IUSO PUBMED listings for Larry Thibos June 27, 2012

Transcription

1 1. Amigo A, Bonaque S, López-Gil N, Thibos L. Simulated effect of corneal asphericity increase (q-factor) as a refractive therapy for presbyopia. J Refract Surg Jun;28(6): doi: / X PMID: [PubMed - in process] PURPOSE: To determine the theoretical effect of an increase in the negative Q-factor (hyperprolateness) on the refractive state and its effect on presbyopia treatment. METHODS: Ray tracing software was used to simulate the Navarro eye model. To simulate refractive therapy, corneal Q-factor ranged from 0 to Refractive state of the model eye was defined as the target vergence required to maximize retinal image quality according to several image quality metrics. The change of refractive state produced by pupil constriction from 6 to 2 mm was estimated. RESULTS: For 0 Q -0.6, spherical aberration of the model eye is positive, therefore, pupil miosis causes a hypermetropic shift in refractive state. Over the range -0.6 Q - 1.5, spherical aberration becomes negative and pupil constriction causes the eye's far point to approach the eye, inducing a myopic shift. A maximum 0.60-diopter myopic shift in refractive state due to pupil constriction occurred for Q= CONCLUSIONS: Optical modeling predicts that surgically induced negative corneal Q- value will produce a change in the refractive state of the eye after pupillary miosis. Copyright 2012, SLACK Incorporated. 2. López-Gil N, Peixoto-de-Matos SC, Thibos LN, González-Méijome JM. Shedding light on night myopia. J Vis Jan 1;12(5). pii: 4. doi: / Print PMID: [PubMed - in process] Free Article First described during the 18th century, the cause of night myopia remains a controversial topic. Whereas several explanations have been suggested in the literature, particularly related with accommodation or chromatic shift in scotopic light conditions, no definitive explanation for its aetiology has been provided. We describe an experiment in which ocular refractive state was objectively and subjectively measured while viewing two kind of stimulus: letters on a bright background and a punctual source of light in a dark background. We found that under photopic conditions the optimum refractive state of the accommodating eye is significantly more myopic when maximizing perceived quality of a point source on a dark background compared to a conventional letter chart with black letters on a white background. Optical modeling suggested this difference in refractive state is due to spherical aberration. Since isolated point sources are more likely encountered at night, whereas extended objects are more likely encountered in the daytime, our results suggest that a significant part of the night myopia phenomenon is determined by the nature of the visual stimulus and the visual task used to assess ocular refractive state. 3. Demirel S, Anderson RS, Dakin SC, Thibos LN. Detection and resolution of vanishing optotype letters in central and peripheral vision. Vision Res Apr 15;59:9-16. Epub 2012 Mar 3. PMID: [PubMed - indexed for MEDLINE] 1

2 Previous studies of peripheral vision have shown that detection acuity is superior to resolution acuity for gratings over a range of contrasts, which is attributed to different limiting mechanisms (contrast insufficiency and neural undersampling) for the two tasks. To extend the analysis to letters in a way that avoided luminance cues, we used "vanishing optotype" characters, conveying second-order information, and constructed from tripole strokes having the same mean luminance as the surround. We measured the minimum letter size for detection and identification tasks for two different pairs of vanishing optotype characters (O vs. + and orthogonally oriented Landolt-C's) as a function of contrast in central and peripheral vision. Foveally there was no significant difference between detection acuity and resolution acuity for either pair of letters over a range of stimulus contrasts from 20% to 100%, indicating performance is contrastlimited for both tasks. The same result was obtained at 30 eccentricity in the peripheral field for the O vs. + letters, again indicating performance is contrast-limited for both tasks. However, resolution acuity for the Landolt-C letters was significantly worse than detection acuity in the periphery over the same range of contrasts, which suggests performance is limited by neural undersampling for these letters. All of our experimental results are explained by a model of neural sampling in which detection acuity is determined by the size of neural receptive fields relative to the dimensions of the tripole responsible for spatial contrast, whereas resolution acuity is determined by the spacing of receptive fields relative to the spacing between strokes responsible for letter form. Copyright 2012 Elsevier Ltd. All rights reserved. 4. Autrusseau F, Thibos L, Shevell SK. Chromatic and wavefront aberrations: L-, M- and S-cone stimulation with typical and extreme retinal image quality. Vision Res Nov;51(21-22): Epub 2011 Aug 31. PMID: [PubMed - indexed for MEDLINE] PMCID: PMC [Available on 2012/11/1] 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. Copyright 2011 Elsevier Ltd. All rights reserved. 2

3 5. Shen J, Thibos LN. Peripheral aberrations and image quality for contact lens correction. Optom Vis Sci Oct;88(10): PMID: PMCID: PMC [Available on 2012/10/1] PURPOSE: Contact lenses (CLs) reduced the degree of hyperopic field curvature present in myopic eyes and rigid CLs reduced spherocylindrical image blur on the peripheral retina, but their effect on higher order aberrations and overall optical quality of the eye in the peripheral visual field is still unknown. The purpose of our study was to evaluate peripheral wavefront aberrations and image quality across the visual field before and after CL correction. METHODS: A commercial Hartmann-Shack aberrometer was used to measure ocular wavefront errors in 5 steps out to 30 of eccentricity along the horizontal meridian in uncorrected eyes and when the same eyes are corrected with soft or rigid CLs. Wavefront aberrations and image quality were determined for the full elliptical pupil encountered in off-axis measurements. RESULTS: Ocular higher order aberrations (HOA) increase away from fovea in the uncorrected eye. Third-order aberrations are larger and increase faster with eccentricity compared with the other HOA. CLs increase all HOA except third-order Zernike terms. Nevertheless, a net increase in image quality across the horizontal visual field for objects located at the foveal far point is achieved with rigid lenses, whereas soft CLs reduce image quality. CONCLUSIONS: Second-order aberrations limit image quality more than HOA in the periphery. Although second-order aberrations are reduced by CLs, the resulting gain in image quality is partially offset by increased amounts of HOA. To fully realize the benefits of correcting HOA in the peripheral field requires improved correction of second-order aberrations as well. 6. Martin J, Vasudevan B, Himebaugh N, Bradley A, Thibos L. Unbiased estimation of refractive state of aberrated eyes. Vision Res Jul 14. [Epub ahead of print] PMID: [PubMed - indexed for MEDLINE] PMCID: PMC [Available on 2012/9/1] 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 diopter steps of defocus. All experiments were performed for two pupil diameters (3mm and 6mm). As reported in the literature, subjective refractive error does not change appreciably when the pupil dilates. For 3mm pupils most metrics yielded objective refractions that were about 0.1D more hyperopic than subjective acuity refractions. When pupil diameter increased to 6mm, 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 3

4 refractive state for medium and large pupils. Thus a variety of image quality metrics may be used to determine ocular refractive state for monochromatic (635nm) light, thereby achieving accurate results without the need for empirical correction factors.copyright 2011 Elsevier Ltd. All rights reserved. 7. Nam J, Thibos LN, Bradley A, Himebaugh N, Liu H. Forward light scatter analysis of the eye in a spatially-resolved double-pass optical system. Opt. Express Apr 11; 19(8): doi: /OE PubMed PMID: An optical analysis is developed to separate forward light scatter of the human eye from the conventional wavefront aberrations in a double pass optical system. To quantify the separate contributions made by these micro- and macro-aberrations, respectively, to the spot image blur in the Shark-Hartmann aberrometer, we develop a metric called radial variance for spot blur. We prove an additivity property for radial variance that allows us to distinguish between spot blurs from macro-aberrations and micro-aberrations. When the method is applied to tear break-up in the human eye, we find that micro-aberrations in the second pass accounts for about 87% of the double pass image blur in the Shack- Hartmann wavefront aberrometer under our experimental conditions Optical Society of America 8. Ravikumar S, Bradley A, Thibos L. Phase changes induced by optical aberrations degrade letter and face acuity. J Vis Dec 16; 10(14):18. doi: / Print PMID: Optical aberrations of the eye reduce image contrast and induce spatial phase shifts in the retinal image. The resulting degradation of retinal image quality hampers recognition of complex objects such as letters and faces. To study the effects of spatial phase shifts on object recognition, we simulated image blur computationally for 4 types of aberrations (defocus, astigmatism, coma, and spherical aberration) present individually or in combinations. Phase errors in the computed images were corrected (by setting phase to zero), or avoided, by removing the affected frequency components (by setting modulation to zero). The resulting images served as visual stimuli to determine the effects of phase errors on visual acuity for single letters, letter clusters, and faces. The results show that 180 phase reversals induced by optical aberrations reduce visual acuity, when there is sufficient contrast in the affected frequency components. In the presence of positive spherical aberration, acuity loss due to phase errors was more for hyperopic defocus than for myopic defocus, because the contrast of phase-reversed components was much higher for hyperopic defocus. Phase shifts introduced by coma are less than 180 and consequently have a smaller impact on acuity. Although visual acuity improved the most when all frequency components were phase-corrected, phase-reversed components were nevertheless found to aid visual acuity, demonstrating phase-reversed resolution. 9. Sawides L, Marcos S, Ravikumar S, Thibos L, Bradley A, Webster M. Adaptation to astigmatic blur. J Vis Oct 18; 10(12):22. Print PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article 4

5 Adapting to blurred or sharpened images alters the perceived focus of subsequently viewed images. We examined whether these adaptation effects could arise from actual sphero-cylindrical refractive errors, by testing aftereffects in images simulating secondorder astigmatism. Image blur was varied from negative (vertical) through isotropic to positive (horizontal) astigmatism while maintaining constant blur strength. A 2AFC staircase was used to estimate the stimulus that appeared isotropically blurred before or after adapting to images with astigmatism. Adaptation to horizontal blur caused isotropically blurred images to appear vertically biased and vice versa, shifting the perceived isotropic point toward the adapting level. Aftereffects were similar for different types of images and showed partial selectivity so that strongest effects generally occurred when testing and adapting images were the same. Further experiments explored whether the adaptation depended more strongly on the blurring or "fuzziness" in the images vs. the apparent "figural" changes introduced by the blur, by comparing how the aftereffects transfer across changes in size or orientation. Our results suggest that strong selective adaptation can occur for different lower order aberrations of the eye and that these may be at least partly driven by the apparent figural changes that blurring introduces into the retinal image. 10. Wei X, Thibos LN. Modal estimation of wavefront phase from slopes over elliptical pupils. Optom Vis Sci Oct; 87(10):E PMID: [PubMed - indexed for MEDLINE] PURPOSE: Measuring the off-axis optical quality of the eye with a Shack-Hartmann wavefront sensor requires methods for reconstructing wavefront from the gradient data defined within an elliptical pupil. Such methods for modal estimation of wavefront aberrations are sensitive to pupil shape. METHODS: We develop a conceptual framework that reconciles two published, but apparently dissimilar, methods for reconstruction over an elliptical pupil based on Zernike analysis. Our unified treatment shows that the two methods have different interpretations but the vectors of Zernike coefficients they produce are related linearly. Two novel methods based on Fourier series are also introduced for a model of gradient sensors based on Southwell geometry. RESULTS: All four methods were evaluated numerically with three test-cases: a defocus wavefront (1), a spherocylindrical wavefront (2), and a random-generated wavefront (3). Under noise-free conditions, all four methods reconstructed the tested wavefronts accurately. The reconstruction error is negligible at the level of numerical computation. Furthermore, the Monte-Carlo simulation with test case 2 revealed small differences in sensitivity to noise between the two Zernike methods but no difference between the two Fourier methods. Because of the smoothing effects, the two Zernikebased methods are more robust to noise than are the two Fourier methods. However, Fourier methods are computationally faster. CONCLUSIONS: All four modal methods are validated methods to reconstruct wavefronts from the gradients over the elliptical pupil. The choice of these methods is application dependent. 11. Aaron MT, Applegate RA, Porter J, Thibos LN, Schallhorn SC, Brunstetter TJ, Tanzer DJ. Why preoperative acuity predicts postoperative acuity in 5

6 wavefront-guided LASIK. Optom Vis Sci Nov; 87(11): PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article PURPOSE: To critically evaluate the following clinical wisdom regarding custom (wavefront-guided) laser in situ keratomileusis (LASIK) that subjects with better-thanaverage best-corrected visual acuity (BCVA) before surgery have a greater risk of losing BCVA postoperatively than do subjects with worse-than-average BCVA before surgery. METHODS: High contrast BCVA was measured once before and 3 months after custom LASIK in one eye of 79 subjects. Preoperative spherical equivalent refractive error ranged between and D. The sample was divided into one of two subsamples: eyes that had better-than-average preoperative BCVA (<-0.11 logmar) and eyes that had average or worse-than-average preoperative BCVA ( logmar). Controls were implemented for retinal magnification and for the statistical phenomenon of regression to the mean of the preoperative acuity measurement. RESULTS: On average, for the entire sample, moving the correction from the spectacle plane to the corneal plane increased letter acuity 4.7% (1 letter, 0.02 logmar). For each subsample, the percentage regression to the mean was 57.24%. After correcting for magnification effects and regression to the mean, eyes with better-than-average preoperative acuity had a small but significant gain in acuity ( 1 letter, p = 0.040) that was nearly identical to the gain for eyes with worse-than-average preoperative acuity ( 1.5 letters, p = 0.002). CONCLUSIONS: Custom LASIK produced a statistically significant gain in visual acuity after correction for magnification effects. Dividing the sample into two subsamples based on preoperative acuity confirmed the common clinical observation that eyes with better-than-average acuity tend to remain the same or lose acuity, whereas eyes with worse-than-average acuity tend to gain acuity. However, when only one acuity measurement is taken at a single time point and the sample is subsampled nonrandomly, this clinical observation is due to a statistical artifact (regression to the mean) and is not attributable to the surgery. 12. Shen J, Clark CA, Soni PS, Thibos LN. Peripheral refraction with and without contact lens correction. Optom Vis Sci Sep; 87(9): PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article PURPOSE: Peripheral refractive error degrades the quality of retinal images and has been hypothesized to be a stimulus for the development of refractive error. The purpose of this study was to investigate the changes in refractive error across the horizontal visual field produced by contact lenses (CLs) and to quantify the effect of CLs on peripheral image blur. METHODS: A commercial Shack-Hartmann aberrometer measured ocular wavefront aberrations in 5 degrees steps across the central 60 degrees of visual field along the horizontal meridian before and after CLs correction. Wavefront refractions for peripheral lines-of-sight were based on the full elliptical pupil encountered in peripheral measurements. Curvature of field is the change in peripheral spherical equivalent relative to the eye's optical axis. 6

7 RESULTS: Hyperopic curvature of field in the naked eye increases with increasing amounts central myopic refractive error as predicted by Atchison (2006). For an eccentricity of E degrees, field curvature is approximately E percent of foveal refractive error. Rigid gas permeable (RGP) lenses changed field curvature in the myopic direction twice as much as soft CLs (SCLs). Both of these effects varied with CLs power. For all lens powers, SCL cut the degree of hyperopic field curvature in half whereas RGP lenses nearly eliminated field curvature. The benefit of reduced field curvature was partly offset by increased oblique astigmatism. The net reduction of retinal blur because of CLs is approximately constant across the visual field. CONCLUSIONS: Both SCL and RGP lenses reduced the degree of hyperopic field curvature present in myopic eyes, with RGP lenses having greater effect. The tradeoff between field curvature and off-axis astigmatism with RGP lenses may limit their effectiveness for control of myopia progression. These results suggest that axial growth mechanisms that depend on retinal image quality will be affected more by RGP than by SCL lenses. 13. Nam J, Rubinstein J, Thibos L. Wavelength adjustment using an eye model from aberrometry data. J Opt Soc Am A Opt Image Sci Vis Jul 1; 27(7): doi: /JOSAA PMID: [PubMed - indexed for MEDLINE] We developed a method to convert aberrometry data obtained in one wavelength to the corresponding data in another wavelength using an eye model. A single map of aberrometry data is used to construct a free-form one-surface eye model. A general algorithm for the surface construction is described and implemented for real aberrometry data. Our method can handle varying conjugate distances of the measurement plane of the aberrometer and can also manage the chief ray prism that may be present. The algorithm is validated with the aid of an artificial plastic eye. The wavefronts in different wavelengths are compared through the Zernike analysis not only for lower-order aberrations, but also for higher-order aberrations. The results show that the changes of the Zernike aberration coefficients due to wavelengths are non-uniform. The defocus term has the highest effect from wavelength changes, which is consistent with the previous literature. Our method is compared with two approximate semianalytical algorithms. The wavelength adjustments from a multi-surface eye model are contrasted with our method. We prove analytically that the conventional method of wavelength adjustment is based on paraxial analysis. In addition, we provide a method of finding the chief ray using back-projection in some cases and discuss different meanings of prism. 14. Cheng X, Bradley A, Ravikumar S, Thibos LN. Visual impact of Zernike and Seidel forms of monochromatic aberrations. Optom Vis Sci May; 87(5): PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article PURPOSE: The aim of this study was to examine the impact of different aberrations modes (e.g., coma, astigmatism, spherical aberration [SA]) and different aberration basis functions (Zernike or Seidel) on visual acuity (VA). 7

