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Author

Xiaoxiao Zhang

Other affiliations: Bosch, Novartis
Bio: Xiaoxiao Zhang is an academic researcher from Indiana University. The author has contributed to research in topics: Chromatic aberration & Intraocular lens. The author has an hindex of 16, co-authored 29 publications receiving 1056 citations. Previous affiliations of Xiaoxiao Zhang include Bosch & Novartis.

Papers
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Journal ArticleDOI
TL;DR: The reduced eye was further modified by changing the refracting surface to an aspherical shape to reduce the amount of spherical aberration, providing an improved account of both the longitudinal and transverse forms of ocular chromatic aberration.
Abstract: New measurements of the chromatic difference of focus of the human eye were obtained with a two-color, vernier-alignment technique. The results were used to redefine the variation of refractive index of the reduced eye over the visible spectrum. The reduced eye was further modified by changing the refracting surface to an aspherical shape to reduce the amount of spherical aberration. The resulting chromatic-eye model provides an improved account of both the longitudinal and transverse forms of ocular chromatic aberration.

297 citations

Journal ArticleDOI
TL;DR: The way in which retinal image quality is affected by chromatic aberration is described and the impact of the aberration on visual performance is assessed.
Abstract: This brief review outlines the theory of ocular chromatic aberration and describes the three primary forms in which the aberration appears: chromatic difference of focus, chromatic difference of magnification, and chromatic difference of position. Our central theme is that all three aspects of chromatic aberration have as their common basis the chromatic dispersion of light. The magnitude of each form of the aberration is related to the others by simple linear formulas in which a key parameter is the location of the pupil relative to the nodal point of the eye. The way in which retinal image quality is affected by chromatic aberration is described and we assess the impact of the aberration on visual performance.

110 citations

Journal ArticleDOI
TL;DR: The single-surface schematic-eye model of ocular chromatic aberration is extended to account for spherical aberration of the eye by allowing the model's single refracting surface to be a member of the family of ellipses with variable shape parameter (eccentricity).
Abstract: We extend the single-surface schematic-eye model of ocular chromatic aberration to account for spherical aberration of the eye. This extension is accomplished by allowing the model's single refracting surface to be a member of the family of ellipses with variable shape parameter (eccentricity). The resulting model, dubbed the "Indiana Eye," may have either positive or negative spherical aberration of varying degree, depending upon the numerical value of the shape parameter. Spherical aberration of the model eye is well described by third-order optical theory for shape parameters in the range 0 < or = p < or = 0.7, but requires fifth-order theory for an accurate description over the parametric range 0.7 < p < or = 1.0. An improved technique was devised for fitting the model to published measurements of ray aberrations while avoiding errors of estimation of the degree of spherical aberration present in eyes which also manifest odd-symmetric aberrations, such as coma. A shape parameter value of approximately p = 0.6 provided the best fit of the model to selected data from the literature.

64 citations

Journal ArticleDOI
TL;DR: A model including typical amounts of spherical aberration and pupil apodization provides a dramatically improved prediction of the effects of defocus on contrast sensitivity with large pupils and can significantly improve defocused image quality and defocused vision, particularly for tasks that require veridical phase perception.
Abstract: Previous optical modeling of the human eye with large pupils has predicted a larger impact of defocus on the human contrast sensitivity function and modulation transfer function than is observed experimentally. Theory predicts that aberrations and the Stiles–Crawford effect (SCE) should both lead to increased depth of focus, resulting in higher contrast sensitivities and veridical (not phase-reversed) perception over a larger range of spatial frequencies in defocused retinal images. Using a wave optics model, we examine these predictions quantitatively and compare them with psychophysical experiments that measure the effect of defocus on contrast sensitivity and perceived phase reversals. We find that SCE apodization has its biggest effect on defocused image quality when defocus and spherical aberration have the same sign. A model including typical amounts of spherical aberration and pupil apodization provides a dramatically improved prediction of the effects of defocus on contrast sensitivity with large pupils. The SCE can significantly improve defocused image quality and defocused vision, particularly for tasks that require veridical phase perception.

63 citations

Journal ArticleDOI
TL;DR: The authors' calculations show that all three chromatic aberrations can introduce luminance modulations in the retinal images of isoluminant gratings and can be more detectable than the original color contrasts at spatial frequencies above 3 cycles/deg.
Abstract: Using a simple model eye with a wavelength-dependent diffraction, a wavelength-dependent refractive error (chromatic difference in refractive error), and a wavelength-dependent displacement of the foveal images (transverse chromatic aberration), we have evaluated the luminance modulations in retinal images of isoluminant color gratings. In cases where the chromatic difference in refractive error has been corrected, the retinal image suffers from chromatic parallax, which creates wavelength-dependent displacements of the retinal image that are similar to those caused by transverse chromatic aberration. Our calculations show that all three chromatic aberrations can introduce luminance modulations in the retinal images of isoluminant gratings. These luminance artifacts generally, but not always, increase with increasing spatial frequency. The contrast in the luminance artifact depends critically on the exact refractive error in the uncorrected eye and the precise position of the eye in the corrected case. Wavelength-dependent diffraction has little effect for large pupils (e.g., 5 mm) but can become a significant factor with small pupils. Luminance artifacts created by chromatic aberrations can be more detectable than the original color contrasts at spatial frequencies above 3 cycles/deg.

