, www.lumetrics.com) was used to sample wavefront slopes of a novel spectacle lens, Defocus Incorporated Multiple Segments (DIMS) (www.hoya.com), incorporating many small, positive-powered lenslets in its periphery. Using wavefront slope and error maps, custom MATLAB software ('Indiana Wavefront Analyzer') was used to compute image-plane point-spread functions (PSF), modulation transfer functions (MTF), simulated images and power distributions created by the dual-focus optic for different pupil sizes and target vergences.

RESULTS

Outside of a central 10 mm zone containing single distance optical power, a hexagonal array of small 1 mm lenslets with nearest-neighbour separations of 0.5 mm were distributed over the lens periphery. Sagittal and curvature-based measures of optical power imperfectly captured the consistent +3.50 D add produced by the lenslets. Image plane simulations revealed multiple PSFs and poor image quality at the lenslet focal plane. Blur at the distance optic focal plane was consistent with a combination of diffraction blur from the distance optic and the approximately +3.50 D of defocus from the 1 mm diameter near optic zones.

CONCLUSION

Converging the defocused beams generated by the multiple small (1 mm diameter) lenslets to a blurred image at the distance focal plane produced a blur magnitude determined by the small lenslet diameter and not the overall pupil diameter. The distance optic located in between the near-add lenslets determines the limits of the optical quality achievable by the lens. When compared to the optics of a traditional concentric-zone dual-focus contact lens, the optics of the DIMS lens generates higher-contrast images at low spatial frequencies (<7 cycles per degree), but lower-contrast at high spatial frequencies.

Combining optical and neural components in physiological visual image quality metrics as functions of luminance and age

Visual image quality metrics combine comprehensive descriptions of ocular optics (from wavefront error) with a measure of the neural processing of the visual system (neural contrast sensitivity). To improve the ability of these metrics to track real-world changes in visual performance and to investigate the roles and interactions of those optical and neural components in foveal visual image quality as functions of age and target luminance, models of neural contrast sensitivity were constructed from the literature as functions of (1) retinal illuminance (Trolands, td), and (2) retinal illuminance and age. These models were then incorporated into calculation of the visual Strehl ratio (VSX). Best-corrected VSX values were determined at physiological pupil sizes over target luminances of 104 to 10-3 cd/m2 for 146 eyes spanning six decades of age. Optical and neural components of the metrics interact and contribute to visual image quality in three ways. At target luminances resulting in >900 td at physiological pupil size, neural processing is constant, and only aberrations (that change as pupil size changes with luminance) affect the metric. At low mesopic luminances below where pupil size asymptotes to maximum, optics are constant (maximum pupil), and only the neural component changes with luminance. Between these two levels, both optical and neural components of the metrics are affected by changes in target luminance. The model that accounted for both retinal illuminance and age allowed VSX, termed VSX(td,a), to best track visual acuity trends (measured at 160 and 200 cd/m2) as a function of age (20s through 70s) from the literature. Best-corrected VSX(td,a) decreased by 2.24 log units between maximum and minimum target luminances in the youngest eyes and by 2.58 log units in the oldest. The decrease due to age was more gradual at high target luminances (0.70 log units) and more pronounced as target luminance decreased (1.04 log units).

Equivalence of two optical quality metrics to predict the visual acuity of multifocal pseudophakic patients

This article studies the relationship between two metrics, the area under the modulation transfer function (MTFa) and the energy efficiency (EE), and their ability to predict the visual quality of patients implanted with multifocal intraocular lenses (IOLs). The optical quality of IOLs is assessed in vitro using two metrics, the MTFa and EE. We measured them for three different multifocal IOLs with parabolic phase profile using image formation, through-focus (TF) scanning, three R, G, B wavelengths, and two pupils. We analyzed the correlation between MTFa and EE. In parallel, clinical defocus curves of visual acuity (VA) were measured and averaged from sets of patients implanted with the same IOLs. An excellent linear correlation was found between the MTFa and EE for the considered IOLs, wavelengths and pupils (R² > 0.9). We computed the polychromatic TF-MTFa, TF-EE, and derived mathematical relationships between each metrics and clinical average VA. MTFa and EE proved to be equivalent metrics to characterize the optical quality of the studied multifocal IOLs and also in terms of clinical VA predictability.

Habitual higher order aberrations affect Landolt but not Vernier acuity

To assess whether the eye's optical imperfections are relevant for hyperacute vision, we measured ocular wave aberrations, visual hyperacuity, and acuity thresholds in 31 eyes of young adults. Although there was a significant positive correlation between the subjects' performance in Vernier- and Landolt-optotype acuity tasks, we found clear differences in how far both acuity measures correlate with the eyes' optics. Landolt acuity thresholds were significantly better in eyes with low higher order aberrations and high visual Strehl ratios (r² = 0.22, p = 0.009), and significantly positively correlated with axial length (r² = 0.15, p = 0.03). A retinal image quality metric, calculated as two-dimensional correlation between perfect and actual retinal image, was also correlated with Landolt acuity thresholds (r² = 0.27, p = 0.003). No such correlations were found with Vernier acuity performance (r² < 0.03, p > 0.3). Based on these results, hyperacuity thresholds are, contrary to resolution acuity, not affected by higher order aberrations of the eye.

