Computational aspects of the visual Strehl ratio.

PURPOSE: The recently defined visual Strehl ratio that is based on the optical transfer function (VSOTF) has a number of previously unidentified limitations in its calculation that need to be addressed. METHOD: The VSOTF is complex, not bounded between zero and one, and can be negative. It is also very sensitive to the presence of prisms in the wavefront aberration. Current reports using the visual Strehl ratio for objectively assessing visual performance use its real part in the analyses. This leads to a metric that differs from the visual Strehl ratio based on the modulation transfer function (VSMTF), even in the case of rotationally symmetric aberrations. RESULTS: An augmented visual Strehl ratio is proposed that overcomes the limitations of its predecessor. CONCLUSIONS: The augmented metric is more robust in the presence of a residual prism than the VSOTF, and it shows in a preliminary study that it could lead to better correlations with visual performance, especially in the presence of larger aberrations.     

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.     

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.     

Retinal image quality, reading and myopia

Analysis was undertaken of the retinal image characteristics of the best-spectacle corrected eyes of progressing myopes (n = 20, mean age = 22 years; mean spherical equivalent = -3.84 D) and a control group of emmetropes (n = 20, mean age = 23 years; mean spherical equivalent = 0.00 D) before and after a 2h reading task. Retinal image quality was calculated based upon wavefront measurements taken with a Hartmann-Shack sensor with fixation on both a far (5.5 m) and near (individual reading distance) target. The visual Strehl ratio based on the optical transfer function (VSOTF) was significantly worse for the myopes prior to reading for both the far (p = 0.01) and near (p = 0.03) conditions. The myopic group showed significant reductions in various aspects of retinal image quality compared with the emmetropes, involving components of the modulation transfer function, phase transfer function and point spread function, often along the vertical meridian of the eye. The depth of focus of the myopes (0.54 D) was larger (p = 0.02) than the emmetropes (0.42 D) and the distribution of refractive power (away from optimal sphero-cylinder) was greater in the myopic eyes (variance of distributions p < 0.05). We found evidence that the lead and lag of accommodation are influenced by the higher order aberrations of the eye (e.g. significant correlations between lead/lag and the peak of the visual Strehl ratio based on the MTF). This could indicate that the higher accommodation lags seen in myopes are providing optimized retinal image characteristics. The interaction between low and high order aberrations of the eye play a significant role in reducing the retinal image quality of myopic eyes compared with emmetropes.     

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.     

Accommodation stimulus-response function and retinal image quality

Accommodation stimulus-response function (ASRF) and its relationship to retinal image quality were investigated using a modified wavefront sensor. Ten subjects were presented with six vergence stimuli between 0.17 D and 5 D. For each vergence distance, ocular wavefronts and subjective visual acuity were measured. Wavefronts were analysed for a fixed 3-mm pupil diameter and for natural pupil sizes. Visual Strehl ratio computed in the frequency domain (VSOTF) and retinal images were calculated for each condition tested. Subjective visual acuity was significantly improved at intermediate vergence distances (1D and 2D; p < 0.01), and only decreased significantly at 5 D compared with 0.17 D (p < 0.05). VSOTF magnitude was associated with subjective visual acuity and VSOTF peak location correlated with accommodation error. Apparent accommodation errors due to spherical aberration were highly correlated with accommodation lead and lag for natural pupils (R(2) = 0.80) but not for fixed 3-mm pupils (R(2) < 0.00). The combination of higher-order aberrations and accommodation errors improved retinal image quality compared with accommodation errors or higher order aberrations alone. Pupil size and higher order aberrations play an important role in the ASRF.     

Contrast polarity differences reduce crowding but do not benefit reading performance in peripheral vision

Previous studies have shown that the spatial extent of crowding in peripheral vision is reduced when a target letter and its flanking letters have opposite contrast polarity. We have examined if this reduction in crowding leads to improved reading performance. We compared the spatial extent of crowding, visual-span profiles (plots of letter-recognition accuracy versus letter position), and reading speed at 10° inferior visual field, using white letters, black letters, or mixtures of white and black letters, presented on a mid-gray background. Consistent with previous studies, the spatial extent of crowding was reduced when the target and flanking letters had opposite contrast polarity. However, using mixed contrast polarity did not lead to improvements in visual-span profiles or reading speed.     