8 METHODS: Computational optics was used to generate retinal images degraded by either the Zernike or Seidel forms of second through fourth-order aberrations for an eye with a 5-mm pupil diameter. High contrast, photopic VA was measured using method of constant stimuli for letters displayed on a computer-controlled, linearized, quasimonochromatic (lambda = 556 nm) display. RESULTS: Minimum angle of resolution (MAR) varied linearly with the magnitude (root mean square error) of all modes of aberration. The impact of individual Zernike lowerand higher-order aberrations (HOAs) varied significantly with mode, e.g., arc minutes of MAR per micrometer of root mean square slopes varied from 7 (spherical defocus) to 0.5 (quadrafoil). Seidel forms of these aberrations always had a smaller visual impact. Notably, Seidel SA had 1/17th the impact of Zernike SA with the same wavefront variance, and about 1/4th the impact of Zernike SA with matching levels of r wavefront error. With lower-order components removed, HOAs near the center of the Zernike pyramid do not have a large visual impact. CONCLUSIONS: The majority of the visual impact of high levels of fourth-order Zernike aberrations can be attributed to the second-order terms within these polynomials. Therefore, the impact of SA can be minimized by balancing it with a defocus term that flattens the central wavefront (paraxial focus) or maximizes the area of the pupil with a flat wavefront. Over this wide range of aberration types and levels, image quality metrics based on the Point Spread Function (PSF) and Optical Transfer Function (OTF) can predict VA as reliably as VA measures can predict retests of VA, and, thus, such metrics may become valuable predictors of both VA and, via optimization, refractions. 15. Kirschen DG, Laby DM, Kirschen MP, Applegate R, Thibos LN. Optical aberrations in professional baseball players. J Cataract Refract Surg Mar; 36(3): PMID: [PubMed - indexed for MEDLINE] PURPOSE: To determine the presence, type, and size of optical higher-order aberrations (HOAs) in professional athletes with superior visual acuity and to compare them with those in an age-matched population of nonathletes. SETTING: Vero Beach and Fort Myers, Florida, USA. METHODS: Players from 2 professional baseball teams were studied. Each player's optical aberrations were measured with a naturally dilated 4.0 mm pupil using a Z-Wave aberrometer and a LADARWave aberrometer. RESULTS: One hundred sixty-two players (316 eyes) were evaluated. The HOAs were less than mum in all cases. Spherical aberration C(4,0) was the largest aberration with both aberrometers. There were small but statistically significant differences between the aberrometers in mean values for trefoil C(3,3) and C(3,-3) and secondary astigmatism C(4,2). Although statistically significant, the differences were clinically insignificant, being similar at approximately diopter (D) of spherical power. A statistically significant difference was found between the professional baseball players and the control population in trefoil C(3,-3). These differences were clinically insignificant, similar to D of spherical power. CONCLUSIONS: Professional baseball players have small higher-order optical aberrations when tested with naturally dilated pupils. No clinically significant differences were found between the 2 aberrometers. Statistically significant differences in trefoil were found between the players and the control population; however, the difference was 8

9 clinically insignificant. It seems as though the visual system of professional baseball players is limited by lower-order aberrations and that the smaller HOAs do not enhance visual function over that in a control population.copyright 2010 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved. 16. Wei X, Thibos L. Design and validation of a scanning Shack Hartmann aberrometer for measurements of the eye over a wide field of view. Opt Express Jan 18; 18(2): doi: /OE PMID: [PubMed - indexed for MEDLINE] Peripheral vision and off-axis aberrations not only play an important role in daily visual tasks but may also influence eye growth and refractive development. Thus it is important to measure off-axis wavefront aberrations of human eyes objectively. To achieve efficient measurement, we incorporated a double-pass scanning system with a Shack Hartmann wavefront sensor (SHWS) to develop a scanning Shack Hartmann aberrometer (SSHA). The prototype SSHA successfully measured the off-axis wavefront aberrations over +/- 15 degree visual field within 7 seconds. In two validation experiments with a wide angle model eye, it measured change in defocus aberration accurately (<0.02microm, 4mm pupil) and precisely (<0.03microm, 4mm pupil). A preliminary experiment with a human subject suggests its feasibility in clinical applications. 17. Liu H, Thibos L, Begley CG, Bradley A. Measurement of the time course of optical quality and visual deterioration during tear break-up. Invest Ophthalmol Vis Sci Jun; 51(6): Epub 2010 Jan 27. PMID: [PubMed - indexed for MEDLINE] Free full text PURPOSE: To compare changes in optical quality and visual performance that accompany tear break-up (TBU) during blink suppression. METHODS: A three-channel optical system was developed that simultaneously measured refractive aberrations (Shack-Hartmann aberrometer), 20/40 letter contrast sensitivity (CS), and TBU (retroillumination, RI). Ten wearers of silicone hydrogel contact lenses were asked to keep one eye open for approximately 18 seconds, while CS, wavefront aberrations, and RI images were collected. The wavefront was reconstructed by zonal methods, and image quality was quantified with a series of metrics including RMS fit error. Novel metrics for quantifying TBU over the contact lens surface were developed by quantifying the contrast of the RI image and by using Fourier descriptors of the first Purkinje (PJ) image shape. RESULTS: There was a full range of TBU over the lens surface, with four subjects showing TBU across the corneal center and one subject with TBU in the inferior peripheral pupil. Among the four subjects with central corneal TBU, RMS fit error, RI contrast, and PJ Fourier descriptors showed high correlation with CS (r(2) range, , , and , respectively). Some of the general optical-quality metrics such as blur strength, neural sharpness, and area of modulation transfer function (MTF) also showed that change correlated with CS loss. CONCLUSIONS: Optical metrics of tear quality and retinal image quality are associated with the decline in vision that occurs with TBU. The evidence supports the hypothesis 9

10 that blurry vision symptoms reported by contact lens wearers are caused by poor quality of the retinal image due to TBU. 18. Evans DW, Wang Y, Haggerty KM, Thibos LN. Effect of sampling array irregularity and window size on the discrimination of sampled gratings. Vision Res Jan; 50(1): Epub. Erratum in: Vision Res May 12; 50(10):995. PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article The effect of sampling irregularity and window size on orientation discrimination was investigated using discretely sampled gratings as stimuli. For regular sampling arrays, visual performance could be accounted for by a theoretical analysis of aliasing produced by undersampling. For irregular arrays produced by adding noise to the location of individual samples, the incidence of perceived orientation reversal declined and the spatial frequency range of flawless performance expanded well beyond the nominal Nyquist frequency. These results provide a psychophysical method to estimate the spatial density and the degree of irregularity in the neural sampling arrays that limit human visual resolution. 19. Chui TY, Thibos LN, Bradley A, Burns SA. The mechanisms of vision loss associated with a cotton wool spot. Vision Res Nov; 49(23): Epub 2009 Aug 22. PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article We characterized the perceptual, functional, and structural abnormalities associated with retinal ischemia during a cotton wool spot episode and its sequelae. The border of the visually salient field anomaly mirrored the quantitatively measured relative scotoma. Results of resolution perimetry and high resolution imaging indicated that there was a substantial loss of retinal ganglion cells within the affected region. A disruption in retinal nerve fiber arrangement was found at the cotton wool spot and within the arcuate relative scotoma. The presence of the arcuate relative scotoma is consistent with the hypothesis of failed signal transmission along the axons that pass through the cotton wool spot. The different levels of loss associated with the arcuate and focal scotomas indicate different underlying pathologies. 20. Wei X, Van Heugten T, Thibos L. Validation of a Hartmann-Moiré wavefront sensor with large dynamic range. Opt Express Aug 3; 17(16): PMID: [PubMed - indexed for MEDLINE] Our goal was to validate the accuracy, repeatability, sensitivity, and dynamic range of a Hartmann-Moiré (HM) wavefront sensor (PixelOptics, Inc.) designed for ophthalmic applications. Methods: Testing apparatus injected a 4 mm diameter monochromatic (532 nm) beam of light into the wavefront sensor for measurement. Controlled amounts of defocus and astigmatism were introduced into the beam with calibrated spherical (- 20D to + 18D) and cylindrical (-8D to + 8D) lenses. Repeatability was assessed with three repeated measurements within a 2-minute period. Results: Correlation coefficients between mean wavefront measurements (n = 3) and expected wavefront vergence for both sphere and cylinder lenses were > For spherical lenses, the sensor was accurate to within 0.1D over the range from -20D to + 18D. For cylindrical lenses, the 10

11 sensor was accurate to within 0.1D over the range from -8D to + 8D. The primary limitation to demonstrating an even larger dynamic range was the increasingly critical requirements for optical alignment. Sensitivity to small changes of vergence was constant over the instrument's full dynamic range. Repeatability of measurements for fixed condition was within 0.01D. Conclusion: The Hartmann-Moiré wavefront sensor measures defocus and astigmatism accurately and repeatedly with good sensitivity over a large dynamic range required for ophthalmic applications. 21. Shen J, Thibos LN. Measuring ocular aberrations and image quality in peripheral vision with a clinical wavefront aberrometer. Clin Exp Optom May; 92(3): PMID: [PubMed - indexed for MEDLINE] BACKGROUND: Clinical aberrometers are accurate, robust instruments for measuring wavefront aberrations for foveal vision, but several practical concerns arise when performing aberrometry of the peripheral field. The purpose of this study was to evaluate these concerns experimentally using a physical eye model. METHODS: A physical model eye was constructed to provide a stable test case that resembled a human eye. Aberrations were measured with a commercial Shack- Hartmann aberrometer along lines-of-sight ranging from zero to 45 degrees of eccentricity. Commercial software for wavefront reconstruction and Zernike analysis was adapted for use with elliptical entrance pupils encountered off-axis. RESULTS: Pupil dimensions estimated from the array of Shack-Hartmann spots captured by the wavefront sensor followed geometrical optics predictions up to 30 degrees eccentricity. With careful attention to detail, aberration analysis over an elliptical pupil was verified with alternative software. Retinal image quality declined slowly as eccentricity increased due to the eye model's spherical aberration. The total RMS computed from Zernike coefficients overestimated the total RMS computed based on the wavefront error of the elliptical pupil.conclusion: Measurement of off-axis wavefront aberrations of a model eye over a restricted range of eccentricities is possible with the COAS clinical wavefront aberrometer and auxiliary lenses to correct astigmatism. When central image quality is good, the off-axis aberrations will have a powerful effect on peripheral image quality. When central image quality is poor, the additional effect of off-axis aberrations will be minor. 22. Iskander DR, Nam J, Thibos LN. The statistics of refractive error maps: managing wavefront aberration analysis without Zernike polynomials. Ophthalmic Physiol Opt May; 29(3): PMID: [PubMed - indexed for MEDLINE] The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such 11

12 as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps. 23. Thibos LN. Retinal image quality for virtual eyes generated by a statistical model of ocular wavefront aberrations. Ophthalmic Physiol Opt May; 29(3): PMID: [PubMed - indexed for MEDLINE] A statistical model of the aberration structure of normal, well-corrected eyes was developed previously (Opthal. Physiol. Opt22, , 2002.) from wavefront aberrations measured for 100 normal eyes (J. Opt. Soc. Am. A.19, , 2002.). The model is capable of generating an unlimited number of wavefront aberration functions for virtual eyes drawn randomly from a multivariate Gaussian distribution of Zernike aberration coefficients. This report provides evidence that monochromatic retinal image quality in virtual eyes, as quantified by 31 different image quality metrics (J. Vis.4, , 2004.), is representative of human eyes but slightly exaggerates the degradation of the retinal image caused by ocular aberrations. A demonstration program for producing virtual eyes is included as an Appendix to this paper. 24. Nam J, Thibos LN, Iskander DR. Zernike radial slope polynomials for wavefront reconstruction and refraction. J Opt Soc Am A Opt Image Sci Vis Apr; 26(4): PMID: [PubMed - indexed for MEDLINE] Ophthalmic wavefront sensors typically measure wavefront slope, from which wavefront phase is reconstructed. We show that ophthalmic prescriptions (in power-vector format) can be obtained directly from slope measurements without wavefront reconstruction. This is achieved by fitting the measurement data with a new set of orthonormal basis functions called Zernike radial slope polynomials. Coefficients of this expansion can be used to specify the ophthalmic power vector using explicit formulas derived by a variety of methods. Zernike coefficients for wavefront error can be recovered from the coefficients of radial slope polynomials, thereby offering an alternative way to perform wavefront reconstruction. 25. Nam J, Thibos LN, Iskander DR. Describing ocular aberrations with wavefront vergence maps. Clin Exp Optom May; 92(3): Epub 2009 Mar 19. PMID: [PubMed - indexed for MEDLINE] A common optometric problem is to specify the eye's ocular aberrations in terms of Zernike coefficients and to reduce that specification to a prescription for the optimum sphero-cylindrical correcting lens. The typical approach is first to reconstruct wavefront phase errors from measurements of wavefront slopes obtained by a wavefront aberrometer. This paper applies a new method to this clinical problem that does not require wavefront reconstruction. Instead, we base our analysis of axial wavefront 12

13 vergence as inferred directly from wavefront slopes. The result is a wavefront vergence map that is similar to the axial power maps in corneal topography and hence has a potential to be favoured by clinicians. We use our new set of orthogonal Zernike slope polynomials to systematically analyse details of the vergence map analogous to Zernike analysis of wavefront maps. The result is a vector of slope coefficients that describe fundamental aberration components. Three different methods for reducing slope coefficients to a spherocylindrical prescription in power vector forms are compared and contrasted. When the original wavefront contains only second order aberrations, the vergence map is a function of meridian only and the power vectors from all three methods are identical. The differences in the methods begin to appear as we include higher order aberrations, in which case the wavefront vergence map is more complicated. Finally, we discuss the advantages and limitations of vergence map representation of ocular aberrations. 26. Applegate RA, Thibos LN, Twa MD, Sarver EJ. Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality. J Cataract Refract Surg Jan; 35(1): PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article PURPOSE: To examine the impact of the location of the fixation target, pupil center, and reference axis of ophthalmic aberrometers and videokeratographers on the measurement of corneal aberrations relevant to vision. SETTING: Clinical Research, Visual Optics Institute, College of Optometry, University of Houston, Houston, Texas, USA. METHODS: The design features of a generic aberrometer and videokeratographer and their interaction with the eye were examined. The results provided a theoretical framework for experimental assessment of pupil translation errors on corneal aberrations relevant to vision and their correction in 129 eyes. RESULTS: Two key principles emerged. First, the aberrometer's measurement axis must coincide with the eye's line-of-sight (LoS). Second, the videokeratographer's measurement axis (the vertex normal) must be parallel with the eye's LoS. When these principles are satisfied, the eye will be in the same state of angular rotation and direct comparison of measurements is justified, provided any translation of the pupil from the vertex normal is taken into account. The error incurred by ignoring pupil displacement in videokeratography varies between eyes and depends on the type of aberration and amount of displacement, with the largest residual correction root-mean-square wavefront error being 1.26 mum over a 6.0 mm pupil, which markedly decreases retinal image quality. CONCLUSION: Translation of the pupil center with respect to the vertex normal in videokeratography should not be ignored in the calculation of the corneal first-surface, internal aberrations of the eye relevant to vision, or the design of refractive corrections based on videokeratography. 27. Wei X, Thibos L. Modeling the eye's optical system by ocular wavefront tomography. Opt Express Dec 8; 16(25): PMID: [PubMed - indexed for MEDLINE] 13

