Neural compensation for the best aberration correction

We use adaptive optics (AO) to study whether neural adaptation influences the amount of higher order aberration correction that produces the best subjective image quality. Three subjects performed two tasks, method of adjustment and matching, while viewing a monochromatic stimulus through the Rochester AO system. In both tasks, after correcting the subject's lower order aberrations with trial lenses, AO was used to modify the subject's higher order aberrations, multiplying it by a scaling factor between 1 and -1. In the adjustment task, subjects adjusted the scaling factor to find the best subjective image quality. In the matching task, subjects viewed the same stimulus sequentially blurred either by defocus or a scaled version of their own wave aberration, adjusting the defocus to match the blur corresponding to different scaled versions of their aberrations. Results from both tasks are consistent with a small amount of neural adaptation because the best subjective image quality occurred when some higher order aberrations were left uncorrected for all three subjects. Neural adaptation slightly modifies the best aberration correction, although this effect averaged only approximately 12% of complete adaptation. These results may have practical consequences for customized vision correction.     

Estimating visual quality from wavefront aberration measurements

PURPOSE: Root mean square (RMS) wavefront error may not be the best metric for predicting a patient's visual function; other metrics should be considered. We describe the most important metrics of optical quality, which are being investigated to predict vision quality and visual performance. METHODS: Optical quality can be described in two different ways. Pupil plane metrics describe variability of the wavefront error at the pupillary plane (eg, RMS wavefront error). Image plane metrics describe the retinal image and do so for either a point source of light (eg, point-spread function [PSF]) or sinusoidal gratings (optical transfer function [OTF]). Visual quality metrics, however, must also consider neural processing and subjective perception. RESULTS: Since vision is more sensitive to rays coming from the center of the pupil, "pupil fraction" appears to be a better predictor of visual acuity (r2 = 0.50) than RMS error (r2 = 0.13). However, image plane metrics, such as the visual Strehl ratio (r2 = 0.62) and the volume between the optical transfer function and neural contrast sensitivity function (r2 = 0.80) appear to be even better. CONCLUSION: Visual perception is highly subjective and involves many aspects of image quality. A single metric to describe all aspects of image quality may be unrealistic. Nevertheless, improved visual quality metrics need further investigation and will likely involve preferential weighing of light passing through the central area of the pupil and/or incorporating neural factors into image quality computation.     

Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses

PURPOSE: To compare experimental optical performance in eyes implanted with spherical and aspheric intraocular lenses (IOLs). METHODS: Corneal, total, and internal aberrations were measured in 19 eyes implanted with spherical (n=9) and aspheric (n=10) IOLs. Corneal aberrations were estimated by virtual ray tracing on corneal elevation maps, and total aberrations were measured using a second-generation laser ray tracing system. Corneal and total wave aberrations were fit to a Zernike polynomial expansion. Internal aberrations were measured by subtracting corneal from total wave aberrations. Optical performance was evaluated in terms of root-mean-square (RMS) wavefront error and Strehl ratio (estimated from the modulation transfer function). Depth-of-field was obtained from through-focus Strehl estimates from each individual eye. RESULTS: Corneal aberrations increased after IOL implantation, particularly astigmatism and trefoil terms. Third and higher order RMS (and the corresponding Strehl ratio) were significantly better in eyes with aspheric IOLs than with spherical IOLs; however, this tendency was reversed when astigmatism was included. Spherical aberration was not significantly different in eyes with aspheric IOLs, whereas it was significantly positive in eyes with spherical IOLs. Third order aberrations were not significantly different across groups. Depth-of-field was significantly larger in eyes with spherical IOLs. Spherical IOLs showed better absolute optical quality in the presence of negative defocus >1.00 D. CONCLUSIONS: Our study shows a good degree of compensation of the corneal spherical aberration in eyes implanted with aspheric IOLs, as opposed to eyes implanted with spherical IOLs. Other sources of optical degradation, both with aspheric and spherical IOLs, are non-symmetric preoperative corneal aberrations, incision-induced aberrations, and third order internal aberrations. Although best corrected optical quality is significantly better with aspheric IOLs, tolerance to defocus tended to be lower.     