Isolating the impact of visual perception on dyslexics' reading ability

A large body of data suggests that phonological deficits play an important causal role in dyslexics' reading difficulties. The functional role of visual impairments is still highly debated. Many recent studies have shown clear visual deficits in large subgroups of dyslexics. However, the relationship between these deficits and visual routines required for reading is not clear. To assess the direct contribution of visual factors to dyslexics' slower and less accurate reading, we composed a task that was similar to single word reading in its basic visual characteristics, but had none of the other (phonological, morphological, semantic, etc.) aspects of reading. Young adult dyslexics, with average or above general cognitive abilities, and controls matched for age and cognitive skills participated in the study. We measured both SOA and contrast thresholds for identifying unfamiliar letters. Letters were chosen from an alphabet graphically similar to Hebrew and English (a subset of Georgian letters), but unfamiliar to the subjects. Effects of decreasing letter size, increasing letter crowding (by adding a flanker letter on each side) and adding white noise, were measured. Dyslexics performed as well as controls under all test conditions, and had similar effect sizes. We thus conclude that, despite the data showing that dyslexics have marked difficulties with single word reading, the cause of these difficulties is not a visual processing deficit.     

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.     

Correlation between optical and psychophysical parameters as a function of defocus.

PURPOSE: To evaluate how ocular optical image quality and psychophysical estimates of visual performance compare to each other as a function of defocus. METHODS: We measured the optical modulation transfer function using a double-pass apparatus and psychophysical estimates of visual performance: contrast sensitivity function (CSF) and visual acuity. Both sets of data were obtained under the same optical conditions. RESULTS: We measured optical and psychophysical parameters as a function of defocus. We studied the correlation between optical parameters (Strehl ratio and the logarithm of the volume in the double-pass image [log_Vol D-P]) and psychophysical parameters (the area under the fitted CSF represented in a logarithmic scale with the spatial frequency in linear scale [Area CSF-log_lin] and visual acuity) for different values of defocus. CONCLUSIONS: Strehl ratio is well correlated with the psychophysical estimates of the visual performance for moderate amount of defocus (within 1 D), whereas the other parameter (log_Vol D-P) is well correlated for larger ranges of defocus (within 2 D) and for different pupil diameters. These results suggest that optical measurements could be used for clinical testing of ophthalmic optics.     

The effect of optical zone decentration on lower- and higher-order aberrations after photorefractive keratectomy in a cat model

PURPOSE: To simulate the effects of decentration on lower- and higher-order aberrations (LOAs and HOAs) and optical quality, by using measured wavefront error (WFE) data from a cat photorefractive keratectomy (PRK) model. METHODS: WFE differences were obtained from five cats' eyes 19 +/-7 weeks after spherical myopic PRK for -6 D (three eyes) and -10 D (two eyes). Ablation-centered WFEs were computed for a 9.0 mm pupil. A computer model was used to simulate decentration of a 6-mm subaperture in 100-microm steps over a circular area of 3000 microm diameter, relative to the measured WFE difference. Changes in LOA, HOA, and image quality (visual Strehl ratio based on the optical transfer function; VSOTF) were computed for simulated decentrations over 3.5 and 6.0 mm. RESULTS: Decentration resulted in undercorrection of sphere and induction of astigmatism; among the HOAs, decentration mainly induced coma. Decentration effects were distributed asymmetrically. Decentrations >1000 microm led to an undercorrection of sphere and cylinder of >0.5 D. Computational simulation of LOA/HOA interaction did not alter threshold values. For image quality (decrease of best-corrected VSOTF by >0.2 log units), the corresponding thresholds were lower. The amount of spherical aberration induced by the centered treatment significantly influenced the decentration tolerance of LOAs and log best corrected VSOTF. CONCLUSIONS: Modeling decentration with real WFE changes showed irregularities of decentration effects for rotationally symmetric treatments. The main aberrations induced by decentration were defocus, astigmatism, and coma. Treatments that induced more spherical aberration were less tolerant of decentration.     

Image metrics for predicting subjective image quality.

PURPOSE: Despite the proliferation of wavefront sensors to characterize the optical quality of individual eyes, there is not yet an accurate way to determine from a wave aberration how severely it will impact the patient's vision. Some of the most commonly used metrics, such as RMS wavefront error and the Strehl ratio, predict subjective image quality poorly. Our goal is to establish a better metric to predict subjective image quality from the wave aberration. METHODS: We describe three kinds of experiments designed to compare the effectiveness of different metrics in determining the subjective impact of the wave aberration. Subjects viewed a visual stimulus through a deformable mirror in an adaptive optics system that compensated for the subject's wave aberration. In the first experiment, we show that some Zernike modes such as spherical aberration and defocus interact strongly in determining subjective image quality. In the second experiment, the subject's wave aberration was replaced by the wave aberration corresponding to an individual Zernike mode. The subject then adjusted the coefficient of the Zernike mode to match the blur of a standard stimulus. In the third experiment, the subject viewed the same stimulus through the wave aberration of one of 59 different postoperative patients who had undergone LASIK and matched the blur by adjusting defocus. We then determined which among many image quality metrics best predicted these matching data. RESULTS: RMS wavefront error was a poor predictor of the data, as was the Strehl ratio. CONCLUSIONS: The neural sharpness metric best described the subjective sharpness of images viewed through the wave aberrations of real eyes. This metric can provide a single number that describes the subjective impact of each patient's wave aberration and will also increase the accuracy of refraction estimates from wavefront-based autorefractors and phoropters.     