Visual and non-visual properties of filters manipulating short-wavelength light

Purpose

Optical filters and tints manipulating short‐wavelength light (sometimes called ‘blue‐blocking’ or ‘blue‐attenuating’ filters) are used in the management of a range of ocular, retinal, neurological and psychiatric disorders. In many cases, the only available quantification of the optical effects of a given optical filter is the spectral transmittance, which specifies the amount of light transmitted as a function of wavelength.

Methods

We propose a novel physiologically relevant and retinally referenced framework for quantifying the visual and non‐visual effects of these filters, incorporating the attenuation of luminance (luminous transmittance), the attenuation of melanopsin activation (melanopsin transmittance), the colour shift, and the reduction of the colour gamut (gamut reduction). Using these criteria, we examined a novel database of spectral transmittance functions of optical filters (n = 121) which were digitally extracted from a variety of sources.

Results

We find a large diversity in the alteration of visual and non‐visual properties. The spectral transmittance properties of the examined filters vary widely, in terms of shapes and cut‐off wavelengths. All filters show relatively more melanopsin attenuation than luminance attenuation (lower melanopsin transmittance than luminous transmittance). Across the data set, we find that melanopsin transmittance and luminous transmittance are correlated.

Conclusions

We suggest that future studies and examinations of the physiological effects of optical filters quantify the visual and non‐visual effects of the filters beyond the spectral transmittance, which will eventually aid in developing a mechanistic understanding of how different filters affect physiology. We strongly discourage comparing the downstream effects of different filters on, e.g. sleep or circadian responses, without considering their effects on the retinal stimulus.

Impact of longitudinal chromatic aberration on through-focus visual acuity

An enhanced adaptive optics visual simulator (AOVS) was used to study the impact of chromatic aberration on vision. In particular, through-focus visual acuity (VA) was measured in four subjects under three longitudinal chromatic aberration (LCA) conditions: natural LCA, compensated LCA and doubled LCA. Ray-tracing simulations using a chromatic eye model were also performed for a better understanding of experimental results. Simulations predicted the optical quality of the retinal images and VA by applying a semi-empirical formula. Experimental and ray tracing results showed a significant agreement in the natural LCA case (R² = 0.92). Modifying the LCA caused an impairment in the predictability of the results, with decreasing correlations between experiment and simulations (compensated LCA, R² = 0.84; doubled LCA, R² = 0.59). VA under modified LCA was systematically overestimated by the model around the best focus position. The results provided useful information on how LCA manipulation affects the depth of focus. Decreased capability of the model to predict VA in modified LCA conditions suggests that neural adaptation may play a role.

Measuring and compensating for ocular longitudinal chromatic aberration

It is well known that the eye's optics and media introduce monochromatic and chromatic aberration unique to each individual. Once monochromatic aberrations are removed with adaptive optics (AO), longitudinal chromatic aberrations (LCA) define the fidelity for multi-wavelength, high-resolution vision testing and retinal imaging. AO vision simulation systems and AO scanning laser ophthalmoscopes (AOSLOs) typically use the average population LCA to compensate for focus offsets between different wavelengths precluding fine, individualized control. The eye's LCA has been characterized extensively using either subjective (visual perception) or objective (imaging) methods. Classically, these have faced inconsistencies due to extraneous factors related to depth of focus, monochromatic aberration, and wavelength-dependent light interactions with retinal tissue. Here, we introduce a filter-based Badal LCA compensator that offers the flexibility to tune LCA for each individual eye and demonstrate its feasibility for vision testing and imaging using multiple wavelengths simultaneously. Incorporating the LCA compensator in an AOSLO allowed the first objective measurements of LCA based on confocal, multi-wavelength foveal cone images and its comparison to measures obtained subjectively. The objective LCA thus obtained was consistent with subjective estimates in the same individuals and hence resolves the prior discrepancies between them. Overall, the described approach will benefit applications in retinal imaging and vision testing where the focus of multiple wavelengths needs to be controlled independently and simultaneously.

Normative best-corrected values of the visual image quality metric VSX as a function of age and pupil size

The visual image quality metric the visual Strehl ratio (VSX) combines a comprehensive description of the optics of an eye (wavefront error) with an estimate of the photopic neural processing of the visual system, and has been shown to be predictive of subjective best focus and well correlated with change in visual performance. Best-corrected visual image quality was determined for 146 eyes, and the quantitative relation of VSX, age, and pupil size is presented, including 95% confidence interval norms for age groups between 20 and 80 years and pupil diameters from 3 to 7 mm. These norms were validated using an independently collected population of wavefront error measurements. The best visual image quality was found in young eyes at smaller pupil sizes. Increasing pupil size caused a more rapid decrease in VSX than increasing age. These objectively determined benchmarks represent the best theoretical levels of visual image quality achievable with a sphere, cylinder, and axis correction in normal eyes and can be used to evaluate both traditional and wavefront-guided optical corrections provided by refractive surgery, contact lenses, and spectacles.