60 citations


Cited by
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DOI
14 Feb 2023
TL;DR: The optical structure and optical properties of the human eye are described, how the retinal image is formed and the factors affecting its quality are described.

626 citations

Journal ArticleDOI
TL;DR: It is inferred that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized, and that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil.
Abstract: A Shack-Hartmann aberrometer was used to measure the monochromatic aberration structure along the primary line of sight of 200 cyclopleged, normal, healthy eyes from 100 individuals. Sphero-cylindrical refractive errors were corrected with ophthalmic spectacle lenses based on the results of a subjective refraction performed immediately prior to experimentation. Zernike expansions of the experimental wave-front aberration functions were used to determine aberration coefficients for a series of pupil diameters. The residual Zernike coefficients for defocus were not zero but varied systematically with pupil diameter and with the Zernike coefficient for spherical aberration in a way that maximizes visual acuity. We infer from these results that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized. We found that the population averages of Zernike coefficients were nearly zero for all of the higher-order modes except spherical aberration. This result indicates that a hypothetical average eye representing the central tendency of the population is nearly free of aberrations, suggesting the possible influence of an emmetropization process or evolutionary pressure. However, for any individual eye the aberration coefficients were rarely zero for any Zernike mode. To first approximation, wave-front error fell exponentially with Zernike order and increased linearly with pupil area. On average, the total wave-front variance produced by higher-order aberrations was less than the wave-front variance of residual defocus and astigmatism. For example, the average amount of higher-order aberrations present for a 7.5-mm pupil was equivalent to the wave-front error produced by less than 1/4 diopter (D) of defocus. The largest pupil for which an eye may be considered diffraction-limited was 1.22 mm on average. Correlation of aberrations from the left and right eyes indicated the presence of significant bilateral symmetry. No evidence was found of a universal anatomical feature responsible for third-order optical aberrations. Using the Marechal criterion, we conclude that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil. Different methods of computing population averages provided upper and lower limits to the mean optical transfer function and mean point-spread function for our population of eyes.

615 citations

Journal ArticleDOI
TL;DR: The new model eye provides spherical aberration values within the limits of empirical results and predicts chromatic aberration for wavelengths between 380 and 750 nm and provides a model for calculating optical transfer functions and predicting optical performance of the eye.
Abstract: There is a need for a schematic eye that models vision accurately under various conditions such as refractive surgical procedures, contact lens and spectacle wear, and near vision. Here we propose a new model eye close to anatomical, biometric, and optical realities. This is a finite model with four aspheric refracting surfaces and a gradient-index lens. It has an equivalent power of 60.35 D and an axial length of 23.95 mm. The new model eye provides spherical aberration values within the limits of empirical results and predicts chromatic aberration for wavelengths between 380 and 750 nm. It provides a model for calculating optical transfer functions and predicting optical performance of the eye.

610 citations

Journal ArticleDOI
TL;DR: It is concluded that objective methods of refraction based on wavefront aberration maps can accurately predict the results of subjective refraction and may be more precise and wavefront methods may become the new gold standard for specifying conventional and/or optimal corrections of refractive errors.
Abstract: We determined the accuracy and precision of 33 objective methods for predicting the results of conventional, sphero-cylindrical refraction from wavefront aberrations in a large population of 200 eyes. Accuracy for predicting defocus (as specified by the population mean error of prediction) varied from -0.50 D to +0.25 D across methods. Precision of these estimates (as specified by 95% limits of agreement) ranged from 0.5 to 1.0 D. All methods except one accurately predicted astigmatism to within +/-1/8D. Precision of astigmatism predictions was typically better than precision for predicting defocus and many methods were better than 0.5D. Paraxial curvature matching of the wavefront aberration map was the most accurate method for determining the spherical equivalent error whereas least-squares fitting of the wavefront was one of the least accurate methods. We argue that this result was obtained because curvature matching is a biased method that successfully predicts the biased endpoint stipulated by conventional refractions. Five methods emerged as reasonably accurate and among the most precise. Three of these were based on pupil plane metrics and two were based on image plane metrics. We argue that the accuracy of all methods might be improved by correcting for the systematic bias reported in this study. However, caution is advised because some tasks, including conventional refraction of defocus, require a biased metric whereas other tasks, such as refraction of astigmatism, are unbiased. We conclude that objective methods of refraction based on wavefront aberration maps can accurately predict the results of subjective refraction and may be more precise. If objective refractions are more precise than subjective refractions, then wavefront methods may become the new gold standard for specifying conventional and/or optimal corrections of refractive errors.

560 citations

Book
18 Apr 2000
TL;DR: The first stage in the process of vision is the formation of images of the outside world on the retina at the back of the eye as discussed by the authors, and the optical structure and optical properties of the human eye are described.
Abstract: The first stage in the process of vision is the formation of images of the outside world on the retina at the back of the eye This article describes the optical structure and optical properties of the human eye, how the retinal image is formed and the factors affecting its quality Brief mention is given to neural factors that combine with the optics to determine how well we see The article concentrates on the optics of healthy eyes

442 citations