14 PURPOSE: Ocular wavefront tomography (OWT) is the process of using wavefront aberration maps obtained along multiple lines-of-sight (LoS) to determine the shape and position of the major refracting elements of an eye. One goal of OWT is to create a customized schematic model eye that is anatomically similar and functionally equivalent to the individual eye over a large field of view. METHODS: Wavefront aberration maps along multiple LoS were used as design goals for configuring a generic, multi-surface model eye with aberrations that match the measurements. The model was constrained by gross anatomical dimensions and optimized to mimic the measured eye. The method was evaluated with two test cases: (1) a physical model eye with a doublet lens measured with a clinical wavefront aberrometer along six LoS between -31 deg and +29 deg eccentricities, and (2) a mathematical model of the myopic eye for which wavefront aberrations were computed by ray tracing. RESULTS: In case 1, the OWT algorithm successfully predicted the structure of the doublet model eye from the experimental on- and off-axis aberration measurements. In case 2, the algorithm started with a symmetric five surface model eye and optimized it to generate the on- and off-axis aberrations of a GRIN myopia model eye. The adjusted model closely mimicked the physical parameters and optical behavior of the expected myopia model eye over a large field of view. The maximum discrepancy between aberrations of the OWT optimized model and measurements was 0.05 microns RMS for test case 1 and 0.2 microns RMS for test case 2. CONCLUSION: Our implementation of OWT is a valid, feasible, and robust method for constructing an optical model that is anatomically and functionally similar to the eye over a wide field of view. 28. Thibos LN. Where is the optimum far-point for a presbyopic eye? J Refract Surg Nov; 24(9): PMID: [PubMed - indexed for MEDLINE] PURPOSE: To resolve the presbyope's dilemma by determining the optimum location of the far-point that maximizes depth-of-field for reading printed text. METHODS: Geometrical optical analysis of defocused retinal images was used to compute the size of retinal blur circles relative to object size. Functional consequences of changes in viewing distance, pupil diameter, and far-point location were assessed using the blur ratio concept. Depth-of-field was specified by the ratio of the maximum distance to the minimum distance for which printed text of a given size is legible. RESULTS: For the emmetropic patient, text that is legible at one viewing distance remains legible at all shorter distances. Conversely, text that is illegible at one distance is illegible at all distances. For myopic (or undercorrected) patients, the location of the far-point determines the center of the depth-of-field, but not its size. The depth-of-field is shown numerically and analytically to be given by the approximate formula: log(far distance/near distance) = 0.174* blur ratio threshold* letter height/pupil diameter. CONCLUSIONS: Location of the far-point is a free parameter that can be adjusted to suit a patient's needs without affecting depth-of-field. This suggests a theoretically based clinical strategy for presbyopic refractive correction that takes account of reading needs, pupil size, text size, and habitual reading distance for the benefit of the presbyopic patient. 14

15 29. Ravikumar S, Thibos LN, Bradley A. Calculation of retinal image quality for polychromatic light. J Opt Soc Am A Opt Image Sci Vis Oct; 25(10): PMID: [PubMed - indexed for MEDLINE] Although the retinal image is typically polychromatic, few studies have examined polychromatic image quality in the human eye. We begin with a conceptual framework including the formulation of a psychophysical linking hypothesis that underlies the utility of image quality metrics based on the polychromatic point-spread function. We then outline strategies for computing polychromatic point-spread functions of the eye when monochromatic aberrations are known for only a single wavelength. Implementation problems and solutions for this strategy are described. Polychromatic image quality is largely unaffected by wavelength-dependent diffraction and higher-order chromatic aberration. However, accuracy is found to depend critically upon spectral sampling. Using typical aberrations from the Indiana Aberration Study, we assessed through-focus image quality for model eyes with and without chromatic aberrations using a polychromatic metric called the visual Strehl ratio. In the presence of typical levels of monochromatic aberrations, the effect of longitudinal chromatic aberration is greatly reduced. The effect of typical levels of transverse chromatic aberration is virtually eliminated in the presence of longitudinal chromatic aberration and monochromatic aberrations. Clinical value and limitations of the method are discussed. 30. Teel DF, Copland RJ, Jacobs RJ, Wells T, Neal DR, Thibos LN. Design and validation of an infrared Badal optometer for laser speckle. Optom Vis Sci Sep; 85(9): PMID: [PubMed - indexed for MEDLINE] PURPOSE: To validate the design of an infrared wavefront aberrometer with a Badal optometer employing the principle of laser speckle generated by a spinning disk and infrared light. The instrument was designed for subjective meridional refraction in infrared light by human patients. METHODS: Validation employed a model eye with known refractive error determined with an objective infrared wavefront aberrometer. The model eye was used to produce a speckle pattern on an artificial retina with controlled amounts of ametropia introduced with auxiliary ophthalmic lenses. A human observer performed the psychophysical task of observing the speckle pattern (with the aid of a video camera sensitive to infrared radiation) formed on the artificial retina. Refraction was performed by adjusting the vergence of incident light with the Badal optometer to nullify the motion of laser speckle. Validation of the method was performed for different levels of spherical ametropia and for various configurations of an astigmatic model eye. RESULTS: Subjective measurements of meridional refractive error over the range -4D to +4D agreed with astigmatic refractive errors predicted by the power of the model eye in the meridian of motion of the spinning disk. CONCLUSIONS: Use of a Badal optometer to control laser speckle is a valid method for determining subjective refractive error at infrared wavelengths. Such an instrument will be useful for comparing objective measures of refractive error obtained for the human eye with autorefractors and wavefront aberrometers that employ infrared radiation. 15

16 31. Validation of an off-eye contact lens Shack-Hartmann wavefront aberrometer. Kollbaum P, Jansen M, Thibos L, Bradley A. Optom Vis Sci Sep;85(9):E PMID: [PubMed - indexed for MEDLINE] Free PMC Article Free full text PMCID: PMC PURPOSE: To evaluate the ability of a commercially available single pass Shack- Hartmann aberrometer to evaluate contact lens aberrations. METHODS: Accuracy of second-order aberration measurements was verified by measuring a series of precision calibration lenses, spectacle lenses, and contact lenses. Power measurements were compared to those expected by an independent measurement or those provided by the lens manufacturer. Accuracy of third-order aberrations was verified by systematically decentering a lens with known amounts of spherical aberration and comparing the magnitude of induced coma to that of optical theory. Fourth-order aberration accuracy was verified by comparing measured longitudinal spherical aberration values to those expected by ray tracing based on the lens design. Accuracy of lower- and higher-order aberrations was verified for measurements of lenses taken in air and within a saline-filled wet cell. Repeatability was also assessed by comparing repeated measurements of the wet cell and lens in a wet cell, before and after manipulation of that cell. RESULTS: In all cases, measured values closely matched the expected values, generally exhibiting errors of <1%. CONCLUSIONS: The instrument demonstrates good accuracy and repeatability in measuring second-, third-, and fourth-order aberrations of contact lenses and provides the industry with an instrument for evaluating the ex vivo optical characteristics of contact lenses. 32. Applegate RA, Marsack JD, Thibos LN. Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity. Optom Vis Sci Sep; 83(9): PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article PURPOSE: The purpose of this study is to determine the ability of single-value metrics of retinal image quality of the eye to predict visual performance as measured by high (HC) and low (LC) -contrast acuity at photopic (P) and mesopic (M) light levels in eyes with 20/17 and better visual acuity. METHODS: Forty-nine normal subjects in good health ranging in age from 21.8 to 62.6 with 20/17 or better monocular high-contrast logarithm of the minimum angle of resolution (logmar) acuity served as subjects. Wavefront error through the 10th Zernike radial order over a 7-mm pupil was measured on each test eye using a custom-built Shack/Hartmann wavefront sensor. For each eye, 31 different single-value retinal image quality metrics were calculated. Visual acuity was measured using HC (95%) and LC (11%) logmar at photopic (270 cd/m) and mesopic (0.75 cd/m) light levels. To determine the ability of each metric of retinal image quality to predict each type of logmar acuity (P HC, P LC, M HC, and M LC), each acuity measure was regressed against each optical quality metric. RESULTS: The ability of the metrics of retinal image quality to predict logmar acuity improved as luminance and/or contrast is lowered. The best retinal image quality metric 16

17 (logpfsc) accounted for 2.6%, 15.1%, 27.6%, and 40.0% of the variance in P HC, P LC, M HC, and M LC logmar acuity, respectively. CONCLUSIONS: In eyes with 20/17 and better P HC acuity, P HC logmar acuity is insensitive to variations in retinal image quality compared with M LC logmar acuity. Retinal image quality becomes increasingly predictive of logmar acuity as contrast and/or luminance is decreased. Everyday life requires individuals to function over a large range of contrast and luminance levels. Clinically, the impact of retinal image quality as a function of luminance and contrast is readily measurable in a time-efficient manner with M LC logmar acuity charts. 33. Barbero S, Rubinstein J, Thibos LN. Wavefront sensing and reconstruction from gradient and Laplacian data measured with a Hartmann-Shack sensor. Opt Lett Jun 15; 31(12): PMID: [PubMed] PMCID: PMC Free PMC Article A new wavefront sensing and reconstruction technique is presented. It is possible to measure Laplacian and gradient information of a wavefront with a Hartmann-Shack setup. By simultaneously using the Laplacian and gradient data we reconstruct the wavefront by sequentially solving two partial differential equations. 34. Barbero S, Thibos LN. Error analysis and correction in wavefront reconstruction from the transport-of-intensity equation. Opt Eng. 2006; 45(9): PMID: [PubMed] PMCID: PMC Free PMC Article Wavefront reconstruction from the transport-of-intensity equation (TIE) is a well-posed inverse problem given smooth signals and appropriate boundary conditions. However, in practice experimental errors lead to an ill-condition problem. A quantitative analysis of the effects of experimental errors is presented in simulations and experimental tests. The relative importance of numerical, misalignment, quantization, and photodetection errors are shown. It is proved that reduction of photodetection noise by wavelet filtering significantly improves the accuracy of wavefront reconstruction from simulated and experimental data. 35. Miller D, Thibos L, Hong X. Requirements for segmented correctors for diffraction-limited performance in the human eye. Opt Express Jan 10; 13(1): PMID: [PubMed - in process] Wavefront correctors have yet to provide diffraction-limited imaging through the human eye's ocular media for large pupils (>/= 6 mm).to guide future improvements in corrector designs that might enable such imaging, we have modeled the performance of segmented piston correctors in conjunction with measured wave aberration data of normal human eyes (mean=34.2 yr; stdev= 10.6 yr). The model included the effects of pupil size and wavelength in addition to dispersion, phase wrapping, and number and arrangement of facets in the corrector. Results indicate that </= 100x100 facets are needed to reach diffraction-limited performance for pupils up to 8 mm (extrapolated) at 0.6 microm wavelength. Required facet density for the eye was found to be substantially higher at the pupil's edge than at its center, which is in stark contrast to the requirements for correcting atmospheric turbulence. Substantially more facets are 17

18 required at shorter wavelengths with performance highly sensitive to facet fill. In polychromatic light, the performance of segmented correctors based on liquid crystal technology was limited by the naturally occurring longitudinal chromatic aberration of the eye rather than phase wrapping and dispersion of the liquid crystal. Required facets to correct defocus alone was found highly sensitive to pupil size and decentration. 36. Chui TY, Yap MK, Chan HH, Thibos LN. Retinal stretching limits peripheral visual acuity in myopia. Vision Res Mar; 45(5): PMID: [PubMed - indexed for MEDLINE] Axial elongation of the myopic eye has the potential to stretch the retina, thereby reducing the sampling density of retinal neurons. Resolution acuity in the peripheral field of normal eyes is known to be sampling-limited, which suggests that retinal stretching in the myopic eye should have a direct effect on resolution acuity everywhere in the visual field except perhaps the fovea, which is usually optically limited. We tested this prediction that neural sampling density is reduced in myopic eyes by measuring resolution acuity for sinusoidal gratings in the fovea plus five peripheral locations in 60 myopic subjects exhibiting a wide range of refractive errors. Control experiments using a detection paradigm to provoke spatial aliasing verified that peripheral resolution was sampling limited. Retinal spatial frequencies of the grating stimulus were computed assuming Knapps' Law of visual optics, which ensures that retinal image size (in mm) is independent of refractive error when axial myopia is corrected by a spectacle lens located in the anterior focal plane of the eye. Results obtained at every retinal locus showed that resolution acuity declined linearly with magnitude of refractive error. Regression of the population data indicated that approximately 15 D of refractive error doubles the spacing between retinal neurons, thereby halving peripheral resolution acuity relative to the emmetropic eye. Several subjects also demonstrated samplinglimited performance in the fovea, which indicated that optical filtering by the eye's optical system failed to protect the fovea from aliasing artifacts of neural undersampling in these eyes. We conclude that stretching of the retina is a primary cause of reduced spatial resolution of the peripheral field, and occasionally of the fovea, in myopic eyes. Stretching appears to be locally uniform over the central +/-15 degrees of visual field but is globally non-uniform since the foveal region appears to stretch more than the globe itself. 37. Thibos LN. Unresolved issues in the prediction of subjective refraction from wavefront aberration maps. J Refract Surg Sep-Oct; 20(5):S Review. PMID: [PubMed - indexed for MEDLINE] Sources of uncertainty in the conversion of wavefront aberration maps to refractive prescriptions are described. These uncertainties highlight the nature of optimum corrections, the imprecise far point in human eyes, multiple strategies for locating an approximate far point, and unresolved aspects of the gold standard for judging success. The conclusion points to future experiments needed to resolve these uncertainties to achieve more accurate and precise methods of objective wavefront refraction. 38. Pesudovs K, Marsack JD, Donnelly WJ 3rd, Thibos LN, Applegate RA. Measuring visual acuity--mesopic or photopic conditions, and high or low 18

19 contrast letters? J Refract Surg Sep-Oct; 20(5):S PMID: [PubMed - indexed for MEDLINE] PURPOSE: To develop single-valued wavefront aberration metrics that correlate strongly with visual performance. The purpose of this study is to explore whether photopic high contrast visual acuity (VA) is an appropriate visual performance reference and whether mesopic and/or low contrast testing provides any advantage. METHODS: Subjects from the Texas Investigation of Cataract Optics study (N = 148) ranged in age from 21.6 to 83.8 years and from clear lens to dense nuclear cataract. Visual acuity was measured under four conditions: photopic high (VA(PHC)) and low (VA(PLC)) contrast, mesopic high (VA(MHC)) and low (VA(MLC)) contrast (photopic = 280 cd/m(2), mesopic = 0.75 cd/m(2)). Variables were tested for compliance with normality (-2.00 < skew and kurtosis < 2.00) and transformed if required. Linear regression and Bland-Altman 95% limits of agreement (+/-1.96 SD) were used to examine relationships between VA variables and between VA and wavefront aberration metrics. RESULTS: The two photopic measures VA(PHC) (skew = 2.57, kurtosis = 12.2) and VA(PLC) (1.67, 5.41) were poorly distributed, but the two mesopic measures VA(MHC) (0.88, 1.67) and VA(MLC) (0.29, -0.18) were normally distributed. Strong correlations existed between the (transformed) VA variables (R: 0.53 to 0.84). However, limits of agreement ranged over 0.30 to 0.42 logmar, whereas retest data suggested a range of All four were offered in stepwise multiple linear regression for 30 wavefront metrics: 20 included VA(MLC) alone, two included VA(PLC), two included VA(MHC) and six included both VA(MLC) and VA(MHC); R(2) averaged 25%. CONCLUSION: Although strongly correlated, low contrast and/or mesopic VA testing provides different information. Wave aberration metrics correlates better with VA(MLC) making this the visual performance test of choice. 39. Thibos LN. The optics of wavefront sensing. Ophthalmol Clin North Am Jun; 17(2):111-7, v. Review. PMID: [PubMed - indexed for MEDLINE] This article reviews the fundamental principles by which wavefront aberrometers measure ocular aberrations. Three different ways of interpreting aberration measurements are described in terms of wavefront phase, slope, and curvature. Although curvature is the more familiar concept from geometrical optics, the wave optics concept of wavefront phase is more useful for understanding the nature of aberrated retinal images and for prescribing treatments to correct high-order aberrations. 40. Zhou F, Hong X, Miller DT, Thibos LN, Bradley A. Validation of a combined corneal topographer and aberrometer based on Shack-Hartmann wavefront sensing. J Opt Soc Am A Opt Image Sci Vis May;21(5): PMID: [PubMed - indexed for MEDLINE] A corneal aberrometer based on Shack-Hartmann wave-front sensing was developed and validated by using calibrated aspheric surfaces. The aberrometer was found to accurately measure corneal reflective aberrations, from which corneal topography and corneal refractive aberrations were derived. Measurements of reflective aberrations correlated well with theory (R2 = to 0.994). The sag error root mean square 19