Individual neural transfer function affects the prediction of subjective depth of focus

Attempts to accurately predict the depth of focus (DoF) based on objective metrics have failed so far. We investigated the effect of the individual neural transfer function (iNTF) on the quality of the prediction of the subjective DoF from objective wavefront measures. Subjective DoF was assessed in 22 participants using subjective through focus curves of visual acuity (VA). Objective defocus curves were calculated for visual Strehl metrics of the optical (VSOTFa) and the modulation transfer function as well as the point spread function. DoF was computed for residual lower order aberrations (rLoA) and incorporation of iNTF. Correlations between subjective and objective DoF did not reach significance, when a) standard metrics were used and b) rLoA were considered (r max  = 0.33, p all  > 0.05). By incorporating the iNTF of the individuals in the calculation of the objective DoF from the VSOTFa metric, a moderate statistically significant correlation was found (r = 0.43, p < 0.01, Pearson). The iNTF of the individual's eye is fundamental for the prediction of subjective DoF using the VSOTFa metric. Individualized predictions could aid future application in the correction of refractive errors like presbyopia using intraocular lenses.

The effect of longitudinal chromatic aberration on the lag of accommodation and depth of field

PURPOSE

Longitudinal chromatic aberration is present in all states of accommodation and may play a role in the accommodation response and the emmetropisation process. We study the change of the depth of field (DOFi) with the state of accommodation, taking into account the longitudinal chromatic aberration.

METHODS

Subjective DOFi was defined as the range of defocus beyond which the blur of the target (one line of optotypes of 0.1 logMAR shown on a black-and-white microdisplay, seen through different colour filters) was perceived as objectionable. The subject's eye was paralysed and different, previously-measured accommodative states (corresponding to the accommodative demands of 0D, 2D and 4D) were simulated with a deformable mirror. Different colour conditions (monochromatic red, green and blue and polychromatic (white) were tested. The DOFi was measured subjectively, using a motorised Badal system.

RESULTS

Taking as reference the average accommodative response for the white stimulus, the blue response exhibits on average a lead of 0.45 ± 0.09D, the green a negligible lead of 0.07 ± 0.02D and red a lag of 0.49 ± 0.10D. The monochromatic DOFi, calculated by averaging DOFi over the red, green and blue colour conditions for each accommodative demand was 1.10 ± 0.10D for 0D, 1.20 ± 0.08D for 2D, and 1.26 ± 0.40D for 4D. The polychromatic white DOFi were greater than the average monochromatic DOFi by 19%, 9% and 14% for 0D, 2D, and 4D of accommodative demand, respectively.

CONCLUSION

The longitudinal chromatic aberration causes a dioptric shift of the monochromatic accommodation response. The study did not reveal this shift to depend on the accommodative demand or to have an effect on the DOFi.

Optical quality of rotationally symmetrical contact lenses derived from their power profiles

PURPOSE

To present a methodology for evaluating the optical quality of rotationally symmetrical contact lenses (CLs) from a single power profile.

METHODS

Simulated rotationally symmetrical power profiles corresponding to different CLs designs (monofocal, two-zone center-near bifocal, and four-zone center-distance bifocal) were used to calculate the wavefront error profile by means of numerical integration. Then, each lens wavefront error profile was spun around the center to obtain the lens wavefront error surface. From the surface, monochromatic optical transfer functions (OTF), simulated images and the visual Strehl ratio based on the OTF (VSOTF) were obtained for different distances and pupil sizes (3 and 5.5mm) after performing a through-focus.

RESULTS

VSOTF variations, taking into account both vergence and pupil size, were presented for the three CLs designs. The monofocal design showed excellent optical quality only for far vision, whereas the bifocal designs exhibited good optical quality for far and near vision. Modulation transfer function (MTF) from each lens design, pupil size, and work distance agreed with the previous results.

CONCLUSIONS

The methodology presented here allows for a rapid and thorough assessment of the optical quality of rotationally symmetrical CLs by means of optical quality metrics, with a special interest in simultaneous image contact lenses. This methodology may be useful for choosing the most suitable lens for each subject's visual demands.