Metrics of optical quality derived from wave aberrations predict visual performance

Wavefront-guided refractive surgery and custom optical corrections have reduced the residual root mean squared (RMS) wavefront error in the eye to relatively low levels (typically on the order of 0.25 microm or less over a 6-mm pupil, a dioptric equivalent of 0.19 D). It has been shown that experimental variation of the distribution of 0.25 microm of wavefront error across the pupil can cause variation in visual acuity of two lines on a standard logMAR acuity chart. This result demonstrates the need for single-value metrics other than RMS wavefront error to quantify the effects of low levels of aberration on acuity. In this work, we present the correlation of 31 single-value metrics of optical quality to high-contrast visual acuity for 34 conditions where the RMS wavefront error was equal to 0.25 microm over a 6-mm pupil. The best metric, called the visual Strehl ratio, accounts for 81% of the variance in high-contrast logMAR acuity.     

Visual acuity and optical parameters in progressive-power lenses.

PURPOSES: The purposes of this study are to explore the effect of astigmatism and high-order aberrations of progressive-power lenses (PPLs) on visual acuity (VA) and to find a good optical metric for evaluating visual performance of PPLs. METHODS: A Hartmann-Shack (HS) wavefront sensor was used to measure PPLs and human eyes either independently or in combination. An additional channel permits the measurement of VA under the same optical conditions. Measurements were taken in six relevant locations of a PPL and in three eyes of different normal subjects. In every case, we obtained the wavefront aberration as Zernike polynomials expansions, the root mean square (RMS) error, and two metrics on point spread function (PSF): Strehl ratio and the common logarithm of the volume under the PSF normalized to one (Log_Vol_PSF). RESULTS: Aberration coupling of the PPL with the eye tends to equalize the retinal image quality between central and peripheral zones of the progressive lenses. In the corridor of the PPL, the combination of small amounts of coma, trefoil, and astigmatism (total RMS 0.1 mum) does not significantly affect VA. The continuous increase of astigmatism from corridor to outside zones reduces moderately the quality of vision. The highest correlations between optical metrics and VA were found for Log_Vol_PSF of the entire system eye plus PPL. CONCLUSIONS: Ocular aberrations reduce optical quality difference between corridor and peripheral zones of PPLs. In the same way, VA through the corridor is similar to that of eyes without a lens and it decreases slowly toward peripheral locations. VA through PPLs is well predicted by the logarithm of metrics directly related with image spread (Log_Vol_PSF or equivalent) of the complete system of the eye with the lens.     

A new approach to the study of ocular chromatic aberrations

We measured the ocular wavefront aberration at six different visible wavelengths (between 450 and 650 nm) in three subjects, using a spatially resolved refractometer. In this technique, the angular deviation of light rays entering the pupil at different locations is measured with respect to a target viewed through a centered pupil. Fits of the data at each wavelength to Zernike polynomials were used to estimate the change of defocus with wavelength (longitudinal chromatic aberration, LCA) and the wavelength-dependence of the ocular aberrations. Measured LCA was in good agreement with the literature. In most cases the wavefront aberration increased slightly with wavelength. The angular deviations from the reference stimulus measured using a magenta filter allowed us to estimate the achromatic axis and both optical and perceived transverse chromatic aberration (TCA), (including the effect of aberrations and Stiles-Crawford effect). The amount of TCA varied markedly across subjects, and between eyes of the same subject. Finally, we used the results from these experiments to compute the image quality of the eye in polychromatic light.     

