The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans
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.
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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
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
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
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
Cites methods from "The chromatic eye: a new reduced-ey..."
...Assuming the eye was well focused for 570 nm when viewing the polychromatic eye chart at 4 m, the eye would also have been focused at infinity for the 633nm laser light used for aberrometry (Thibos et al., 1992)....
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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
References
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TL;DR: In this paper, the response of a defocused aberration-free optical system to line-frequencies in the object is studied analytically, and curves are given showing the response as a function of line-frequency for a range of values of defect of focus.
Abstract: The response of a defocused aberration-free optical system to line-frequencies in the object is studied analytically. Curves are given showing the response as a function of line-frequency for a range of values of defect of focus. A comparison is made with the results to be expected from geometrical optics. A tolerance for defect of focus is obtained, which accords well with published experimental results. Both circular and rectangular apertures are considered.
489 citations
TL;DR: The only finding reminiscent of perceptual “saccadic suppression” and mislocation effects is that a target which steps to a position ahead of a saccade is sometimes ignored.
356 citations
300 citations
TL;DR: One implication of these results is that, although the eye has substantial chromatic aberration, the pupil is positioned so as to minimize the transverse component of the aberration for central vision, thereby optimizing foveal image quality for polychromatic objects.
258 citations
TL;DR: It is concluded that setting optical instruments about 0.4 diopter more negatively in dim than in bright light is justified on the basis of the chromatic aberration of the eye.
Abstract: It has been reported that the human eye behaves as though relatively short-sighted in dim light. Observers tend to compensate for this change by setting optical instruments more negatively in dim than in bright light. New measurements of telescope settings by 21 observers reveal an average increase in power of the eye in dim light of 0.59 diopter (range +1.4 diopters to −3.4 diopters). The dilation of the pupil in dim light does not contribute significantly to this phenomenon. The chromatic aberration of the eye was measured in 14 observers with a specially designed spectral stigmatoscope. The refractive power of the eye increases about 3.2 diopters between 750 and 365 mμ. For this reason the Purkinje shift of maximum visual sensitivity from 560 mμ in bright light to 505 mμ in dim light produces a relative myopia in dim light of 0.35 to 0.40 diopter. Persons who display changes larger or smaller than this do so because of involuntary changes in the accommodation in bright and dim light. In dim light the eye enters a state of relatively fixed focus, little different from its condition when the accommodation is paralyzed with homatropine. In this fixed state the accommodation may be relaxed, or it may add as much as 3 diopters to the refractive power of the eye. Experienced observers focus optical instruments in dim light close to the optimal settings determined objectively. Departures of more than 0.5 diopter in either direction from the optimal focus depress the visual sensitivity and acuity. It is concluded that setting optical instruments about 0.4 diopter more negatively in dim than in bright light is justified on the basis of the chromatic aberration of the eye. Many observers gain a further advantage from individual adjustments of focus in dim light, appropriate to their accommodative behavior.
238 citations