Influence of interocular differences in the Strehl ratio on binocular summation

The aim of this work is to determine the influence of interocular differences in retinal image quality on binocular visual performance. We measured the contrast sensitivity function (both monocular and binocular) and we computed binocular summation. Data on retinal image quality were taken from a double-pass device ( oqas™, Optical Quality Analysis System; Visiometrics SL. Tarrasa, Spain), providing the Strehl ratio as a parameter to quantify retinal image quality. A total of 28 observers took part in the experiments. Binocular summation for the contrast sensitivity function was found to be significantly ( p  < 0.001) correlated with interocular differences in the Strehl ratio. The higher the interocular differences in the Strehl ratio, the lower the binocular summation. Binocular summation is less effective as the interocular differences in retinal image increase.     

Crowding and eccentricity determine reading rate

Bouma's law of crowding predicts an uncrowded central window through which we can read and a crowded periphery through which we cannot. The old discovery that readers make several fixations per second, rather than a continuous sweep across the text, suggests that reading is limited by the number of letters that can be acquired in one fixation, without moving one's eyes. That "visual span" has been measured in various ways, but remains unexplained. Here we show (1) that the visual span is simply the number of characters that are not crowded and (2) that, at each vertical eccentricity, reading rate is proportional to the uncrowded span. We measure rapid serial visual presentation (RSVP) reading rate for text, in both original and scrambled word order, as a function of size and spacing at central and peripheral locations. As text size increases, reading rate rises abruptly from zero to maximum rate. This classic reading rate curve consists of a cliff and a plateau, characterized by two parameters, critical print size and maximum reading rate. Joining two ideas from the literature explains the whole curve. These ideas are Bouma's law of crowding and Legge's conjecture that reading rate is proportional to visual span. We show that Legge's visual span is the uncrowded span predicted by Bouma's law. This result joins Bouma and Legge to explain reading rate's dependence on letter size and spacing. Well-corrected fluent observers reading ordinary text with adequate light are limited by letter spacing (crowding), not size (acuity). More generally, it seems that this account holds true, independent of size, contrast, and luminance, provided only that text contrast is at least four times the threshold contrast for an isolated letter. For any given spacing, there is a central uncrowded span through which we read. This uncrowded span model explains the shape of the reading rate curve. We test the model in several ways. We use a "silent substitution" technique to measure the uncrowded span during reading. These substitutions spoil letter identification but are undetectable when the letters are crowded. Critical spacing is the smallest distance between letters that avoids crowding. We find that the critical spacing for letter identification predicts both the critical spacing and the span for reading. Thus, crowding predicts the parameters that characterize both the cliff and the plateau of the reading rate curve. Previous studies have found worrisome differences across observers and laboratories in the measured peripheral reading rates for ordinary text, which may reflect differences in print exposure, but we find that reading rate is much more consistent when word order is scrambled. In all conditions tested--all sizes and spacings, central and peripheral, ordered and scrambled--reading is limited by crowding. For each observer, at each vertical eccentricity, reading rate is proportional to the uncrowded span.     

The inter-relationship between magnification, field of view and contrast reserve: the effect on reading performance.

For the reading task, contrast reserve is defined as the ratio of the letter contrast of the printed letters, to the reader's contrast threshold. Acuity reserve is the ratio of the print size used for the reading task, to the reader's visual acuity. The effects of low contrast reserve on reading performance were investigated at various magnifications, ranging from 3x to 7.5x, with the field of view systematically controlled. Eye movements were recorded whilst normally sighted subjects read using the magnifiers. It was shown that with adequate contrast reserve, increasing the field of view improved the reading rate because of the resulting increase in forward saccade length. Conversely, reducing the contrast reserve slowed the reading rate by decreasing the length of forward saccades and increasing the mean fixation duration, suggesting that the perceptual span is reduced at low contrast reserve. This study also shows that when the contrast reserve is low, providing magnification higher than that required for letter recognition (that is, increasing the acuity reserve) will not improve the reading performance. Furthermore, even when the contrast reserve was high, reading rates were lower for the magnifications of 5x and higher, because increases in saccade length do not match those of the retinal image size at these magnifications.     

From scattering to wavefronts--what's in between?