Wavefront aberrations and subjective quality of vision after wavefront-guided LASIK: first results

PURPOSE: To investigate the clinical impact of the postoperative ocular wavefront error (WFE) on subjective quality of vision (SQV) after LASIK. METHOD: Forty-one myopic eyes of 21 patients underwent uneventful LASIK (median -4.63 D). Preoperatively and 1 month postoperatively, WFE measurements were performed and overall SQV was assessed for two lighting conditions (photopic and mesopic) with a questionnaire. Three different WFE representations were computed for a pupil diameter of 6 mm: (1) the visual quality metric VSOTF (visual Strehl ratio based on the optical transfer function), (2) RMS (root mean square) values of the Zernike orders 2-5, and (3) individual Zernike coefficient for orders 2-5. The impact of the postoperative WFE on SQV was calculated using linear regression analysis. RESULTS: For photopic conditions R(2) was 0.24 for model 1 (VSOTF), 0.31 for model 2 (RMS values), and 0.29 for model 3 (Zernike coefficients). Second-and fifth-order aberrations had significant influence on SQV. For mesopic conditions, results were similar. CONCLUSION: Subjective quality of vision after wavefront-guided LASIK could be explained partially by the ocular WFE.     

A method to predict refractive errors from wave aberration data.

We explored the impact of the eye's higher-order aberrations on subjective refraction comparing two classes of methods for estimating refractive state, one based directly on the wave aberration defined in the pupil plane and another based on the retinal image plane. The method defined in the pupil plane chose the sphere and cylinder that either minimized the wave aberration root mean square or minimized the sum of all the spherical and cylindrical components in the wave aberration. The method defined in the image plane chose the sphere and cylinder that optimized an image-quality metric such as the Strehl intensity ratio, the entropy and the intensity variance of the point-spread function, the volume under the modulation transfer function, or the volume under the contrast-sensitivity function. All these methods were compared in a population of six eyes for which we measured both the wave aberration with a Shack-Hartmann wavefront sensor and the subjective refraction under identical conditions. Pupil plane methods predicted subjective refraction poorly. The mean absolute error of the prediction, in spherical equivalent, was about 0.5 D (range, 0.1 to 0.8 D) and increased with increases in higher-order aberrations. However, for all the retinal image plane methods, the mean error between predicted and subjective refraction was about 0.1 D (range, 0 to 0.25 D). The reliability of the method based on the image-quality optimization was further confirmed in a large population of 146 eyes. In conclusion, higher-order aberrations influence the amount of sphere and cylinder required to correct vision. The results indicate that subjective refraction can be predicted from the eye's optics alone by optimizing computed retinal image quality.     

Relationship between residual aberration and light-adapted pupil size.

PURPOSE: The relationship between residual aberration (residual astigmatism and higher-order aberration) and light-adapted pupil size was investigated in human subjects to verify that the pupil size is adjusted to provide good image quality on the retina through control of the image sharpness and illuminance. METHODS: Monochromatic wave aberration and light-adapted pupil diameters were measured from 20 subjects. The measured wave aberration was reconstructed using a sixth-order Zernike polynomial expansion; the neural sharpness was computed as a metric of the residual aberration. Subsequently, the correlation of the neural sharpness and the light-adapted pupil diameter was examined statistically across the subjects in each luminance level. RESULTS: The light-adapted pupil diameter showed a significant positive correlation with the neural sharpness, except under dark-adapted conditions. In contrast, the pupil diameter showed no significant correlation with the spherical equivalent, as previously shown. CONCLUSION: Our results suggest that the level of aberration present in an eye has an influence on pupil size.     

Effects of Zernike wavefront aberrations on visual acuity measured using electromagnetic adaptive optics technology

PURPOSE: This study measured the changes in visual acuity induced by individual Zernike ocular aberrations of various root-mean-square (RMS) magnitudes. METHODS: A crx1 Adaptive Optics Visual Simulator (Imagine Eyes) was used to modify the wavefront aberrations in nine eyes. After measuring ocular aberrations, the device was programmed to compensate for the eye's wavefront error up to the 4th order and successively apply different individual Zernike aberrations using a 5-mm pupil. The generated aberrations included defocus, astigmatism, coma, trefoil, and spherical aberration at a level of 0.1, 0.3, and 0.9 microm. Monocular visual acuity was assessed using computer-generated Landolt-C optotypes. RESULTS: Correction of the patients' aberrations improved visual acuity by a mean of 1 line (-0.1 logMAR) compared to best sphero-cylinder correction. Aberrations of 0.1 microm RMS resulted in a limited decrease in visual acuity (mean +0.05 logMAR), whereas aberrations of 0.3 microm RMS induced significant visual acuity losses with a mean reduction of 1.5 lines (+0.15 logMAR). Larger aberrations of 0.9 microm RMS resulted in greater visual acuity losses that were more pronounced with spherical aberration (+0.64 logMAR) and defocus (+0.62 logMAR), whereas trefoil (+0.22 logMAR) was found to be better tolerated. CONCLUSIONS: The electromagnetic adaptive optics visual simulator effectively corrected and generated wavefront aberrations up to the 4th order. Custom wavefront correction significantly improved visual acuity compared to best-spectacle correction. Symmetric aberrations (eg, defocus and spherical aberration) were more detrimental to visual performance.     