20 (RMS) was small, ranging from 0.1 to 0.17 microm for four of the five calibrated surfaces with the fifth at 0.36 microm as a result of residual defocus. Measured refractive aberrations matched with theory and whole-eye aberrometry to within a small fraction of a wavelength. Measurements on three human corneas revealed very large refractive astigmatism ( microm) and appreciable levels of trefoil ( microm), coma ( microm), and spherical aberration ( microm). The mean values of these aberrations were significantly larger than the RMS in repeated measurements. 41. Thibos LN, Hong X, Bradley A, Applegate RA. Accuracy and precision of objective refraction from wavefront aberrations. J Vis Apr 23; 4(4): PMID: [PubMed - indexed for MEDLINE] Free full text 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 D to 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. 42. Marsack JD, Thibos LN, Applegate RA. Metrics of optical quality derived from wave aberrations predict visual performance. J Vis Apr 23; 4(4): PMID: [PubMed - indexed for MEDLINE] Free full text 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 20

21 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. 43. Cheng X, Bradley A, Thibos LN. Predicting subjective judgment of best focus with objective image quality metrics. J Vis Apr 23; 4(4): PMID: [PubMed - indexed for MEDLINE] Free full text PURPOSE: To determine the impact of higher-order monochromatic aberrations on lower-order subjective sphero-cylindrical refractions. METHODS: Computationally-aberrated, monochromatic Sloan letters were presented on a high luminance display that was viewed by an observer through a 2.5mm pupil. Through-focus visual acuity (VA) was determined in the presence of spherical aberration (Z40) at three levels (0.10, 0.21 and 0.50D). Analogous through-astigmatism experiments measured visual acuity in the presence of secondary astigmatism (Z4+/-2) or coma (Z3-1). Measured visual acuity was correlated with 31 different metrics of image quality to determine which metric best predicts performance for degraded retinal images. The defocus and astigmatism levels that optimized each metric were compared with those that produced best visual acuity to determine which metric best predicts subjective refraction. RESULTS: Spherical aberration, coma and secondary astigmatism all reduced VA and increased depth of focus. The levels of defocus and primary astigmatism that produced the best performance varied with levels of spherical aberration and secondary astigmatism, respectively. The presence of coma, however, did not affect cylindrical refraction. Image plane metrics, especially those that take into account the neural contrast sensitivity threshold (e.g. the visual Strehl ratio, VSOTF), are good predictors of visual acuity in both the through-focus and through-astigmatism experiments (R = for VSOTF). Subjective sphero-cylindrical refractions were accurately predicted by some image-quality metrics (e.g., pupil fraction, VSOTF and standard deviation of PSF light distribution). CONCLUSION: Subjective judgment of best focus does not minimize RMS wavefront error (Zernike defocus = 0), nor create paraxial focus (Seidel defocus = 0), but makes the retina conjugate to a plane between these two. It is possible to precisely predict subjective sphero-cylindrical refraction for monochromatic light using objective metrics. 44. Anderson RS, Thibos LN. The filtered Fourier difference spectrum predicts psychophysical letter discrimination in the peripheral retina. Spat Vis. 2004; 17(1-2):5-15. PMID: [PubMed - indexed for MEDLINE] We wished to devise a measure of dissimilarity (D) which could predict psychophysical discrimination performance for Snellen letter pairs in peripheral vision. Threshold size for discriminating 33 pairs of Snellen letters was measured at 30 degrees eccentricity in the nasal retina for two subjects. D was computed for each pair by performing an overlap subtraction in the spatial domain, followed by a Fast Fourier Transform on this difference image, and dividing the total power in the resultant 'difference spectrum' by the sum of the powers of the individual letter spectra. A plot of D vs. psychophysical threshold letter size gave a mean correlation of R = When D was calculated for 21

22 letters that were low-pass filtered at different cut-off frequencies, the correlation with psychophysical performance was greatest when cut-off was between cycles/letter (R = -0.85). Conversely, when the difference spectrum was high-pass filtered at different cut-off frequencies, the correlation decreased continuously as the cut-off increased. These results imply that the band of frequencies between zero and 1.25 cycles/letter are most important for letter discrimination in peripheral vision. 45. Cheng X, Himebaugh NL, Kollbaum PS, Thibos LN, Bradley A. Test-retest reliability of clinical Shack-Hartmann measurements. Invest Ophthalmol Vis Sci Jan;45(1): PMID: [PubMed - indexed for MEDLINE] Free full text PURPOSE: To evaluate the stability of clinical monochromatic aberrometry measurements over a wide range of time scales. METHODS: Monochromatic aberrations in four normal eyes were measured with a clinical Shack-Hartmann aberrometer. A chin rest or a supplemental bite bar attachment was used to stabilize head and eye position. Five repeated measurements were taken within one test (5 frames, t < 1 second) without realignment. With realignment between each measurement, aberration measurements were repeated five times (t < 1 hour) on each day, at the same time of day on five consecutive days, and again on 5 days at monthly intervals. A control experiment studied the effect of systematically misaligning the eye to determine whether fixation errors can account for the variation in the repeated measurements. RESULTS: Variability of wavefront root mean square (RMS) error (excluding defocus and astigmatism) was tracked across repeated measurements. Variances for different time scales were: 8.10 x 10(-5) microm2 (t < 1 second), 3.24 x 10(-4) microm2 (t < 1 hour), 4.41 x 10(-4) microm2 (t < 1 week), 9.73 x 10(-4) microm2 (t < 1 year). Bite bar and chin rest data were almost identical. Rotational fixation error up to 3 degrees accounts for only part of the variability. CONCLUSIONS: Increased variability in aberration maps between days and months indicates biological fluctuations that are large enough to prevent achievement of "perfect vision," even in the unlikely event that spherical and astigmatic refractive errors are corrected perfectly. However, lack of stability does not justify withholding treatment. A lasting benefit of aberration correction is expected despite temporal variability. 46. Cheng X, Thibos LN, Bradley A. Estimating visual quality from wavefront aberration measurements. J Refract Surg Sep-Oct; 19(5):S PMID: [PubMed - indexed for MEDLINE] 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 22

23 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. 47. Cheng X, Himebaugh NL, Kollbaum PS, Thibos LN, Bradley A. Validation of a clinical Shack-Hartmann aberrometer. Optom Vis Sci Aug; 80(8): PMID: [PubMed - indexed for MEDLINE] PURPOSE: To validate the accuracy, tolerance, and repeatability of the complete ophthalmic analysis system aberrometer (COAS, Wavefront Sciences Inc.) with model eyes and normal human eyes. METHOD: Model eyes were constructed from six polymethyl methacrylate, singlesurface lenses with known characteristics. Accuracy of second-order aberrations was verified by measuring defocus and astigmatism induced by series of spherical and cylindrical trial lenses. Accuracy of higher-order aberrations was evaluated by comparing ray-tracing predictions with measured spherical aberration and coma of the aspheric model eyes. Tolerance to axial and lateral misalignment was measured by controlled displacements of the model eye relative to the aberrometer. Repeatability was tested on the same model eyes with repeated measurements taken within 1 s or within half an hour with realignment between each trial. Analyses were based on a 5- mm pupil diameter. RESULTS: Defocus and astigmatism were accurately measured within the working range of the instrument automatic focus adjustment (e.g., measured defocus was within +/-0.25 diopters over a to D range of refractive error). Accuracy of spherical aberration and coma agreed closely with theoretical predictions (e.g., for all six aspheric models, the mean absolute difference between predicted and measured Z(4)0 was microm). Axial displacements over the range +/-2.5 mm had little effect on measurements for myopic and emmetropic model eyes. Also, lateral displacements over the range +/-1.5 mm did not produce significant coma. The standard deviations of repeated measurements of higher-order root mean square on model eyes were <1% of the mean with repeated measures within 1 s and 10% of the mean for five individual measurements with realignment in between each. Tolerance to small lateral displacements was also observed for human eyes. CONCLUSION: The complete ophthalmic analysis system aberrometer can measure second-, third-, and fourth-order aberrations accurately and repeatedly on model eyes. 48. Thibos LN, Cheng X, Bradley A. Design principles and limitations of wavefront guided contact lenses. Eye Contact Lens Jan; 29(1 Suppl):S167-23

24 70; discussion S190-1, S Review. PMID: [PubMed - indexed for MEDLINE] The concept of the wave-front guided design of contact lenses is presented from three vantage points: ray optics, wave front aberrations, and optical path-length errors. We argue that the goal of contact lenses is to make all of the optical paths from a distant object to the retina equal in length, regardless of where the path intersects the plane of the eye's pupil. The aberration map of an eye is a prescription for such a lens. Unfortunately, variability of measured aberration maps is a fundamental limit to our knowledge of the true aberration structure of an eye. Variability arises because the eye is a biologic system that changes over time for normal, physiologic reasons. Furthermore, uncertainty in our measurement of the aberration map because of such variable factors, such as alignment of the aberrometer to the eye by the clinician or small fixation errors committed by the patient, will make it difficult to achieve a full measure of success with aberration-correcting contact lenses. The clinical implication of these findings is that multiple measurements of the aberration map should be collected using a protocol that includes realignment of the instrument and then averaging the aberration maps to reduce the level of uncertainty associated with any single measurement. 49. Barrett BT, Pacey IE, Bradley A, Thibos LN, Morrill P. Nonveridical visual perception in human amblyopia. Invest Ophthalmol Vis Sci Apr; 44(4): PMID: [PubMed - indexed for MEDLINE] Free full text PURPOSE: Amblyopia is a developmental disorder of spatial vision. There is evidence to suggest that some amblyopes misperceive spatial structure when viewing with the affected eye. However, there are few examples of these perceptual errors in the literature. This study was an investigation of the prevalence and nature of misperceptions in human amblyopia. METHODS: Thirty amblyopes with strabismus and/or anisometropia participated in the study. Subjects viewed sinusoidal gratings of various spatial frequencies, orientations, and contrasts. After interocular comparison, subjects sketched the subjective appearance of those stimuli that had nonveridical appearances. RESULTS: Nonveridical visual perception was revealed in 20 amblyopes (approximately 67%). In some subjects, misperceptions were present despite the absence of a deficit in contrast sensitivity. The presence of distortions was not simply linked to the depth of amblyopia, and anisometropes were affected as well as those with strabismus. In most cases, these spatial distortions arose at spatial frequencies far below the contrast detection acuity cutoff. Errors in perception became more severe at higher spatial frequencies, with low spatial frequencies being mostly perceived veridically. The prevalence and severity of misperceptions were frequently found to depend on the orientation of the grating used in the test, with horizontal orientations typically less affected than other orientations. Contrast had a much smaller effect on misperceptions, although there were cases in which severity was greater at higher contrasts. CONCLUSIONS: Many types of misperceptions documented in the present study have appeared in previous investigations. This suggests that the wide range of distortions 24

25 previously reported reflect genuine intersubject differences. It is proposed that nonveridical perception in human amblyopia has its origins in errors in the neural coding of orientation in primary visual cortex. 50. Himebaugh NL, Thibos LN, Bradley A, Wilson G, Begley CG. Predicting optical effects of tear film break up on retinal image quality using the Shack-Hartmann aberrometer and computational optical modeling. Adv Exp Med Biol. 2002; 506(Pt B): No abstract available. PMID: [PubMed - indexed for MEDLINE] 51. Applegate RA, Marcos S, Thibos LN. Aberrometry: clinical and research applications. Optom Vis Sci Feb; 80(2):85-6. No abstract available. PMID: [PubMed - indexed for MEDLINE] 52. Himebaugh NL, Wright AR, Bradley A, Begley CG, Thibos LN. Use of retroillumination to visualize optical aberrations caused by tear film breakup. Optom Vis Sci Jan; 80(1): PMID: [PubMed - indexed for MEDLINE] PURPOSE: The aim of the current study was to develop quantitative methods to assess optical aberrations caused by tear film disruption. METHODS: We used standard fluorescein imaging (FL) and a novel retroillumination (RI) method to image tear film disruption in 12 eyes. Using a clinical slit lamp biomicroscope, we alternated between widefield blue and narrow-beam white light to obtain an interleaved series of FL and RI images of the time course and pattern of tear film break-up. We developed an optical analysis that indicates that the RI image should be proportional to the spatial derivative of the FL image. Intensity fluctuations in the RI images are due to thickness changes in the tear film, whereas intensity fluctuations in FL images are directly determined by tear film thickness. RESULTS: As predicted by optical analysis of RI, the spatial distribution of gaps in the tear film seen with fluorescein appeared as pairs of light and dark contours in the RI images, and a precise correspondence between the spatial derivative of the FL image (slope) and the RI image was found. Both methods showed a gradual spreading of the tear disruption during blink suppression that varied tremendously among eyes in both time and spatial pattern. Resumption of normal blinking did not produce an immediate reconstitution of the normal tear film, and areas of tear break-up created during blink suppression remained abnormal for up to several minutes of normal blinking. CONCLUSIONS: Our analysis indicates that both FL and RI have the potential to quantify optical changes occurring during tear break-up. These results support an interpretation of RI as an intensity-based method for mapping the highly irregular optical aberrations of the eye produced by tear film disruption. 53. Cheng X, Bradley A, Hong X, Thibos LN. Relationship between refractive error and monochromatic aberrations of the eye. Optom Vis Sci Jan; 80(1):43-9. PMID: [PubMed - indexed for MEDLINE] 25