PURPOSE: Some optical errors are too localized and random to be detected by commercial wavefront devices and Zernike polynomial expression. We looked beyond aberrations defined by Zernike expression to discuss implications of fine irregularities associated with highly aberrated corneal surfaces and complex surface roughness that can lead to light scattering. METHODS: Most fine irregularities are related to postoperative surface roughness, complexities of corneal ablation, and the laser in situ keratomileusis (LASIK) flap. These can be characterized mathematically by a random function that includes local surface tilts, the correlation radius of irregularities (Ic), surface roughness, and other terms. The Kirchoff method of scatter analysis characterizes fine surface irregularities by replacing each point on the surface with a tangential plane, allowing it to be governed by Snellen and Fresnel laws. RESULTS: The joint action of the continuum of microbeams defines a complex point spread function that can be expressed by the Strehl ratio. Small, highly irregular steep central islands and flap striae may not be adequately detected by Zernike expression and may have a surface irregularity diameter of 0.1 to 2.0 mm and height of 10 to 20 microm that results in a reduced Strehl ratio below 0.8. Laser ablation inhomogeneities may have dimensions of 1 to 10 microm, resulting in a root mean square tilt value approaching 1.0 and a Strehl ratio below 0.5. CONCLUSION: Corneal surface irregularities after laser vision correction may induce significant optical aberrations and distortions apart from classical wavefront or scattering errors. As these may not be detected by commercial wavefront devices, and yet contribute to the degradation of optical performance, alternate techniques should be evaluated to detect and describe these surface irregularities.     

现代视功能检查在微创白内障手术中的应用意义

随着微创白内障手术的发展和日趋增多的新型人工晶状体(IOL)的临床应用,患者的功能性视力得到越来越大的提高。以往临床上一直作为评价术后疗效的主要指标——裸眼及最佳矫正视力,已很难涵盖视觉质量的全部内容。本文介绍功能性视力、波前像差、视网膜散射光、点扩散函数、调制传递函数、对比敏感度等现代视功能检查及其在白内障手术中的应用原理和临床意义。这些检查不仅对白内障的早期诊断、手术适应证把握、手术并发症处理、个性化IOL选择及植入术后视觉质量的评价有重要指导意义,而且有助于客观分析白内障术后患者主观视觉质量差的原因并加以处理。熟悉围术期视觉质量评价的内容和意义,有助于提高白内障的手术水平,使患者获得更好的术后视觉质量。     

如何做好波前像差引导的准分子激光角膜原位磨镶术

在诸多的个体化手术中,波前像差引导的准分子激光角膜原位磨镶术（LASIK）不仅可以提高术后裸眼视力和矫正视力,也能在一定程度上减少术后高阶像差的增加幅度,改善夜间视力,降低眩光和光晕的发生率,提高对比敏感度。主要阐述以下几个问题的观点：（1）如何理解波前像差对LASIK术后视觉质量的影响？（2）如何正确获得波前像差的检测数据,筛选手术适应证？（3）如何界定波前像差引导的LASIK手术设计的金标准？（4）如何将波前像差检查的数据转化为最优化的手术设计方案？（5）手术执行过程中需注意哪些问题？（6）波前像差引导的LASIK应该达到怎样的术后效果？     

Letter-recognition and reading speed in peripheral vision benefit from perceptual learning

Visual-span profiles are plots of letter-recognition accuracy as a function of letter position left or right of the midline. Previously, we have shown that contraction of these profiles in peripheral vision can account for slow reading speed in peripheral vision. In this study, we asked two questions: (1) can we modify visual-span profiles through training on letter-recognition, and if so, (2) are these changes accompanied by changes in reading speed? Eighteen normally sighted observers were randomly assigned to one of three groups: training at 10 degrees in the upper visual field, training at 10 degrees in the lower visual field and a no-training control group. We compared observers' characteristics of reading (maximum reading speed and critical print size) and visual-span profiles (peak amplitude and bits of information transmitted) before and after training, and at trained and untrained retinal locations (10 degrees upper and lower visual fields). Reading speeds were measured for six print sizes at each retinal location, using the rapid serial visual presentation paradigm. Visual-span profiles were measured using a trigram letter-recognition task, for a letter size equivalent to 1.4x the critical print size for reading. Training consisted of the repeated measurement of 20 visual-span profiles (over four consecutive days) in either the upper or lower visual field. We also tracked the changes in performance in a sub-group of observers for up to three months following training. We found that the visual-span profiles can be expanded (bits of information transmitted increased by 6 bits) through training with a letter-recognition task, and that there is an accompanying increase (41%) in the maximum reading speed. These improvements transferred, to a large extent, from the trained to an untrained retinal location, and were retained, to a large extent, for at least three months following training. Our results are consistent with the view that the visual span is a bottleneck on reading speed, but a bottleneck that can be increased with practice.