Accounting for the phase,spatial frequency and orientation demands of the task improves metrics based on the visual Strehl ratio

Advances in ophthalmic instrumentation have allowed high order aberrations to be measured in vivo. These measurements describe the distortions to a plane wavefront entering the eye, but not the effect they have on visual performance. One metric for predicting visual performance from a wavefront measurement uses the visual Strehl ratio, calculated in the optical transfer function (OTF) domain (VSOTF) (Thibos et al., 2004). We considered how well such a metric captures empirical measurements of the effects of defocus, coma and secondary astigmatism on letter identification and on reading. We show that predictions using the visual Strehl ratio can be significantly improved by weighting the OTF by the spatial frequency band that mediates letter identification and further improved by considering the orientation of phase and contrast changes imposed by the aberration. We additionally showed that these altered metrics compare well to a cross-correlation-based metric. We suggest a version of the visual Strehl ratio, VS_combined, that incorporates primarily those phase disruptions and contrast changes that have been shown independently to affect object recognition processes. This metric compared well to VSOTF for letter identification and was the best predictor of reading performance, having a higher correlation with the data than either the VSOTF or cross-correlation-based metric.     

Accuracy and precision of objective refraction from wavefront aberrations

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.     

Wellenfrontaberrationen und subjektive optische Qualität nach wellenfrontgeführter LASIK

Purpose

To investigate the clinical impact of the postoperative ocular wavefront error (WFE) on subjective quality of vision (SQV) after LASIK.

Method

Forty-one myopic eyes of 21 patients underwent uneventful LASIK (median –4.63 D). Preoperatively and 1 month postoperatively, WFE measurements were performed and overall SQV was assessed for two lighting conditions (photopic and mesopic) with a questionnaire. Three different WFE representations were computed for a pupil diameter of 6 mm: (1) the visual quality metric VSOTF (visual Strehl ratio based on the optical transfer function), (2) RMS (root mean square) values of the Zernike orders 2–5, and (3) individual Zernike coefficient for orders 2–5. The impact of the postoperative WFE on SQV was calculated using linear regression analysis.

Results

For photopic conditions R² was 0.24 for model 1 (VSOTF), 0.31 for model 2 (RMS values), and 0.29 for model 3 (Zernike coefficients). Second-and fifth-order aberrations had significant influence on SQV. For mesopic conditions, results were similar.

Conclusion

Subjective quality of vision after wavefront-guided LASIK could be explained partially by the ocular WFE.     

Adaptive optics for vision: the eye's adaptation to point spread function

PURPOSE: Despite the fact that ocular aberrations blur retinal images, our subjective impression of the visual world is sharp, which suggests that the visual system compensates for subjective influence. If the brain adjusts for specific aberrations of the eye, vision should be clearest when looking through a subject's typical wave aberration rather than through an unfamiliar one. We used adaptive optics techniques to control the eye's aberrations in order to evaluate this hypothesis. METHODS: We used adaptive optics to produce point spread functions (PSFs) that were rotated versions of the eye's typical PSF by angles in 45 degrees intervals. Five normal subjects were asked to view a stimulus with their own PSF or with a rotated version, and to adjust the magnitude of the aberrations in the rotated case to match the subjective blur of the stimulus to that seen when the wave aberration was in typical orientation. RESULTS: The magnitude of the rotated wave aberration required to match the blur with the typical wave aberration was 20% to 40% less, indicating that subjective blur for the stimulus increased significantly when the PSF was rotated. CONCLUSION: These results support the hypothesis that the neural visual system is adapted to an eye's aberrations and has important implications for correcting higher order aberrations with customized refractive surgery or contact lenses. The full visual benefit of optimizing optical correction requires that the nervous system compensate for the new correction.     