26 PURPOSE: To examine the relationship between ametropia and optical aberrations in a population of 200 normal human eyes with refractive errors spanning the range from to D. METHODS: Using a reduced-eye model of ametropia, we tested the hypothesis that the optical system of the eye is uncorrelated with the degree of ametropia. These predictions were evaluated experimentally with a Shack-Hartmann aberrometer that measured the monochromatic aberrations across the central 6 mm of the dilated pupil in well-corrected, cyclopleged eyes. RESULTS: Optical theory predicted, and control experiments on a model eye verified, that Shack-Hartmann measurements of spherical aberration will vary with axial elongation of the eye even if the dioptric components of the eye are fixed. Contrary to these predictions, spherical aberration was not significantly different from emmetropic eyes. Root mean square of third-order aberrations, fourth-order aberrations, and total higher aberrations (third to 10th) in myopic and hyperopic eyes were also uncorrelated with refractive error. Astigmatic eyes tended to have larger total higher-order aberrations than nonastigmatic eyes. CONCLUSIONS: We conclude that a reduced-eye model of myopia assuming fixed optical parameters and variable axial length is not tenable. 54. Hong X, Thibos LN, Bradley A, Woods RL, Applegate RA. Comparison of monochromatic ocular aberrations measured with an objective crosscylinder aberroscope and a Shack-Hartmann aberrometer. Optom Vis Sci Jan;80(1): PMID: [PubMed - indexed for MEDLINE] Repeated measures of wavefront aberrations were taken along the line-of-sight of seven eyes using two instruments: an objective, cross-cylinder aberroscope (OA) and a Shack-Hartmann (SH) aberrometer. Both instruments were implemented on the same optical table to facilitate interleaved measurements on the same eyes under similar experimental conditions. Variability of repeated measures of individual coefficients tended to be much greater for OA data than for SH data. Although Zernike coefficients obtained from a single measurement were generally larger when measured with the OA than with the SH, the averages across five trials were often smaller for the OA. The Zernike coefficients obtained from the two instruments were not significantly correlated. Radial modulation-transfer functions and point-spread functions derived from the two sets of measurements were similar for some subjects, but not all. When average Zernike coefficients were used to determine optical quality, the OA indicated superior optics in some eyes, but the reverse trend was true if Zernike coefficients from individual trials were used. Possible reasons for discrepancies between the OA and SH measurements include difference in sampling density, quality of data images, alignment errors, and temporal fluctuations. Multivariate statistical analysis indicated that the SH aberrometer discriminated between subjects much better than did the objective aberroscope. 55. Thibos LN, Applegate RA, Marcos S. Aberrometry: the past, present, and future of optometry. Optom Vis Sci Jan; 80(1):1-2. No abstract available. PMID: [PubMed - indexed for MEDLINE] 26

27 56. Thibos LN, Hong X, Bradley A, Cheng X. Statistical variation of aberration structure and image quality in a normal population of healthy eyes. J Opt Soc Am A Opt Image Sci Vis Dec;19(12): PMID: [PubMed - indexed for MEDLINE] 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 wavefront 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. 57. Thibos LN. Are higher order wavefront aberrations a moving target unworthy of clinical treatment? J Refract Surg Nov-Dec;18(6): No abstract available. PMID: [PubMed - indexed for MEDLINE] 58. Thibos LN, Applegate RA, Schwiegerling JT, Webb R. Standards for reporting the optical aberrations of eyes. VSIA Standards Taskforce Members. Vision science and its applications. J Refract Surg Sep- Oct;18(5):S PMID: [PubMed - indexed for MEDLINE] In response to a perceived need in the vision community, an OSA taskforce was formed at the 1999 topical meeting on vision science and its applications (VSIA-99) and charged with developing consensus recommendations on definitions, conventions, and standards for reporting of optical aberrations of human eyes. Progress reports were 27

28 presented at the 1999 OSA annual meeting and at VSIA-2000 by the chairs of three taskforce subcommittees on (1) reference axes, (2) describing functions, and (3) model eyes. 59. Thibos LN, Bradley A, Hong X. A statistical model of the aberration structure of normal, well-corrected eyes. Ophthalmic Physiol Opt Sep;22(5): PMID: [PubMed - indexed for MEDLINE] A statistical model of the wavefront aberration function of the normal, well-corrected eye was constructed based on normative data from 200 eyes which show that, apart from spherical aberration, the higher-order aberrations of the human eye tend to be randomly distributed about a mean value of zero. The vector of Zernike aberration coefficients describing the aberration function for any individual eye was modelled as a multivariate, Gaussian, random variable with known mean, variance and covariance. The model was verified by analysing the statistical properties of 1000 virtual eyes generated by the model. Potential applications of the model include computer simulation of individual variation in aberration structure, retinal image quality, visual performance, benefit of novel designs of ophthalmic lenses, or outcome of refractive surgery. 60. Salmon TO, Thibos LN. Videokeratoscope-line-of-sight misalignment and its effect on measurements of corneal and internal ocular aberrations. J Opt Soc Am A Opt Image Sci Vis Apr;19(4): Erratum in: J Opt Soc Am A Opt Image Sci Vis Jan;20(1):195. PMID: [PubMed - indexed for MEDLINE] A growing number of research laboratories are using the new technologies of videokeratoscopy and Shack-Hartmann aberrometry, in combination, to study the optical structure of the human eye. A potential source of error arises, however, because the two instruments are designed to measure the human eye along different reference axes. The Shack-Hartmann aberrometer is usually aligned coaxially with the line of sight, but videokeratoscopes usually are not. Thus far, corneal optics research has not adequately addressed the problem of videokeratoscope-line-of-sight misalignment and its effect on the computation of corneal and internal ocular aberrations. We measured corneal, ocular, and internal aberrations for three normal human eyes, developed a method to compensate for videokeratoscope-line-of-sight misalignment, and analyzed the importance of compensating for the misalignment. Our results show that when the value of angle lambda (the angle between the line of sight and the pupillary axis) is larger than 2 degrees-3 degrees, the misalignment, if ignored, can lead to incorrect estimates of corneal and internal aberrations as well as the corneal/internal aberration balance. 61. Hong X, Himebaugh N, Thibos LN. On-eye evaluation of optical performance of rigid and soft contact lenses. Optom Vis Sci Dec;78(12): PMID: [PubMed - indexed for MEDLINE] A Shack-Hartmann aberrometer was used to assess the optical performances of eyes corrected with rigid or soft contact lenses compared with spectacles. Metrics of optical quality derived from the measured wave aberrations were consistent with the subjective rating of visual clarity by subjects. Optical aberration analysis illustrated the differences 28

29 in aberration structures of eyes wearing different optical corrections. For our subjects, correction with a rigid gas-permeable lens yielded significantly better optical quality than did the soft contact lens or spectacle lens. This was due to a reduction in the eye's asymmetric (odd-order) aberrations and a reduction in the amount of the eye's positive spherical aberration. These observations can be explained by theoretical calculations of the aberrations of the eye plus lens optical system. We conclude that aberrometry provides a better understanding of the optical effects of contact lenses in situ and could be useful for optimizing future designs of contact lenses. 62. Munson K, Hong X, Thibos LN. Use of a Shack-Hartmann aberrometer to assess the optical outcome of corneal transplantation in a keratoconic eye. Optom Vis Sci Dec;78(12): PMID: [PubMed - indexed for MEDLINE] We report the optical outcome of corneal transplantation treatment on a keratoconic eye as measured with a Shack-Hartmann aberrometer, and we compare the results with the recovery of visual acuity after surgery. Before surgery, the naked keratoconic eye exhibited extremely large aberrations that could not be measured unless the patient wore a rigid gas-permeable contact lens. With the lens, the computed point-spread function of the eye was large and multimodal, and simulated retinal images confirmed the patient's subjective report of multiple, overlapping images. After full recovery from surgery, aberrations of the corrected eye were much smaller compared with the presurgical eye, which implied a more compact point-spread function and clearer retinal images. These optical changes were mirrored by an improvement in uncorrected visual acuity from 1.3 logarithm of the minimum angle of resolution (logmar) before surgery to 0 logmar with spectacle correction after full recovery. We conclude that the Shack- Hartmann aberrometer provides an objective, quantitative assessment of the optical outcome of penetrating keratoplasty that allows the clinician to measure retinal image quality objectively and to accurately simulate the complex visual distortions associated with keratoconus. 63. Thibos LN. Wavefront data reporting and terminology. J Refract Surg Sep-Oct;17(5):S No abstract available. PMID: [PubMed - indexed for MEDLINE] 64. Applegate RA, Thibos LN, Hilmantel G. Optics of aberroscopy and super vision. J Cataract Refract Surg Jul;27(7): Review. PMID: [PubMed - indexed for MEDLINE] This paper (1) reviews the fundamental limits to visual performance imposed by optical imaging and photoreceptor sampling to determine the limits to the potential gains offered by ideal corrections; (2) examines the predicted losses in vision induced by chromatic aberration, phase shifts, typical ocular aberrations, and the gains possible by correcting the monochromatic aberrations of the eye; (3) discusses the principles of aberration measurement in the eye; and (4) presents methods for measuring and classifying monochromatic aberrations of the eye. 29

30 65. Thibos LN, Horner D. Power vector analysis of the optical outcome of refractive surgery. J Cataract Refract Surg Jan;27(1):80-5. PMID: [PubMed - indexed for MEDLINE] PURPOSE: To demonstrate the power vector method of representing and analyzing spherocylindrical refractive errors. SETTING: School of Optometry, Indiana University, Bloomington, Indiana, USA. METHODS: Manifest and keratometric refractive errors were expressed as power vectors suitable for plotting as points in a 3-dimensional dioptric space. The 3 Cartesian coordinates (x, y, z) of each power vector correspond to the powers of 3 lenses that, in combination, fulfill a refractive prescription: a spherical lens of power M, a Jackson crossed cylinder of power J0 with axes at 90 degrees and 180 degrees, and a Jackson crossed cylinder of power J45 with axes at 45 degrees and 135 degrees. The Pythagorean length of the power vector, B, is a measure of overall blurring strength of a spherocylindrical lens or refractive error. Changes in refractive error due to surgery were computed by the ordinary rules of vector subtraction. RESULTS: Frequency distributions of blur strength (B) clearly demonstrate the effectiveness of refractive surgery in reducing the overall blurring effect of uncorrected refractive error. CONCLUSIONS: Power vector analysis also revealed a reduction in the astigmatic component of these refractive errors. Paired comparisons revealed that the change in manifest astigmatism due to surgery was well correlated with the change in keratometric astigmatism. Power vectors aid the visualization of complex changes in refractive error by tracing a trajectory in a uniform dioptric space. The Cartesian components of a power vector are mutually independent, which simplifies mathematical and statistical analysis of refractive errors. Power vectors also provide a natural link to a more comprehensive optical description of ocular refractive imperfections in terms of wavefront aberration functions and their description by Zernike polynomials. Comment in Correcting astigmatism. [J Cataract Refract Surg. 2002]Correcting astigmatism. Naeser K. J Cataract Refract Surg Feb; 28(2): Tutt R, Bradley A, Begley C, Thibos LN. Optical and visual impact of tear break-up in human eyes. Invest Ophthalmol Vis Sci Dec;41(13): PMID: [PubMed - indexed for MEDLINE] Free full text PURPOSE: The purpose of this study was to examine the optical and visual impact of tear break-up. METHODS: Optical quality of the eye was assessed during periods of nonblinking by quantifying vessel contrast in the fundus image and by monitoring the psychophysical contrast sensitivity and the spatial distribution of tear thickness changes by retroillumination. All measures were obtained from three eyes either with or without a soft contact lens. RESULTS: A noticeable decrease in retinal vessel contrast and contrast sensitivity were observed soon after a blink. Both of these measures of optical quality of the eye showed a similar pattern of image degradation both with and without a soft contact lens. 30

31 Although trial-to-trial variability was considerable, sample means show that image contrast in the low spatial frequency range can drop to between 20% and 40% of initial values after 60 seconds of nonblinking. Retroillumination of the tear film showed local intensity fluctuations that progressively spread across the pupil with increasing time after the blink. CONCLUSIONS: Optical aberrations created by tear break-up contribute to the decline in image quality observed objectively and psychophysically. The decline in image quality that accompanies tear break-up may be a direct cause of the blurry vision complaints commonly encountered in dry-eye patients. 67. Applegate RA, Thibos LN, Bradley A, Marcos S, Roorda A, Salmon TO, Atchison DA. Reference axis selection: subcommittee report of the OSA Working Group to establish standards for measurement and reporting of optical aberrations of the eye. J Refract Surg Sep-Oct;16(5):S PMID: [PubMed - indexed for MEDLINE] It is the committee's recommendation that the ophthalmic community use the line of sight as the reference axis for the purposes of calculating and measuring the ocular optical aberrations. 68. Thibos LN, Applegate RA, Schwiegerling JT, Webb R. Report from the VSIA taskforce on standards for reporting optical aberrations of the eye. J Refract Surg Sep-Oct;16(5):S No abstract available. PMID: [PubMed - indexed for MEDLINE] 69. Hong X, Thibos LN. Longitudinal evaluation of optical aberrations following laser in situ keratomileusis surgery. J Refract Surg Sep- Oct;16(5):S PMID: [PubMed - indexed for MEDLINE] Objective measurements of the optical aberrations of an eye were taken with a Shack- Hartmann aberrometer immediately before, immediately after, and at regular intervals over a two month recovery period following LASIK refractive surgery. Results indicate that the surgery induced large amounts of positive spherical aberration which regressed slightly during recovery. Computed point-spread functions for various pupil diameters indicate that retinal image quality was the same before and after surgery for small and medium sized pupils (<4 mm diameter) but was significantly degraded for large pupils (>4 mm). 70. Thibos LN. Principles of Hartmann-Shack aberrometry. J Refract Surg Sep-Oct;16(5):S Review. No abstract available. PMID: [PubMed - indexed for MEDLINE] 71. Thibos LN. The prospects for perfect vision. J Refract Surg Sep- Oct;16(5):S Review. No abstract available. PMID: [PubMed - indexed for MEDLINE] 31

32 72. Thibos LN, Hong X. Clinical applications of the Shack-Hartmann aberrometer. Optom Vis Sci Dec;76(12): PMID: [PubMed - indexed for MEDLINE] The efficacy of the Shack-Hartmann technique for measuring the optical aberrations of the eye was evaluated for four classes of clinical conditions associated with optically abnormal eyes. These categories (with specific examples) are: anomalies of the tear film (dry eye), corneal disease (keratoconus), corneal refractive surgery [laser-assisted in situ keratomileusis (LASIK)], and lenticular cataract. We show that in each of these cases, it is possible to obtain at least a partial topographic map of the refractive aberrations of the patient's eyes, but severe losses of data integrity can occur. We further show that the Shack-Hartmann aberrometer provides additional information about the eye's imperfections on a very fine spatial scale (< 0.4 mm) which scatter light and further degrade the quality of the retinal image. Taken together, spatial maps of the variation of optical aberrations and scatter across the eye's entrance pupil represents an improved description of the optical imperfections of the abnormal eye. 73. Anderson RS, Thibos LN. Sampling limits and critical bandwidth for letter discrimination in peripheral vision. J Opt Soc Am A Opt Image Sci Vis Oct;16(10): PMID: [PubMed - indexed for MEDLINE] We develop and test two functional hypotheses based on the sampling theory of visual resolution that might account for letter acuity in peripheral vision. First, a letter smaller than the acuity limit provides insufficient veridical energy for performing the task, and, second, the available veridical energy is masked by increased amounts of visible but aliased energy. These two hypotheses make opposite predictions about the effect of low-pass filtering on letter acuity, which we tested experimentally by using filtered letters from the tumbling-e alphabet. Our results reject the masking hypothesis in favor of the energy insufficiency hypothesis. Additional experiments in which high-pass-filtered letters were used permitted the isolation of a critical band of spatial frequencies, which is necessary and sufficient for achieving maximum visual acuity. This critical band varied with the particular pair of letters to be discriminated but was in the range cycles per letter. 74. Anderson RS, Thibos LN. Relationship between acuity for gratings and for tumbling-e letters in peripheral vision. J Opt Soc Am A Opt Image Sci Vis Oct;16(10): PMID: [PubMed - indexed for MEDLINE] Earlier studies have reported that grating resolution is sampling-limited in peripheral vision but that letter acuity is generally poorer than grating acuity. These results suggest that peripheral resolution of objects with rich Fourier spectra may be limited by some factor other than neural sampling. To examine this suggestion we formulated and tested the hypothesis that letter acuity in the periphery is sampling-limited, just as it is for extended and truncated gratings. We tested this hypothesis with improved methodology to avoid the confounding factors of target similarity, alphabet size, individual variation, peripheral refractive error, and stimulus size. Acuity was measured for an orientationdiscrimination task (horizontal versus vertical) for a three-bar resolution target and for a block-e letter in which all strokes have the same length. We confirmed previous reports in the literature that acuity for these targets is worse than for extended sinusoidal 32