Interaction of aberrations, diffraction, and quantal fluctuations determine the impact of pupil size on visual quality

Our purpose is to develop a computational approach that jointly assesses the impact of stimulus luminance and pupil size on visual quality. We compared traditional optical measures of image quality and those that incorporate the impact of retinal illuminance dependent neural contrast sensitivity. Visually weighted image quality was calculated for a presbyopic model eye with representative levels of chromatic and monochromatic aberrations as pupil diameter was varied from 7 to 1 mm, stimulus luminance varied from 2000 to 0.1  cd/m², and defocus varied from 0 to -2 diopters. The model included the effects of quantal fluctuations on neural contrast sensitivity. We tested the model's predictions for five cycles per degree gratings by measuring contrast sensitivity at 5  cyc/deg. Unlike the traditional Strehl ratio and the visually weighted area under the modulation transfer function, the visual Strehl ratio derived from the optical transfer function was able to capture the combined impact of optics and quantal noise on visual quality. In a well-focused eye, provided retinal illuminance is held constant as pupil size varies, visual image quality scales approximately as the square root of illuminance because of quantum fluctuations, but optimum pupil size is essentially independent of retinal illuminance and quantum fluctuations. Conversely, when stimulus luminance is held constant (and therefore illuminance varies with pupil size), optimum pupil size increases as luminance decreases, thereby compensating partially for increased quantum fluctuations. However, in the presence of -1 and -2 diopters of defocus and at high photopic levels where Weber's law operates, optical aberrations and diffraction dominate image quality and pupil optimization. Similar behavior was observed in human observers viewing sinusoidal gratings. Optimum pupil size increases as stimulus luminance drops for the well-focused eye, and the benefits of small pupils for improving defocused image quality remain throughout the photopic and mesopic ranges. However, restricting pupils to <2  mm will cause significant reductions in the best focus vision at low photopic and mesopic luminances.

In vivo subjective and objective longitudinal chromatic aberration after bilateral implantation of the same design of hydrophobic and hydrophilic intraocular lenses

PURPOSE

To measure the longitudinal chromatic aberration in vivo using psychophysical and wavefront-sensing methods in patients with bilateral implantation of monofocal intraocular lenses (IOLs) of similar aspheric design but different materials (hydrophobic Podeye and hydrophilic Poday).

SETTING

Instituto de Optica, Consejo Superior de Investigaciones Cientificas, Madrid, Spain.

DESIGN

Prospective observational study.

METHODS

Measurements were performed with the use of psychophysical (480 to 700 nm) and wavefront-sensing (480 to 950 nm) methods using a custom-developed adaptive optics system. Chromatic difference-of-focus curves were obtained from best-focus data at each wavelength, and the longitudinal chromatic aberration was obtained from the slope of linear regressions to those curves.

RESULTS

The longitudinal chromatic aberration from psychophysical measurements was 1.37 diopters (D) ± 0.08 (SD) (hydrophobic) and 1.21 ± 0.08 D (hydrophilic). From wavefront-sensing, the longitudinal chromatic aberration was 0.88 ± 0.07 D and 0.73 ± 0.09 D, respectively. At 480 to 950 nm, the longitudinal chromatic aberration was 1.27 ± 0.09 D (hydrophobic) and 1.02 ± 0.13 D (hydrophilic). The longitudinal chromatic aberration was consistently higher in eyes with the hydrophobic IOL than in eyes with the hydrophilic IOL (a difference of 0.16 D and 0.15 D, respectively). Similar to findings in young phakic eyes, the longitudinal chromatic aberration from the psychophysical method was consistently higher than from wavefront-sensing, by 0.48 D (35.41%) for the hydrophobic IOL and 0.48 D (39.43%) for the hydrophilic IOL.

CONCLUSION

Longitudinal chromatic aberrations were smaller with hydrophilic IOLs than with hydrophobic IOLs of the same design.

FINANCIAL DISCLOSURE

No author has a financial or proprietary interest in any material or method mentioned.

The natural statistics of blur

Blur from defocus can be both useful and detrimental for visual perception: It can be useful as a source of depth information and detrimental because it degrades image quality. We examined these aspects of blur by measuring the natural statistics of defocus blur across the visual field. Participants wore an eye-and-scene tracker that measured gaze direction, pupil diameter, and scene distances as they performed everyday tasks. We found that blur magnitude increases with increasing eccentricity. There is a vertical gradient in the distances that generate defocus blur: Blur below the fovea is generally due to scene points nearer than fixation; blur above the fovea is mostly due to points farther than fixation. There is no systematic horizontal gradient. Large blurs are generally caused by points farther rather than nearer than fixation. Consistent with the statistics, participants in a perceptual experiment perceived vertical blur gradients as slanted top-back whereas horizontal gradients were perceived equally as left-back and right-back. The tendency for people to see sharp as near and blurred as far is also consistent with the observed statistics. We calculated how many observations will be perceived as unsharp and found that perceptible blur is rare. Finally, we found that eye shape in ground-dwelling animals conforms to that required to put likely distances in best focus.