超常视力眼波前像差与对比度视力相关性研究

目的 分析超常视力眼波前像差与不同对比度视力的相关关系,探讨与视力相关的像差函数.方法 应用Snellcn视力表检测裸眼视力≥1.5者81例(81只眼),用WASCA波阵面像差仪测眼波前像差,用多功能电子视力测量仪测量、暗环境下对比度分别为100%、25%、10%和5%的视力.用多元线性相关与回归分析波前像差与不同对比度视力的相关关系.结果 总像差、各阶像差及各Zemike函数与亮、暗环境中对比度为100%和25%视力间的直线相关关系均无统计学意义(P＞0.05).总像差、2阶像差及离焦像差与亮、暗环境中对比度为10%和5%视力间直线相关关系均有统计学意义(P＜0.01)相关系数分别为-0.30、-0.35和-0.28、-0.35:-0.33、-0.38和-0.28、-0.39;-0.31、-0.39和-0.28、-0.39(P＜0.01).其余像差与对比度为10%利5%视力间直线相关关系均无统计学意义(P＞0.05).结论 超常视力眼波前像差与高对比度视力无直线相关关系,与低对比度视力有直线相关关系,总像差、2阶像差和离焦像差越小,低对比度视力越好.     

角膜塑型术后眼波前像差变化

目的 探讨角膜塑型术后眼波前像差变化及其影响因素，了解第3代角膜塑型术对视觉质量的影响。方法 对进行角膜塑型术的21例（42眼）进行了前瞻性临床研究，将角膜塑型术术前及术后达最佳裸眼视力时的眼波前像差情况作测量与比较。检查结果通过Matlab软件分析．直接获取35项Zemike系数及每阶Zemike系数的RMS值。结果 角膜矫型术后总像差，第3、第4、第5、第7阶RMS值较术前增加，且差异有显著性（P〈0．05）。第2、第6阶RMS值较术前增加，但差异无显著性（P〉0．05）。结论 角膜塑型术后眼的像差增加，降低了视觉质量。角膜光学区直径的缩小以及偏离、角膜表面的非规则性增加，角膜非生理形态的改变等是导致像差增加的原因。     

Effect of higher-order wavefront aberrations on binocular summation

PURPOSE: To determine the effect of individual Zernike wavefront aberrations on binocular summation and binocular visual acuity. METHODS: A 0.25-microm wavefront aberration of second, third and fourth order Zernike modes were introduced into a set of log minimum angle of resolution unit (logMAR) visual acuity charts convolved by CTView. Subjects were dilated and fitted with an artificial pupil of 3 mm. For each set of charts, right eye, left eye, and binocular acuity was measured. The gain in binocular visual acuity over monocular visual acuity was defined as binocular summation. The visual acuity lost binocularly reading aberrated charts was normalized for each subject and defined as the aberration induced loss in acuity. RESULTS: Binocular summation was 10.0% (95% limits of agreement 8.8 to 11.1%) in the unaberrated state and ranged from 17.3 to 3.4% in the Zernike modes studied. Binocular summation was greatest in defocus followed by coma and astigmatism. The aberration induced loss in monocular and binocular acuity was higher for Zernike modes with low angular frequency compared to those with high angular frequency. Linear regression showed a significant relationship between aberration-induced loss of visual acuity and binocular summation. CONCLUSIONS: A fixed amount of root mean square (RMS) aberration has a varied effect on binocular vision depending on the angular frequency and radial order of Zernike mode. Binocular vision has a positive effect in reducing the visual impact of aberrations as Zernike modes that suffer from the most loss of visual acuity also experience the greatest amounts of binocular summation.     