33 gratings. To account for these results quantitatively, we used difference-spectrum analysis to identify those frequency components of the targets that might form a basis for performing the visual discrimination task. We find that discrimination performance for the three-bar targets and the block-e letters can be accounted for by a sampling-limited model, provided that the limited number of cycles that are present in the characteristic frequency of the stimulus is taken into account. Quantitative differences in acuity for discriminating other letter pairs (e.g., right versus left letters E or characters with short central strokes) could not be attributed to undersampling of either the characteristic frequency or the frequency of maximum energy in the difference spectrum. These results suggest additional tests of the sampling theory of visual resolution, which are the subject of a companion paper. 75. Zhang X, Ye M, Bradley A, Thibos L. Apodization by the Stiles-Crawford effect moderates the visual impact of retinal image defocus. J Opt Soc Am A Opt Image Sci Vis Apr;16(4): PMID: [PubMed - indexed for MEDLINE] 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. 76. Salmon TO, Thibos LN, Bradley A. Comparison of the eye's wave-front aberration measured psychophysically and with the Shack-Hartmann wavefront sensor. J Opt Soc Am A Opt Image Sci Vis Sep;15(9): PMID: [PubMed - indexed for MEDLINE] The Shack-Hartmann wave-front sensor offers many theoretical advantages over other methods for measuring aberrations of the eye; therefore it is essential that its accuracy be thoroughly tested. We assessed the accuracy of a Shack-Hartmann sensor by directly comparing its measured wave-front aberration function with that obtained by the Smirnov psychophysical method for the same eyes. Wave-front profiles measured by the two methods agreed closely in terms of shape and magnitude with rms differences of approximately lambda/2 and approximately lambda/6 (5.6-mm pupil) for two eyes. Primary spherical aberration was dominant in these profiles, and, in one subject, secondary coma was opposite in sign to primary coma, thereby canceling its effect. Discovery of an unusual, subtle wave-front anomaly in one individual further 33

34 demonstrated the accuracy and sensitivity of the Shack-Hartmann wave-front sensor for measuring the optical quality of the human eye. 77. Bradley A, Zhang H, Applegate RA, Thibos LN, Elsner AE. Entoptic image quality of the retinal vasculature. Vision Res Sep;38(17): PMID: [PubMed - indexed for MEDLINE] Spatial details of entoptically visible retinal vessels were investigated using transcleral and Maxwellian-view stimulators. Nine normal subjects provided detailed drawings of the entoptic images which were digitized and superimposed onto digitized fundus photographs and fluorescein angiograms from the same eyes. Subjects also used a tracing method to locate visible entoptic features. The trans-scleral method provided images similar in detail to standard fundus photography (lacking capillary detail, but capturing larger arteries, veins, arterioles and venules) in the macula and around the disk. The Maxwellian-view method illuminated the fovea (7.7 degree field) and provided foveola capillary detail (capillaries traversing the foveola, the capillary arcade forming the FAZ) as well as the larger foveal vessels supplying the foveola, and often contained more foveal detail that available with fluorescein angiography. 78. Thibos LN. Acuity perimetry and the sampling theory of visual resolution. Optom Vis Sci Jun;75(6): Review. PMID: [PubMed - indexed for MEDLINE] Visual resolution is limited by neural sampling of the retinal image everywhere in the visual field except the fovea, where optical limitations usually dominate. Consequently, measurements of resolution acuity may be interpreted as estimates of the spatial density of the mosaic of photoreceptors (in parafoveal retina) or ganglion cells (in peripheral retina) of the living human eye. Recent experiments in the basic visual sciences have paved the way for clinical applications of this approach to the problem of detecting the loss of photoreceptors and ganglion cells during aging and in a variety of retinal diseases. 79. Wang YZ, Bradley A, Thibos LN. Interaction between sub- and supra- Nyquist spatial frequencies in peripheral vision. Vision Res Sep;37(18): PMID: [PubMed - indexed for MEDLINE] In peripheral vision, high-frequency gratings beyond the Nyquist limit are visible as aliased patterns but, as shown previously, their visibility can be masked by superimposed sub-nyquist gratings. Is the converse also true? Can supra-nyquist gratings affect the detectability of sub-nyquist gratings? In this study, we investigated the masking effect of high contrast, supra-nyquist components of a compound grating on the contrast detection of sub-nyquist components by employing a temporal threealternative, forced-choice (3AFC) masking paradigm. We found that high-frequency, aliased gratings with contrast just 2 or 3 times above threshold can have a powerful masking effect on low-frequency, resolved gratings in peripheral vision. This result was surprising because prior results from sub-nyquist masking studies in the fovea and the periphery have indicated that masking occurs only when the mask contrast is at least 5 times greater than threshold. Strong masking by supra-nyquist gratings that are only just visible may be accounted for by an irregular sampling model in which the alias of 34

35 the mask is distributed over a band of frequencies in the sub-nyquist range. Furthermore, if undersampling is the explanation for the results of this study, then masking must occur after spatial sampling. 80. Wang YZ, Thibos LN, Bradley A. Effects of refractive error on detection acuity and resolution acuity in peripheral vision. Invest Ophthalmol Vis Sci Sep;38(10): PMID: [PubMed - indexed for MEDLINE] Free full text PURPOSE: To evaluate the effect of refractive error on detection acuity and resolution acuity in peripheral vision. METHODS: Detection acuity, defined as the highest spatial frequency for which luminance gratings can be discriminated from a uniform field, and resolution acuity, defined as the highest spatial frequency for which spatial patterns are perceived veridically, was determined for vertical and horizontal gratings located at 20 degrees, 30 degrees, and 40 degrees of eccentricity. Resolution was also measured for tumbling-e discrimination at these locations. Refractive state of the eye for test targets was manipulated by introducing an ophthalmic trial lens into the line of sight for the stimulus while holding accommodative state fixed. RESULTS: Detection acuity in the periphery varied significantly with the amount of optical defocus, whereas acuity for grating resolution or letter discrimination was unaffected by defocus over a large range (up to 6 D). These results are consistent with the working hypothesis that detection acuity in the periphery is limited by contrast insufficiency under normal viewing conditions, but resolution is limited by ambiguity because of neural undersampling. CONCLUSIONS: The large depth of focus for resolution acuity measured for peripheral vision indicates that spatial resolution is likely to remain sampling-limited even when peripheral refractive errors are not fully corrected, thus relaxing the methodologic requirements for obtaining noninvasive estimates of neural sampling density of the living eye in a clinical setting. 81. Thibos LN, Bradley A. Use of liquid-crystal adaptive-optics to alter the refractive state of the eye. Optom Vis Sci Jul;74(7): PMID: [PubMed - indexed for MEDLINE] We evaluated the potential of wavefront shaping with liquid-crystals for modulating the eye's refractive state. A spatial light modulator with 127 liquid crystals cells was imaged in the entrance pupil of the eye and programmed to induce prismatic, spherical, and astigmatic refractive changes. Psychophysical evaluation of these optical effects was in agreement with expectations for prisms up to approximately 0.08 D and for lenses up to approximately 1.5 D. These maximum dioptric values represent wavefront retardation of about 3 to 4 wavelengths of 584 nm light across a 3-mm diameter pupil. Optical aliasing of high-power prisms was traced to spatial undersampling of the wavefront retardation function by the discrete array of liquid crystal cells. Undersampling may also be the factor which limits the useful dioptric range of the technique. 82. Zhang X, Thibos LN, Bradley A. Wavelength-dependent magnification and polychromatic image quality in eyes corrected for longitudinal chromatic 35

36 aberration. Optom Vis Sci Jul;74(7): PMID: [PubMed - indexed for MEDLINE] Theoretical calculations using a simple model eye in combination with achromatizing lenses or artificial pupils show that correcting wavelength-dependent refractive error or its effects can exaggerate wavelength-dependent magnification by up to a factor of 7. These calculations are confirmed experimentally, and their effects on retinal image quality are modeled. Because of the increased wavelength-dependent magnification, gains in polychromatic image quality produced by correcting wavelength-dependent refractive error (or minimizing its effects with small pupils) are generally restricted to a small region of the retina. 83. Wang YZ, Thibos LN. Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface. Optom Vis Sci Jul;74(7): PMID: [PubMed - indexed for MEDLINE] The oblique (off-axis) astigmatism of the Indiana Eye, an aspheric reduced-eye model of ocular chromatic aberration and spherical aberration, is computed across the visual field by using Coddington's equations for nonspherical surfaces of revolution. Our results show that the amount of astigmatism varies significantly with the shape of the refracting surface and with the axial location of the pupil. For a pupil located 1.91 mm from the apex of the refracting surface (as originally specified for the model), the calculated Sturm's interval was larger than that reported in the literature. However, by moving the model's pupil 0.84 mm axially away from the apex toward the nodal point, a close match was achieved between Sturm's interval of the model eye and published data from human eyes for eccentricities up to 60 degrees. These results demonstrate that the aspheric reduced-eye model is capable of simultaneously accounting for the chromatic, spherical, and oblique astigmatic aberrations typically found in human eyes. Comment in Oblique astigmatism of the Indiana eye. [Optom Vis Sci. 1998]Oblique astigmatism of the Indiana eye. Atchison D. Optom Vis Sci Apr; 75(4): Thibos LN, Ye M, Zhang X, Bradley A. Spherical aberration of the reduced schematic eye with elliptical refracting surface. Optom Vis Sci Jul;74(7): Review. PMID: [PubMed - indexed for MEDLINE] 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 36

37 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. Comment in Oblique astigmatism of the Indiana eye. [Optom Vis Sci. 1998]Oblique astigmatism of the Indiana eye. Atchison D. Optom Vis Sci Apr; 75(4): Thibos LN.The new visual optics. Optom Vis Sci Jul;74(7): No abstract available. PMID: [PubMed - indexed for MEDLINE] 86. Thibos LN, Wheeler W, Horner D. Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error. Optom Vis Sci Jun;74(6): Review. PMID: [PubMed - indexed for MEDLINE] The description of sphero-cylinder lenses is approached from the viewpoint of Fourier analysis of the power profile. It is shown that the familiar sine-squared law leads naturally to a Fourier series representation with exactly three Fourier coefficients, representing the natural parameters of a thin lens. The constant term corresponds to the mean spherical equivalent (MSE) power, whereas the amplitude and phase of the harmonic correspond to the power and axis of a Jackson cross-cylinder (JCC) lens, respectively. Expressing the Fourier series in rectangular form leads to the representation of an arbitrary sphero-cylinder lens as the sum of a spherical lens and two cross-cylinders, one at axis 0 degree and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vector representation of the power profile. Advantages of this power vector representation of a sphero-cylinder lens for numerical and graphical analysis of optometric data are described for problems involving lens combinations, comparison of different lenses, and the statistical distribution of refractive errors. Comment in Accommodation and induced with-the-rule astigmatism in emmetropes. [Optom Vis Sci. 2001]Accommodation and induced with-the-rule astigmatism in emmetropes. Mutti DO, Enlow NL, Mitchell GL. Optom Vis Sci Jan; 78(1):6-7. A perspective from Mopane. [Optom Vis Sci. 1997]A perspective from Mopane. Harris WF. Optom Vis Sci Jun; 74(6): Wang YZ, Bradley A, Thibos LN. Aliased frequencies enable the discrimination of compound gratings in peripheral vision. Vision Res Feb;37(3): PMID: [PubMed - indexed for MEDLINE] Although gratings beyond the Nyquist limit of the peripheral retina are visible as aliased percepts when presented in isolation, the reported lack of aliasing for targets with 37

38 complex spectra (edges, lines, letters) suggests that aliased frequency components are invisible in the presence of sub-nyquist image components. We tested this hypothesis by systematically exploring a range of stimulus parameters in search of conditions which would enable subjects to detect the supra-nyquist components of a compound grating. A three-alternative forced-choice masking paradigm was used, which required subjects to discriminate a 2.5 deg patch of compound grating (mask + test) from a simple grating (mask only). Using a 2 c/deg grating as the masking component, which is well below the 4 c/deg Nyquist limit to veridical perception at 20 deg in the horizontal nasal field, we varied the spatial frequency of the test grating over a range extending above and below the Nyquist frequency. We found that aliased, supra-nyquist components are reliably detected in the presence of high contrast, sub-nyquist gratings, provided they have sufficient contrast. Contrast threshold for detecting the aliased gratings was higher when presented as a component of the compound grating than when presented in isolation. This masking effect of the sub-nyquist component was not specific to supra-nyquist test targets, however, since a similar masking effect also occurred for sub-nyquist targets. These results suggest that the invisibility of aliasing described previously for edges or square wave gratings is due primarily to the combination of the low amplitudes of supra-nyquist harmonics in such stimuli and a high contrast threshold of the peripheral retina. The additional masking effects of the sub-nyquist, fundamental component of a square wave on the supra-nyquist harmonics make the detection of aliasing impossible even for very high contrast square wave gratings presented in the periphery. 88. Wang YZ, Thibos LN, Lopez N, Salmon T, Bradley A. Subjective refraction of the peripheral field using contrast detection acuity. J Am Optom Assoc Oct;67(10): PMID: [PubMed - indexed for MEDLINE] BACKGROUND: Although peripheral resolution acuity is relatively unaffected by uncorrected refractive error, recent investigations of peripheral vision indicate that contrast detection is optically limited. It should be possible, therefore, to perform a subjective refraction in the peripheral visual field using a contrast detection task. METHODS: For a range of trial lenses, contrast detection acuities for vertical and horizontal gratings were measured with a two-interval forced-choice paradigm. Lens powers that maximized detection acuity were taken as the subjective refraction estimates. These powers were compared with objective refractions determined with retinoscopy and autorefractometry. RESULTS: Contrast detection acuity varied significantly with lens power at all retinal locations tested. Defocusing by one diopter from the optimum lens power reduced detection acuity by about a factor of two at 20 degrees eccentricity, and slightly less in the far periphery. Objective retinoscopy and autorefractometry agreed with subjective measurements for most conditions tested. CONCLUSIONS: Contrast detection acuity in the peripheral visual field varies with refractive blur, demonstrating the feasibility of performing subjective refraction in the periphery for a contrast detection task. Results suggest that visual fields measured with standard perimetry, which is based on contrast detection, may be affected by uncorrected peripheral refractive errors. 38

39 89. Wang YZ, Thibos LN, Bradley A. Undersampling produces non-veridical motion perception, but not necessarily motion reversal, in peripheral vision. Vision Res Jun;36(12): PMID: [PubMed - indexed for MEDLINE] We investigated motion perception in peripheral vision (10-40 deg eccentricity) for drifting gratings above and below the Nyquist limit set by neural sampling of the retinal image. We found that psychometric functions for motion discrimination rarely exhibited worse-than-chance performance indicative of motion reversal. A series of control experiments indicated that failure to demonstrate motion reversal could not be attributed to: (1) failure to detect the contrast of the stimulus; (2) failure to detect the motion of the stimulus; (3) use of an inappropriate range of spatial frequencies. Although consistent motion reversal was not observed, additional experiments demonstrated that motion perception was nevertheless non-veridical for spatial frequencies above the Nyquist limit. These seemingly contradictory results were reconciled by the observation that aliased patterns could appear to move in several different directions, all of which were different from the direction of stimulus, but only of which was opposite to the stimulus direction. Nyquist limits inferred from motion discrimination lie near the predictions for P- ganglion cells in human retina and well above M-cell predictions, which implies the M- cell array is too sparse to account for the limits to verdical motion perception in peripheral vision. 90. Anderson RS, Evans DW, Thibos LN. Effect of window size on detection acuity and resolution acuity for sinusoidal gratings in central and peripheral vision. J Opt Soc Am A Opt Image Sci Vis Apr;13(4): PMID: [PubMed - indexed for MEDLINE] Detection and resolution of square patches of sinusoidal gratings were measured in central and peripheral vision (30 degrees horizontal temporal visual field) for highcontrast gratings as a function of the number of cycles in the stimulus. We determined performance in a forced-choice paradigm for a fixed number of stimulus cycles by arranging for stimulus diameter to vary inversely with spatial frequency. For both psychophysical tasks and for both target locations, the psychometric function relating performance to log spatial frequency shifted to higher frequencies without changing slope significantly as the number of cycles in the stimulus was increased. Thus the entire effect could be captured by an analysis of spatial acuity, which increased with increasing number of grating cycles over the range cycles but remained constant over the range 6-14 cycles. In the central field, resolution acuity and detection acuity were equal regardless of the number of cycles in the stimulus. In the peripheral field, detection acuity exceeded resolution acuity and perceptual aliasing occurred for stimuli in the range 1-14 cycles. From this result we conclude that resolution acuity is sampling limited in the periphery, provided that the stimulus contains at least one full cycle of the grating. Essential features of the results could be accounted for by Fourier analysis of the stimulus. 91. Thibos LN, Still DL, Bradley A. Characterization of spatial aliasing and contrast sensitivity in peripheral vision. Vision Res Jan;36(2): PMID: [PubMed - indexed for MEDLINE] 39