Differences of Longitudinal Chromatic Aberration (LCA) between Eyes with Intraocular Lenses from Different Manufacturers

Several researchers have studied the longitudinal chromatic aberration (LCA) of eyes implanted with an intraocular lens (IOL). We investigated the LCA of eyes implanted with yellow-colored IOLs from three different manufacturers: Alcon Inc., HOYA Corp., and AMO Inc. The number of subjects was 11, 16, and 16, respectively. The LCA of eyes implanted with SN60WF and SN60AT (Alcon Inc.), and with XY-1 (HOYA Corp.), was the same as that of phakic eyes. The LCA of eyes with ZCB00V (AMO Inc.) was smaller than that of phakic eyes. The LCA of eyes implanted with Alcon’s and HOYA’s IOLs, but not the LCA of eyes implanted with AMO’s IOLs, was positively correlated with the powers of the IOLs. We also performed simulations to verify the impacts of LCA on visual performance for 4-mm pupil diameter; the simulations were a polychromatic modulation transfer function (MTF) and a visual Strehl ratio computed on the basis of an optical transfer function (VSOTF). We concluded that the differences between the LCA of different manufacturers do not affect visual performances when some extent of higher-order aberration (HOA) exists. The smaller HOA of AMO IOLs may enhance visual performance.

Image Quality Analysis of Eyes Undergoing LASER Refractive Surgery

Laser refractive surgery for myopia increases the eye’s higher-order wavefront aberrations (HOA’s). However, little is known about the impact of such optical degradation on post-operative image quality (IQ) of these eyes. This study determined the relation between HOA’s and IQ parameters (peak IQ, dioptric focus that maximized IQ and depth of focus) derived from psychophysical (logMAR acuity) and computational (logVSOTF) through-focus curves in 45 subjects (18 to 31yrs) before and 1-month after refractive surgery and in 40 age-matched emmetropic controls. Computationally derived peak IQ and its best focus were negatively correlated with the RMS deviation of all HOA’s (HORMS) (r≥-0.5; p<0.001 for all). Computational depth of focus was positively correlated with HORMS (r≥0.55; p<0.001 for all) and negatively correlated with peak IQ (r≥-0.8; p<0.001 for all). All IQ parameters related to logMAR acuity were poorly correlated with HORMS (r≤|0.16|; p>0.16 for all). Increase in HOA’s after refractive surgery is therefore associated with a decline in peak IQ and a persistence of this sub-standard IQ over a larger dioptric range, vis-à-vis, before surgery and in age-matched controls. This optical deterioration however does not appear to significantly alter psychophysical IQ, suggesting minimal impact of refractive surgery on the subject’s ability to resolve spatial details and their tolerance to blur.

Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus

PURPOSE

To examine the role of Zernike secondary spherical aberration and its component terms on refraction, image quality and depth of focus.

METHODS

Computational methods were used to define wavefronts with controlled levels of r(6) , r(4) and r(2) terms, and image quality associated with these terms for a range of target vergences. Target vergences that generated maximum image quality were used as an objective measures of refractive error.

RESULTS

Unlike primary Zernike spherical aberration, which generates peak image quality with a near paraxial focus, in the absence of other higher order aberrations, peak image quality with secondary spherical aberration is achieved with a near marginal focus. When alone, positive primary and secondary spherical aberration induce small hyperopic shifts in refraction, but in the presence of other higher order aberrations, secondary spherical aberration can induce significant myopic shifts in refractive error, as predicted by the combined lower order r(4) & r(2) component of Z60. The predicted expansion in depth of focus associated with increased primary or secondary spherical aberration is mostly absent if a strict image quality criterion is applied. The expansion of depth of focus observed with a low image quality criterion when opposite sign Z40 and Z60 are combined is primarily due to the elevated r(4) term.

CONCLUSIONS

Secondary Zernike spherical aberration can have a significant impact on refractive error, image quality and depth of focus, but mostly due to the lower order components within this polynomial. Our analysis shows that the r(6) term that defines secondary spherical aberration actually narrows rather than expands depth of focus, when in the presence of the r(4) term within Z60. Therefore, a multifocal lens generated with exclusively primary spherical aberration is likely to be more effective than one that includes opposite sign of primary and secondary spherical aberration.

Effects of intraocular lenses with different diopters on chromatic aberrations in human eye models

BACKGROUND

In this study, the effects of intraocular lenses (IOLs) with different diopters (D) on chromatic aberration were investigated in human eye models, and the influences of the central thickness of IOLs on chromatic aberration were compared.

METHODS

A Liou-Brennan-based IOL eye model was constructed using ZEMAX optical design software. Spherical IOLs with different diopters (AR40e, AMO Company, USA) were implanted; modulation transfer function (MTF) values at 3 mm of pupil diameter and from 0 to out-of-focus blur were collected and graphed.

RESULTS

MTF values, measured at 555 nm of monochromatic light under each spatial frequency, were significantly higher than the values measured at 470 to 650 nm of polychromatic light. The influences of chromatic aberration on MTF values decreased with the increase in IOL diopter when the spatial frequency was ≤12 c/d, while increased effects were observed when the spatial frequency was ≥15 c/d. The MTF values of each IOL eye model were significantly lower than the MTF values of the Liou-Brennan eye models when measured at 555 nm of monochromatic light and at 470 to 650 nm of polychromatic light. The MTF values were also found to be increased with the increase in IOL diopter.