Unbiased estimation of refractive state of aberrated eyes

We seek unbiased methods for estimating the target vergence required to maximize visual acuity based on wavefront aberration measurements. Experiments were designed to minimize the impact of confounding factors that have hampered previous research. Objective wavefront refractions and subjective acuity refractions were obtained for the same monochromatic wavelength. Accommodation and pupil fluctuations were eliminated by cycloplegia. Unbiased subjective refractions that maximize visual acuity for high contrast letters were performed with a computer controlled forced choice staircase procedure, using 0.125 diopter steps of defocus. All experiments were performed for two pupil diameters (3 mm and 6 mm). As reported in the literature, subjective refractive error does not change appreciably when the pupil dilates. For 3 mm pupils most metrics yielded objective refractions that were about 0.1 D more hyperopic than subjective acuity refractions. When pupil diameter increased to 6 mm, this bias changed in the myopic direction and the variability between metrics also increased. These inaccuracies were small compared to the precision of the measurements, which implies that most metrics provided unbiased estimates of refractive state for medium and large pupils. Thus a variety of image quality metrics may be used to determine ocular refractive state for monochromatic (635 nm) light, thereby achieving accurate results without the need for empirical correction factors.     

Age-related changes in ocular aberrations with accommodation

This study investigates the changes in aberrations with monocular accommodation as a function of age. Second-order and higher order wavefront aberrations and pupil size were measured as a function of accommodation demand over the range of 0-4 D in the right eyes of 47 normal subjects with ages between 17 and 56 years. Higher order ocular Zernike aberrations were analyzed for the natural pupil size in terms of their equivalent defocus and were also determined for fixed pupil diameters of 4.5 mm in the unaccommodated eyes and 2.5 mm in the accommodating eyes. With relaxed accommodation (0 D accommodation stimulus), the major change with age was in the value of C4(0), which increased in positive value over the age range studied, although the total higher order RMS wavefront aberration did not increase. When the data were analyzed for natural pupils, spherical aberration was again found to change systematically in the positive direction with age. The equivalent defocus of total higher order RMS error for natural pupils showed no significant correlation with age (p > .05). With active accommodation, spherical aberration was found to decrease and become negative as the accommodative response increased in the younger subjects (<40 years). Near-zero spherical aberration was found at accommodation levels of about 0.50 D in the youngest subjects (<20 years) and at around 2-3 D in subjects between 20 and 39 years. In the older subjects (>40 years), the spherical aberration showed only small changes, some of which were positive, within the limited amplitude of accommodation available. Other higher order aberrations and the RMS of higher order aberrations did not appear to change systematically with accommodation, except in the oldest subjects. The change with age in the relationship between aberration and accommodation is interpreted in terms of the changing gradients of refractive index and surface curvatures of the crystalline lens.     

Age-related changes in monochromatic wave aberrations of the human eye

PURPOSE. To investigate the relations between age and the optical aberrations of the whole eye. The eye's optical quality, as measured by the modulation transfer function (MTF), degrades with age, but the MTF does not provide a means to assess the contributions of individual aberrations, such as coma, spherical aberration, and other higher order aberrations to changes in optical quality. The method used in this study provides measures of individual aberrations and overall optical quality. METHODS. Wave aberrations in 38 subjects were measured psychophysically using a spatially resolved refractometer. Data were fit with Zernike polynomials up to the seventh order to provide estimates of 35 individual aberration terms. MTFs and root mean square (RMS) wavefront errors were calculated. Subjects ranged in age from 22.9 to 64.5 years, with spherical equivalent corrections ranging from +0.5 to -6.0 D. RESULTS. Overall RMS wavefront error (excluding tilts, astigmatism, and defocus) was significantly positively correlated with age (r = 0.33, P = 0.042). RMS error for the highest order aberrations measured (fifth through seventh order) showed a strong positive correlation with age (r = 0.57, P = 0.0002). Image quality, as quantified by the MTF, also degraded with age. CONCLUSIONS. Wave aberrations of the eye increase with age. This increase is consistent with the loss of contrast sensitivity with age observed by other investigators.