40 Psychometric performance was measured for contrast detection and spatial resolution tasks in foveal and peripheral vision. Objective evidence was obtained for a quantitative difference between resolution acuity and detection acuity in the peripheral field. These two types of spatial acuity differed by up to an order of magnitude (3 vs 30 c/deg at 30 deg eccentricity) and they varied with stimulus contrast in distinctly different ways. Contrast sensitivity at the resolution limit was an order of magnitude above the absolute threshold of unity and the shape of the contrast sensitivity function was significantly different from that measured for foveal vision. The results suggest that current models of eccentricity scaling of contrast sensitivity be re-evaluated to take account of the extensive aliasing zone of spatial frequencies which becomes functional in peripheral vision when the retinal image is well focused. 92. Rynders M, Lidkea B, Chisholm W, Thibos LN. Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle psi in a population of young adult eyes. J Opt Soc Am A Opt Image Sci Vis Oct;12(10): PMID: [PubMed - indexed for MEDLINE] Subjective transverse chromatic aberration (stca) manifest at the fovea was determined for a population of 85 young adults (19-38 years old) by means of a twodimensional, two-color, vernier alignment technique. The statistical distribution of stca was well fitted by a bivariate Gaussian function with mean values that were not significantly different from zero in either the horizontal or the vertical direction. We conclude from this result that a hypothetical, average eye representing the population mean of human eyes with medium-sized pupils is free of foveal stca. However, the absolute magnitude of stca for any given individual was often significantly greater than zero and ranged from 0.05 to 2.67 arcmin for the red and the blue lights of a computer monitor (mean wavelengths, 605 and 497 nm, respectively). The statistical distribution of the absolute magnitude of stca was well described by a Rayleigh probability distribution with a mean of 0.8 arcmin. A simple device useful for population screening in a clinical setting was also tested and gave concordant results. Assuming that stca at the fovea is due to decentering of the pupil with respect to the visual axis, we infer from these results that the pupil is, on average, well centered in human eyes. The average magnitude of pupil decentration in individual eyes is less than 0.5 mm, which corresponds to psi = 3 deg for the angle between the achromatic and the visual axes of the eye. 93. Winn B, Bradley A, Strang NC, McGraw PV, Thibos LN. Reversals of the colour-depth illusion explained by ocular chromatic aberration. Vision Res Oct;35(19): PMID: [PubMed - indexed for MEDLINE] Although many colour-depth phenomena are predictable from the interocular difference in monocular chromatic diplopia caused by the eye's transverse chromatic aberration (TCA), several reports in the literature suggest that other factors may also be involved. To test the adequacy of the optical model under a variety of conditions, we have determined experimentally the effects of background colour on perceived monocular chromatic diplopia and perceived depth (chromostereopsis). A Macintosh colour monitor was used to present red, blue, and green test stimuli which were viewed monocularly or binocularly (haploscopically) through 1.78 mm artificial pupils. These apertures were 40

41 displaced nasally and temporally from the visual axis under controlled conditions to induce a variable degree of TCA. Monocular chromatic diplopia and binocular chromostereopsis were measured for red and blue targets, and also for red and green targets, presented on either a black background or on a background which was composed of the sum of the targets' spectral composition (e.g. red and blue presented on magenta; red and green presented on yellow). In all cases, chromatic diplopia and chromostereopsis were found experimentally to reverse in sign with this change in background. Furthermore, we found that a given coloured target could be located in different depth planes within the same display when located on different background colours. These seemingly paradoxical results could nevertheless be explained by a simple model of optical TCA without the need to postulate additional factors or mechanisms. 94. Atchison DA, Bradley A, Thibos LN, Smith G. Useful variations of the Badal Optometer. Optom Vis Sci Apr;72(4): PMID: [PubMed - indexed for MEDLINE] The simple Badal Optometer consists of a movable target and a fixed positive power lens placed at its focal distance away from the eye. The perceived angular size of the target is independent of target position and the power scale is linear. Limitations of the simple Badal Optometer include restriction of negative (myopic) ocular vergence range, the need for targets to be small, and the problem of "proximal" accommodation. We describe two modifications to the Badal system in which these limitations may be overcome by the use of a movable auxiliary optical system. In one modification, the movable auxiliary system consists of a target and positive lens which together may provide a virtual "target" for the Badal lens and thus increase the negative range. In the second modification, the Badal lens is positioned as it would normally be, but the target is an image of a distant stimulus created by the auxiliary lens. The target position (and hence the ocular vergence) is changed by moving the auxiliary lens. The distant target eliminates the proximal accommodative stimulus and allows spatial detail near the resolution limit to be displayed. 95. Thibos LN, Elliott DB, Bradley A. Vision and aging: introduction. Optom Vis Sci Dec;71(12): No abstract available. PMID: [PubMed - indexed for MEDLINE] 96. Levick WR, Thibos LN. Neurophysiology of central retinal degeneration in cat. Vis Neurosci May-Jun;10(3): PMID: [PubMed - indexed for MEDLINE] Receptive fields of ganglion cells have been studied in cats possessing a chronic, arrested lesion of central retinal degeneration. Lesions were characterized by an ophthalmoscopically sharp border separating apparently normal retina from the region of the lesion. Under direct ophthalmoscopic guidance, a succession of recordings was obtained from ganglion cells having cell bodies at various positions relative to the lesion. Cells located more than 1 deg outside the ophthalmoscopic border had normal visual sensitivity as assessed by area-threshold experiments. Inside the lesion cells within 1 deg of the border had reduced sensitivity which often precluded functional classification 41

42 by the usual visual tests. Ganglion cells located more than 1 deg inside the border of large lesions were blind and some had abnormal patterns of maintained discharge of action potentials. Nevertheless, the antidromic latencies of these blind cells fell into the familiar conduction groups (T1/T2/T3). Receptive-field maps of cells near the border of the lesion often appeared truncated, with the missing portion of the field covered by the lesion. These observations were consistent with the abnormal form of area-threshold curves. Although the responsiveness of cells near the lesion was abnormally low for grating stimuli, cutoff spatial frequency and orientation bias of these cells were within normal limits. 97. Thibos LN, Bradley A. New methods for discriminating neural and optical losses of vision. Optom Vis Sci Apr;70(4): Review. PMID: [PubMed - indexed for MEDLINE] Visual acuity, the premier test of visual function, is analyzed as a three-stage, hierarchical sequence beginning with the detection of spatial contrast, followed by the resolution of that contrast into spatially separate elements, and ending with the identification of a particular arrangement of elements as one of several possible test objects, e.g., a letter in the Snellen alphabet. Each stage in this process has its own inherent limitations which are associated with different stages of the visual pathway. New methods are described for testing each stage of the hierarchy individually for the purpose of identifying the weak link in the chain, thus paving the way for differential diagnosis of optical and neural losses of vision. 98. Atchison DA, Thibos LN. Diffractive properties of the Diffrax bifocal contact lens. Ophthalmic Physiol Opt Apr;13(2): PMID: [PubMed - indexed for MEDLINE] We have verified that the Pilkington Diffrax lens behaves optically as a diffractive bifocal contact lens. The longitudinal chromatic aberration of the lens is similar to that predicted by theory, both on and off the eye. The over-refraction with the lens on the eye is similar to the distance subjective refraction, which is also as predicted. 99. Zhang X, Bradley A, Thibos LN. Experimental determination of the chromatic difference of magnification of the human eye and the location of the anterior nodal point. J Opt Soc Am A Feb;10(2): PMID: [PubMed - indexed for MEDLINE] Theory predicts that retinal image size will vary with wavelength. However, this chromatic difference of magnification (CDM) is likely to be very small (< 1% between 400 and 700 nm) under natural viewing conditions. There has been only one attempt to measure CDM experimentally, and the results were inconsistent with optical theory. Using a technique described by Ogle [Research in Binocular Vision, Hafner, New York (1964)], which is sensitive to even small interocular differences in retinal image size, we measured the apparent tilts in the frontoparallel plane induced by interocular differences in wavelength. We obtained the ocular CDM by determining the afocal lens magnification necessary to cancel the apparent frontoparallel plane tilt caused by interocular differences in wavelength. We show that (1) the ocular CDM can be 42

43 considerably less than theoretical model predictions, (2) the relationship among delta Rx (wavelength-dependent refractive error), CDM, and pupil position is consistent with our theoretical model, (3) CDM increases considerably when an artificial pupil in front of the eye is used, (4) the location of the anterior nodal point of the eye may be inferred from the data, and (5) unlike in the case for delta Rx, large intersubjective differences may exist for CDM. The results suggest caution in the use of artificial pupils experimentally with polychromatic stimuli because of amplification of CDM and concomitant losses of image contrast Ye M, Bradley A, Thibos LN, Zhang X. The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles- Crawford effect and chromatic aberrations. Vision Res Nov;32(11): PMID: [PubMed - indexed for MEDLINE] Several studies have reported that the magnitude of chromostereopsis changes as the pupil size changes. Einthoven's theory, that chromostereopsis is determined by interocular differences of monocular transverse chromatic aberration, can not easily explain this change. Therefore, several alternative hypotheses have been introduced, most notably by Vos [(1960) Vision Research, 6, ], who argues that shifts in chromostereopsis with pupil size are due to decentration of the peak of the Stiles- Crawford effect (SCE) with respect to the pupil. We tested this hypothesis by measuring chromostereopsis under both scotopic (no SCE) and photopic conditions with centered and decentered artificial pupils. The results show that the SCE plays an important role in the effect of pupil size on chromostereopsis. Similar changes were also measured in monocular chromatic diplopia which supports the hypothesis that the effect of pupil size on chromostereopsis is due to monocular mechanisms Atchison DA, Ye M, Bradley A, Collins MJ, Zhang X, Rahman HA, Thibos LN. Chromatic aberration and optical power of a diffractive bifocal contact lens. Optom Vis Sci Oct;69(10): PMID: [PubMed - indexed for MEDLINE] Although diffractive contact lenses have been well documented in theory, no definitive experimental data have been reported which confirm that the near image is in fact created by diffraction rather than by refraction. We have tested the diffraction hypothesis for one type of diffractive contact lens (the Hydron Echelon bifocal) experimentally by measuring its longitudinal chromatic aberration in isolation and when worn on the eye. The basis of this test is that, according to theory, diffractive lenses should have chromatic aberration which is opposite in sign to that measured for the eye. Objective measurements of chromatic aberration were made with a focimeter when the lens was in a wet cell. Subjective measurements were made with a Badal optometer when the lens was worn on the eye. Four control experiments were conducted to provide baseline measurements of the eye's chromatic aberration, against which we compared the results obtained for the diffractive contact lens. The data were also compared with conventional measurements of refractive error obtained by standard subjective techniques and by an automated infrared refractor. Our results showed that the longitudinal chromatic aberration of the diffraction image of the Echelon bifocal lens was about one-half that obtained under the four control conditions: for the naked eye, 43

44 for the nondiffraction image of the Echelon lens, or for either image of a refractive bifocal contact lens (CIBA Bisoft). These results are consistent with the theoretical prediction that the negative chromatic aberration of a diffractive contact lens should partially cancel the positive chromatic aberration of the human eye.(abstract TRUNCATED AT 250 WORDS) 102. Bradley A, Zhang X, Thibos L. Failures of isoluminance caused by ocular chromatic aberrations. Appl Opt Jul 1;31(19): doi: /AO PMID: [PubMed - in process] Using a simple model eye with a wavelength-dependent diffraction, a wavelengthdependent refractive error (chromatic difference in refractive error), and a wavelengthdependent 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 Thibos LN, Ye M, Zhang X, Bradley A. The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans. Appl Opt Jul 1;31(19): doi: /AO PMID: [PubMed - in process] 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 chromaticeye model provides an improved account of both the longitudinal and transverse forms of ocular chromatic aberration Thibos LN, Kirschen DG. Electronic submission of abstracts for the annual meeting of the American Academy of Optometry. Optom Vis Sci Jul;69(7): PMID: [PubMed - indexed for MEDLINE] Recently the American Academy of Optometry conducted a 2-year trial in which abstracts submitted for presentation at the Annual Meeting could be transmitted to the Academy in electronic form. Electronic submission has many advantages for the author as well as for the Academy and therefore has now been endorsed as the preferred 44

45 method of submission for future meetings. Step-by-step procedures for electronic submission are described Thibos LN, Bradley A. Use of interferometric visual stimulators in optometry. Ophthalmic Physiol Opt Apr;12(2): PMID: [PubMed - indexed for MEDLINE] Professor Fergus Campbell and colleagues pioneered the use of the interferometric visual stimulator as a tool for separating optical from neural factors which limit spatial vision. The device is now commercially available as a clinical instrument which 'bypasses the optics of the eye' to measure the potential visual acuity of the neural portion of the visual system. However, the clinician needs to be aware of limitations of current instrument designs and recent advances in our understanding of peripheral vision, to correctly interpret patient data gathered with these devices Bradley A, Thibos L, Wang YZ, Haggerty K, Poorman A. Imaging FWC. Ophthalmic Physiol Opt Apr;12(2):128. No abstract available. PMID: [PubMed - indexed for MEDLINE] 107. Anderson RS, Wilkinson MO, Thibos LN. Psychophysical localization of the human visual streak. Optom Vis Sci Mar;69(3): PMID: [PubMed - indexed for MEDLINE] In a topographical study of the human retina, Curcio and Allen documented the presence of the human visual streak, which they described as a prominent nasotemporal asymmetry in ganglion cell density. This asymmetry could also be expected to be measurable in any visual function limited by ganglion cell density. By using an interferometer we sought to test the hypothesis of Thibos et al. that peripheral resolution acuity is limited by the spacing of ganglion cells and should therefore reflect the anatomical asymmetry of the visual streak, once the attenuating effects of the eye's optics have been removed. This proved to be the case and differences predicted by a ganglion cell density of 2:1 were easily measurable. This study has potential clinical implications for the detection of disease or abnormalities of the visual system that cause death or dysfunction of retinal ganglion cells Bradley A, Zhang XX, Thibos LN. Achromatizing the human eye. Optom Vis Sci Aug;68(8): Review. PMID: [PubMed - indexed for MEDLINE] Ocular chromatic dispersion manifests itself as wavelength-dependent image planes, image sizes, and image positions, and it has been suggested that ocular chromatic aberration is the most important of the eye's optical aberrations. Most attempts to correct for the eye's chromatic aberration (achromatize the human eye) have concentrated on correcting the wavelength-dependent image planes or chromatic difference of refractive error (CDRx). There are two optical techniques that correct for CDRx (special achromatizing lenses and multiple channel display systems) by making the ocular image planes of all wavelengths coincident. A different approach simply avoids the effects of ocular CDRx by using small pupils which effectively make all images diffraction-limited irrespective of wavelength-dependent differences in image 45