CONCLUSION

With higher diopters of IOLs, the central thickness increased accordingly, which could have created increased chromatic aberration and decreased the retinal image quality. To improve the postoperative visual quality, IOLs with lower chromatic aberration should be selected for patients with short axial lengths.

Statistical characteristics of aberrations of human eyes after small incision lenticule extraction surgery and analysis of visual performance with individual eye model

Preoperative and postoperative wavefront aberrations of 73 myopic eyes with small incision lenticule extraction surgery are analyzed in this paper. Twenty-eight postoperative individual eye models are constructed to investigate the visual acuity (VA) of human eyes. Results show that in photopic condition, residual defocus, residual astigmatism, and higher-order aberrations are relatively small. 100% of eyes reach a VA of 0.8 or better, and 89.3% of eyes reach a VA of 1.0 or better. In scotopic condition, the residual defocus and the higher-order aberrations are, respectively, 1.9 and 8.5 times the amount of that in photopic condition, and the defocus becomes the main factor attenuating visual performance.

Focus correction in an apodized system with spherical aberration

We performed a theoretical and computational analysis of the through-focus axial irradiance in a system with a Gaussian amplitude pupil function and fourth- and sixth-order spherical aberration (SA). Two cases are analyzed: low aberrated systems, and the human eye containing significant levels of SA and a natural apodization produced by the Stiles-Crawford effect. Results show that apodization only produces a refraction change of the plane that maximized the Strehl ratio for eyes containing significant levels of negative SA.

Longitudinal chromatic aberration of the human eye in the visible and near infrared from wavefront sensing, double-pass and psychophysics

Longitudinal Chromatic Aberration (LCA) influences the optical quality of the eye. However, the reported LCA varies across studies, likely associated to differences in the measurement techniques. We present LCA measured in subjects using wavefront sensing, double-pass retinal images, and psychophysical methods with a custom-developed polychromatic Adaptive Optics system in a wide spectral range (450-950 nm), with control of subjects' natural aberrations. LCA measured psychophysically was significantly higher than that from reflectometric techniques (1.51 D vs 1.00 D in the 488-700 nm range). Ours results indicate that the presence of natural aberrations is not the cause for the discrepancies across techniques.

Chromatic aberration and polychromatic image quality with diffractive multifocal intraocular lenses

PURPOSE

To evaluate the impact of target distance on polychromatic image quality in a virtual model eye implanted with hybrid refractive-diffractive intraocular lenses (IOLs).

SETTING

School of Optometry, Indiana University, Bloomington, Indiana, USA.

DESIGN

Experimental study.

METHODS

A pseudophakic model eye was constructed by incorporating a phase-delay map for a diffractive optical element into a reduced eye model incorporating ocular chromatic aberration, pupil apodization, and higher-order monochromatic aberrations. The diffractive element was a monofocal IOL with a +3.2 diopter (D) diffractive power or 2 types of bifocal IOLs (nonapodized or apodized) with a +2.92 D addition (add) power. Polychromatic point-spread functions and image quality for white and monochromatic light were quantified for a series of target vergences, wavelengths, and pupil diameters using modulation transfer functions and image-quality metrics.

RESULTS

Ocular longitudinal chromatic aberration was largely corrected by the monofocal design and by both bifocal designs for near targets. In the bifocal design, add power and the ratio of distance:near image quality changed significantly with wavelength and pupil size. Also, image quality for distance was better with the apodized design.

CONCLUSIONS

Achromatization by the diffractive IOL provided significant improvement in polychromatic retinal image quality. Along with apodization and higher-order aberrations, it can significantly affect the near-distance balance provided by a diffractive multifocal IOL.

FINANCIAL DISCLOSURE

No author has a financial or proprietary interest in any material or method mentioned.

Polychromatic refractive error from monochromatic wavefront aberrometry

PURPOSE

To determine if measurement of monochromatic wavefront aberrations in near-infrared light can accurately and precisely predict subjective refractive error for polychromatic light. Our approach requires knowledge of the monochromatic wavelength-in-focus (WiF) when polychromatic light is well focused, for which new empirical measurements are reported.

METHODS

With accommodation paralyzed, subjective refractive error was measured as a function of wavelength using a Badal optometer by optimally focusing a letter chart illuminated with monochromatic or white light (color temperature, 4575 K). Wavelength-in-focus was determined by interpolation as that wavelength for which monochromatic refractive error matches white light refractive error. The population-based mean value of WiF, used in conjunction with the Indiana Eye model of chromatic aberration, corrected for monochromatic (842 nm) estimates of refractive error obtained from wavefront aberration measurements, predicts the absolute refractive error of individual eye for polychromatic light for comparison with empirical measurements.

RESULTS

Average WiF for eight subjects was 569 nm (SE = 3.6 nm) for a 3-mm pupil and 575 nm (SE = 3.0 nm) for an 8-mm pupil. For small (3 mm) pupils, the mean (±SD) error in predicting refractive error for white light was 0.20 (±0.05) diopters (D) (range, +0.70 to -0.46 D), and for large (>8 mm) pupils, the mean (±SD) prediction error was 0.004 (±0.12) D (range, +0.56 to -0.52 D). The population mean of prediction errors was statistically not different from zero for large pupils but was slightly hyperopic for small pupils.

CONCLUSIONS

Subjective refractive error for white light can be accurately and precisely predicted objectively from monochromatic wavefront aberrations obtained for near-infrared light, but intersubject variability limits accuracy for individual subjects.

Volumetric optoacoustic imaging with multi-bandwidth deconvolution

Optoacoustic (photoacoustic) imaging based on cylindrically focused 1-D transducer arrays comes with powerful characteristics in visualizing optical contrast. Parallel reading of multiple detectors arranged around a tissue cross section enables capturing data for generating images of this plane within micro-seconds. Dedicated small animals scanners and handheld systems using 1-D cylindrically focused ultrasound transducer arrays have demonstrated real-time cross-sectional imaging and high in-plane resolution. Yet, the resolution achieved along the axis perpendicular to the focal plane, i.e., the elevation resolution, is determined by the focusing capacities of the detector and is typically lower than the in-plane resolution. Herein, we investigated whether deconvolution of the sensitivity field of the transducer could lead to tangible image improvements. We showcase the findings on experimental measurements from phantoms and animals and discuss the features and the limitations of the approach in improving resolution along the elevation dimension.

Comparing the optical properties of soft contact lenses on and off the eye

PURPOSE

The purpose of the current study was to examine the on- and off-eye optical performance of two types of soft contact lenses (hydrogel and silicone hydrogel).

METHODS

The monochromatic aberrations (λ = 850 nm) of contact lenses were measured on-eye using a clinical Shack-Hartmann ocular aberrometer. In addition, we used an off-eye single-pass contact lens aberrometer (λ = 540 nm) in which the soft contact lens was placed within a wet cell. Comparison of the lower and higher order aberrations measured with these two methods required compensation for different wavelengths and knowledge of the refractive index of the contact lens materials.

RESULTS

The measured on-eye sphere and spherical aberration values were generally similar to those measured off-eye and those specified by the lens manufacturers for both types of soft contact lenses. However, there were notable differences, especially for high plus-powered lenses, which typically exhibited lower sphere power on the eye than expected from the lens specifications and from the off-eye measured powers, both of which were almost identical. Longitudinal spherical aberration varied with lens power in the hydrogel lenses, as expected from geometric optics theory. Longitudinal spherical aberration measurements on- and off-eye, however, deviated significantly from that expected of a thin lens with spherical surfaces due to surface asphericities. The difference between on- and off-eye optics can be modeled as a tear lens or as relative lens thickness changes caused by lens flexure.

CONCLUSIONS

The results of the current study reveal that the major difference between the on-eye lens optics and the manufacturers' specifications is not due to lens errors but due to eye-lens interactions, which could be either lens flexure or a tear lens forming behind the soft contact lens.

Analysis of the speckle properties in a laser projection system based on a human eye model

In this paper, the properties of the speckle that is observed by humans in laser projection systems are theoretically analyzed. The speckle pattern on the fovea of the human retina is numerically simulated by introducing a chromatic human eye model. The results show that the speckle contrast experienced by humans is affected by the light intensity of the projected images and the wavelength of the laser source when considering the paracentral vision. Furthermore, the image quality is also affected by these two parameters. We believe that these results are useful for evaluating the speckle noise in laser projection systems.

Retinal image quality during accommodation

PURPOSE

We asked if retinal image quality is maximum during accommodation, or sub-optimal due to accommodative error, when subjects perform an acuity task.

METHODS

Subjects viewed a monochromatic (552 nm), high-contrast letter target placed at various viewing distances. Wavefront aberrations of the accommodating eye were measured near the endpoint of an acuity staircase paradigm. Refractive state, defined as the optimum target vergence for maximising retinal image quality, was computed by through-focus wavefront analysis to find the power of the virtual correcting lens that maximizes visual Strehl ratio.

RESULTS

Despite changes in ocular aberrations and pupil size during binocular viewing, retinal image quality and visual acuity typically remain high for all target vergences. When accommodative errors lead to sub-optimal retinal image quality, acuity and measured image quality both decline. However, the effect of accommodation errors of on visual acuity are mitigated by pupillary constriction associated with accommodation and binocular convergence and also to binocular summation of dissimilar retinal image blur. Under monocular viewing conditions some subjects displayed significant accommodative lag that reduced visual performance, an effect that was exacerbated by pharmacological dilation of the pupil.

CONCLUSIONS

Spurious measurement of accommodative error can be avoided when the image quality metric used to determine refractive state is compatible with the focusing criteria used by the visual system to control accommodation. Real focusing errors of the accommodating eye do not necessarily produce a reliably measurable loss of image quality or clinically significant loss of visual performance, probably because of increased depth-of-focus due to pupil constriction. When retinal image quality is close to maximum achievable (given the eye's higher-order aberrations), acuity is also near maximum. A combination of accommodative lag, reduced image quality, and reduced visual function may be a useful sign for diagnosing functionally-significant accommodative errors indicating the need for therapeutic intervention.

Study on chromatic aberration in a population of Chinese myopic eyes by means of optical design

Two kinds of individual eye models, involving and without involving the angle between visual axis and optical axis, are established by means of optical design. We use them to study the properties of the transverse chromatic aberration (TCA) and longitudinal chromatic aberration (LCA) over the visible spectrum. Then the effects of the LCA and TCA on the visual quality of human eyes are evaluated. The statistical averages of TCA and LCA over the visible spectrum for Chinese myopic eyes are obtained. Results show that both TCA and LCA restrict the visual performance, and LCA is more detrimental than TCA.

Modeling acuity for optotypes varying in complexity

Watson and Ahumada (2008) described a template model of visual acuity based on an ideal-observer limited by optical filtering, neural filtering, and noise. They computed predictions for selected optotypes and optical aberrations. Here we compare this model's predictions to acuity data for six human observers, each viewing seven different optotype sets, consisting of one set of Sloan letters and six sets of Chinese characters, differing in complexity (Zhang, Zhang, Xue, Liu, & Yu, 2007). Since optical aberrations for the six observers were unknown, we constructed 200 model observers using aberrations collected from 200 normal human eyes (Thibos, Hong, Bradley, & Cheng, 2002). For each condition (observer, optotype set, model observer) we estimated the model noise required to match the data. Expressed as efficiency, performance for Chinese characters was 1.4 to 2.7 times lower than for Sloan letters. Efficiency was weakly and inversely related to perimetric complexity of optotype set. We also compared confusion matrices for human and model observers. Correlations for off-diagonal elements ranged from 0.5 to 0.8 for different sets, and the average correlation for the template model was superior to a geometrical moment model with a comparable number of parameters (Liu, Klein, Xue, Zhang, & Yu, 2009). The template model performed well overall. Estimated psychometric function slopes matched the data, and noise estimates agreed roughly with those obtained independently from contrast sensitivity to Gabor targets. For optotypes of low complexity, the model accurately predicted relative performance. This suggests the model may be used to compare acuities measured with different sets of simple optotypes.

Creating effective focus cues in multi-plane 3D displays

Focus cues are incorrect in conventional stereoscopic displays. This causes a dissociation of vergence and accommodation, which leads to visual fatigue and perceptual distortions. Multi-plane displays can minimize these problems by creating nearly correct focus cues. But to create the appearance of continuous depth in a multi-plane display, one needs to use depth-weighted blending: i.e., distribute light intensity between adjacent planes. Akeley et al. [ACM Trans. Graph. 23, 804 (2004)] and Liu and Hua [Opt. Express 18, 11562 (2009)] described rather different rules for depth-weighted blending. We examined the effectiveness of those and other rules using a model of a typical human eye and biologically plausible metrics for image quality. We find that the linear blending rule proposed by Akeley and colleagues [ACM Trans. Graph. 23, 804 (2004)] is the best solution for natural stimuli.

Chromatic and wavefront aberrations: L-, M- and S-cone stimulation with typical and extreme retinal image quality

The first physiological process influencing visual perception is the optics of the eye. The retinal image is affected by diffraction at the pupil and several kinds of optical imperfections. A model of the eye (Thibos & Bradley, 1999), which takes account of pupil aperture, chromatic aberration and wavefront aberrations, was used to determine wavelength-dependent point-spread functions, which can be convolved with any stimulus specified by its spectral distribution of light at each point. The resulting retinal spectral distribution of light was used to determine the spatial distribution of stimulation for each cone type (S, M and L). In addition, individual differences in retinal-image quality were assessed using a statistical model (Thibos, Bradley, & Hong, 2002) for population values of Zernike coefficients, which characterize imperfections of the eye's optics. The median and relatively extreme (5th and 95th percentile) modulation transfer functions (MTFs) for the S, M and L cones were determined for equal-energy-spectrum (EES) 'white' light. The typical MTF for S cones was more similar to the MTF for L and M cones after taking wavefront aberrations into account but even with aberrations the S-cone MTF typically was below the M- or L-cone MTF by a factor of at least 10 (one log unit). More generally, the model presented here provides a technique for estimating retinal image quality for the S, M and L cones for any stimulus presented to the eye. The model is applied to some informative examples.