46 planes. Theoretical and experimental evidence shows that achromatizing lenses provide an accurate correction for CDRx. In spite of the pre-eminence of chromatic aberrations, and the effectiveness of the corrections, no obvious improvements in vision accompany correction. We show that loss of retinal image quality due to CDRx may be subthreshold (less than ocular depth of focus). We also show that achromatizing methods can introduce their own chromatic aberrations that can easily exceed those present in the uncorrected eye. The precise location of the eye with respect to the achromatizing device determines the amount of these additional aberrations. Therefore, in order to achromatize the eye effectively, careful control of eye position is essential Thibos LN, Bradley A, Zhang XX. Effect of ocular chromatic aberration on monocular visual performance. Optom Vis Sci Aug;68(8): Review. PMID: [PubMed - indexed for MEDLINE] 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 Thibos LN, Bradley A, Still DL. Interferometric measurement of visual acuity and the effect of ocular chromatic aberration. Appl Opt Jun 1;30(16): doi: /AO PMID: [PubMed - in process] Ocular chromatic aberration is expected on theoretical grounds to affect the quality of polychromatic interference fringes generated on the retina if the interferometer is not perfectly centered on the eye's visual axis. Of primary concern is a loss of contrast resulting from wavelength-dependent phase shifts of the fringes. By using an interferometer with just two wavelengths of light, we demonstrated this phase shift directly and measured its magnitude as a function of interferometer displacement. Then, using white-light fringes we measured visual acuity and found a threefold loss of acuity when the light from the interferometer entered the eye near the margin of the pupil. These results are consistent with predictions based on a simple optical model of ocular chromatic aberration Zhang XX, Thibos LN, Bradley A. Relation between the chromatic difference of refraction and the chromatic difference of magnification for the reduced eye. Optom Vis Sci Jun;68(6): PMID: [PubMed - indexed for MEDLINE] We provide a simple model for calculating the chromatic difference of magnification for the human eye. Spectral differences in image size are proportional to the eye's longitudinal chromatic aberration and the axial distance between the entrance pupil and 46

47 nodal point. We verify that the model provides magnification estimates equal to previously published predictions, and we show the significant increase in this aberration produced by experimental use of artificial pupils Zhang XX, Bradley A, Thibos LN. Achromatizing the human eye: the problem of chromatic parallax. J Opt Soc Am A Apr;8(4): PMID: [PubMed - indexed for MEDLINE] Attempts to correct the chromatic difference of focus of the human eye will introduce unwanted chromatic parallax if the eye is misaligned with the optical axis of the achromatizing system. Using geometrical optics, we show that the amount of parallax is approximately proportional to the amount of misalignment of the eye, with the constant of proportionality equal to the eye's chromatic difference of refractive error. This prediction was confirmed by the experimental determination of chromatic parallax for two commercially available achromatizing lenses. On the basis of these results, we calculated that anticipated improvements in the polychromatic modulation transfer function of the eye offered by achromatizing lenses will be canceled by approximately 0.4 mm of the misalignment between the lens and the eye. Our prediction that further misalignment would severely reduce image quality of the achromatized eye was verified by psychophysical measurements of contrast sensitivity Ye M, Bradley A, Thibos LN, Zhang XX. Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils. Vision Res. 1991;31(10): PMID: [PubMed - indexed for MEDLINE] Chromostereopsis has been attributed previously to interocular differences in foveal transverse chromatic aberration (TCA). We tested this hypothesis by measuring chromostereopsis as a function of the separation of small artificial pupils. We also measured the monocular transverse chromatic aberration under the same conditions. Our results show that chromostereopsis with small pupils can be precisely accounted for by the interocular difference in monocular transverse chromatic aberration. This relationship is closely predicted by a simple water eye model Bradley A, Thibos L, Still D. Visual acuity measured with clinical Maxwellian-view systems: effects of beam entry location. Optom Vis Sci Nov;67(11): PMID: [PubMed - indexed for MEDLINE] Maxwellian-view projection systems are used clinically to evaluate visual acuity in cataract patients because they allow the clinician to direct a beam of light around any localized opacity. However, theory predicts that, as the beam is displaced from the visual axis, acuity will suffer with those instruments using white light due to the effects of ocular chromatic aberration. Using three commercially available Maxwellian-view instruments, we examined the decline of visual acuity with beam decentration in the clear pupil of normal subjects. With all three instruments (Lotmar interferometer, Randwal interferometer, and the Potential Acuity Meter) acuity fell by a factor of 3 for beams placed near the edge of a dilated pupil. Control experiments with monochromatic light indicated that lateral chromatic aberration was the primary cause of acuity loss with the two interferometers, but other off-axis aberrations also contributed to the acuity loss 47

48 with the Potential Acuity Meter. A detailed analysis of the beam in the pupil plane indicates that the beam's complex structure may be altered if the beam strikes the iris or an opacity in the ocular media. These findings indicate that potential acuity may be significantly underestimated with polychromatic Maxwellian-view systems Thibos LN. Optical limitations of the Maxwellian view interferometer. Appl Opt Apr 1;29(10): doi: /AO PMID: [PubMed - in process] Le Grand's technique for producing interference fringes directly on the retina was analyzed to determine the effect of ocular chromatic aberration on fringe parameters. For monochromatic light, fringe period is largely independent of refractive index of the ocular medium and of the axial location of the interferometer relative to the eye. Lateral displacement of the interferometer, however, shifts the retinal fringes by an amount which depends on wavelength. To close approximation, the relative shift between fringes of different colors is directly proportional to the amount of lateral displacement of the instrument, with the constant of proportionality equal to the longitudinal chromatic aberration of the eye. The net effect is a significant loss of retinal contrast for polychromatic fringes Thibos LN, Bradley A, Still DL, Zhang X, Howarth PA. Theory and measurement of ocular chromatic aberration. Vision Res. 1990;30(1): PMID: [PubMed - indexed for MEDLINE] We have determined the transverse chromatic aberration of the human eye by measuring the apparent offset of a two-color vernier viewed foveally through a displaced, pinhole aperture. For the same subjects, we also determined the longitudinal chromatic aberration for foveal viewing by the method of best focus. In both cases, the results were closely predicted by a simple, reduced-eye optical-model for which transverse and longitudinal chromatic aberration are directly proportional, with the constant of proportionally being the amount of displacement of the pinhole from the visual axis. Further measurements revealed that the natural pupil was closely centered on the visual axis for two subjects and slightly displaced in the temporal direction for three other subjects. 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 Howarth PA, Zhang XX, Bradley A, Still DL, Thibos LN. Does the chromatic aberration of the eye vary with age? J Opt Soc Am A Dec;5(12): PMID: [PubMed - indexed for MEDLINE] The longitudinal chromatic aberration of the eye has been reported to decline with age. Using three different methods, we have measured the aberration in a group of young subjects (27-33 years old) and a group of older subjects (48-72 years old). In two of the methods we used a Badal optometer, either with or without an achromatizing lens incorporated, to examine the effect of wavelength on refractive error. In the third method we used a vernier-alignment apparatus to assess chromatic dispersion directly. None of the results of the experiments performed revealed any difference in aberration between 48

49 the groups. Furthermore, a linear regression of aberration against age showed no relationship between these variables. We conclude that, for human adults, the magnitude of chromatic aberration is independent of age Thibos LN. Calculation of the influence of lateral chromatic aberration on image quality across the visual field. J Opt Soc Am A Aug;4(8): PMID: [PubMed - indexed for MEDLINE] The magnitude of lateral chromatic aberration and its effect on image contrast were computed for a modified, reduced-eye model of the human eye, using geometrical optics. The results indicate that lateral chromatic aberration is a major factor affecting image quality for obliquely incident rays of polychromatic light. Modulation transfer functions for white sinusoidal gratings decline monotonically with spatial frequency, with eccentricity of the stimulus in the peripheral visual field, with grating orientation relative to the visual meridian, and with decentering of the pupil. Image contrast is largely independent of the color temperature of white light over the range 2800 to 12,000 K, but it improves significantly for the polychromatic green light of the P-31 oscilloscope phosphor. Selective filtering by macular pigment increases image contrast by an amount that grows with spatial frequency to about a factor of 1.5 at the foveal resolution limit. Reduced contrast caused by lateral chromatic aberration accounts for most of the threefold loss of acuity that occurs for foveal viewing through a decentered pupil. The aberration probably has negligible effect on peripheral acuity but may act to limit aliasing of peripheral patterns Thibos LN, Cheney FE, Walsh DJ. Retinal limits to the detection and resolution of gratings. J Opt Soc Am A Aug;4(8): PMID: [PubMed - indexed for MEDLINE] The maximum spatial frequency for the detection and resolution of sinusoidal gratings was determined as a function of stimulus location across the visual field. Stimuli were produced directly on the retina as interference fringes, thus avoiding possible loss of image quality, which may occur when the optical system of the eye is used to form the retinal image. Contrary to earlier reports, we found that subjects could detect gratings with spatial frequencies much higher than the resolution limit. At 5 degrees of eccentricity from the fovea, the detection limit was about three times the resolution limit, and this factor increased to about 10 as the test stimulus was moved 35 degrees into the periphery. Quantitative comparison of the data with retinal anatomy and physiology suggests that pattern resolution is limited by the spacing of primate beta (midget) retinal ganglion cells, whereas pattern detection is limited by the size of individual cones Thibos LN, Walsh DJ, Cheney FE. Vision beyond the resolution limit: aliasing in the periphery. Vision Res. 1987;27(12): PMID: [PubMed - indexed for MEDLINE] Pattern resolution is generally considered a prerequisite for spatial vision because details too fine to be resolved cannot be distinguished from a uniform field. However, our experiments using peripheral vision demonstrate that reliable pattern detection is possible for images far beyond the resolution limit. The visual percept which arises in this case is an illusion called aliasing in which the apparent spatial structure of the 49

50 stimulus is quite different from that actually present. Aliasing begins at spatial frequencies just above the classical resolution limit, which is taken as evidence that peripheral resolution is limited by the coarse spacing of visual neurons rather than by increased size of their receptive fields. At a given eccentricity, the very finest pattern which produces aliasing has a spatial period which approaches the smallest anatomical dimension: the diameter of a single cone photoreceptor Thibos LN, Levick WR. Orientation bias of brisk-transient y-cells of the cat retina for drifting and alternating gratings. Exp Brain Res. 1985;58(1):1-10. PMID: [PubMed - indexed for MEDLINE] Brisk-transient ganglion cells of the cat's retina were examined for orientation bias using two different stimuli: drifting gratings and alternating gratings, both of fixed contrast (50%) and fixed temporal frequency (2 Hz). Some cells were strongly biased for both stimuli; some were not biassed for either while still others were strongly biased for only one or other stimulus. The preferred orientations for the two types of grating tended to be the same, on average, but substantial differences were not uncommon. A systematic preference for radially-oriented gratings was evident when the stimulus was drifting but there was an additional preference for tangentially-oriented gratings when the stimulus was alternating. Orientation bias for drifting gratings often extended over a broad range of spatial frequencies and was maximum near the resolution limit. For alternating gratings, bias was evident only at the highest spatial frequencies. Results indicate that the arrangement of receptive field components responsible for linear and nonlinear kinds of behaviour may sometimes possess different axes of symmetry Levick WR, Thibos LN, Cohn TE, Catanzaro D, Barlow HB. Performance of cat retinal ganglion cells at low light levels. J Gen Physiol Sep;82(3): PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article Responses of brisk-sustained cat retinal ganglion cells were examined using receiver operating characteristic (ROC) analysis. Stimuli were brief luminance changes superimposed upon a weak steady pedestal ranging from 27 to 47,000 quanta (507 nm) per second at the cornea. Overall quantum efficiencies of cells ranged up to approximately 13% and were compatible with previous estimates at absolute threshold. The main work was done on on-center cells, but a small sample of off-center units behaved similarly. Experimental ROC curves verified a set of qualitative predictions based on a theoretical treatment of performance, assuming that response variability resulted solely from quantum fluctuations. However, quantitative predictions were not fulfilled. The discrepancy could be resolved by postulating a source of added internal variance, R, the value of which could then be deduced from the experimental measurements. A ganglion cell model limited by a fixed amount of added variance from physiological sources and having access to a fixed fraction of incident quanta can account quantitatively for (a) slopes of ROC curves, (b) variation of detectability with magnitude of both increments and decrements, and (c) performance over a range of pedestal intensities. Estimates of the proportion of incident quanta used ranged up to 29% under some conditions, a figure approximately matching estimates of the fraction of corneal quanta that isomerize rhodopsin in the cat. 50

51 123. Thibos LN, Levick WR. Bimodal receptive fields of cat retinal ganglion cells. Vision Res. 1983;23(12): PMID: [PubMed - indexed for MEDLINE] Receptive fields of cat retinal ganglion cells were stimulated by a drifting, sinusoidal luminance pattern of fixed contrast. The amplitudes and phases of the harmonic components in the response were determined as a function of spatial frequency. For most cells, the graphs of response vs spatial frequency (when plotted on linear scales) were unimodal and skewed towards zero frequency for all stimulus orientations. However, some cells had bimodal frequency response functions when the stimulus was in the non-preferred orientation. These unusual cells also exhibited a sudden phasereversal of pi radians which occurred at the frequency of the changeover between the two modes. Calculations based on the experimental data predicted two distinctly separate regions of high sensitivity within the receptive centres of such cells. A narrow bar stimulus was used to confirm that the receptive fields had, in effect, double centres Thibos LN, Levick WR. Spatial frequency characteristics of brisk and sluggish ganglion cells of the cat's retina. Exp Brain Res. 1983;51(1): PMID: [PubMed - indexed for MEDLINE] Receptive fields of cat retinal ganglion cells were stimulated by a drifting sinusoidal luminance pattern of fixed (50%) contrast and the amplitude of the fundamental frequency component of response was determined as a function of spatial frequency. Frequency response functions for most cells were unimodal and skewed towards zero frequency when plotted on linear scales. At a fixed retinal location, cells of different classes had different frequency response functions. Heterogeneity within some of the classes could be largely removed by normalizing the axes, thus, revealing a common shape of function for the class. At a fixed retinal location, the maximum response obtained at each spatial frequency was always obtained from a cell of the brisk, rather than sluggish, classes. Spatial frequency resolution was highest for brisk-sustained cells and usually lowest for brisk transient cells Levick WR, Thibos LN. Analysis of orientation bias in cat retina. J Physiol Aug;329: PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article 1. Responses of cat retinal ganglion cells to a drifting sinusoidal grating stimulus were measured as a function of the grating orientation and spatial frequency.2. The response at fixed frequency and contrast varied with orientation in the manner of a cosine function. A new measure was introduced to quantify this orientation bias in the response domain on an absolute scale of 0-100%. Under experimental conditions designed to maximize the effect, the mean bias for 250 cells was 16% and the range was 0-46%. In 70% of cells there was significant bias.3. Orientation bias varied with spatial frequency and was maximal near the high-frequency limit. The majority of biassed cells preferred the same orientation at high and low frequencies but in some cells a reversal occurred: the orientation which gave maximum response at high frequencies gave minimum response at low frequencies. The greatest variation of cut-off frequency with orientation was (2/3) octave.4. Orientation bias was due to neural, not optical, factors. 51

52 Nevertheless, the phenomenon could often be imitated by deliberately introduced optical astigmatism of up to 4 dioptres for brisk-sustained units and over 10 dioptres for brisk-transient units.5. The grating orientation preferred by cells varied systematically with position in the visual field. The central tendency was for the grating which yielded maximum response to lie parallel to the line joining the cell to the area centralis. This generalization failed for units within 2 degrees of the centre of the area centralis.6. Analysis of orientation bias indicates a functional asymmetry of receptive fields such that the centre mechanism, and sometimes also the surround mechanism, is elongated along the line joining cell to area centralis Thibos LN, Levick WR. Astigmatic visual and deprivation in cat: behavioral, optical and retinophysiological consequences. Vision Res. 1982;22(1): PMID: [PubMed - indexed for MEDLINE] Kittens were deprived of clear vision in one eye only by +7D or -7D cylindrical lenses worn from eye opening until 7.5 months of age. Behavioral measurements subsequently demonstrated diminished acuity through the affected eye relative to the opposite control eye. However, single unit recordings at 3.5 years of age from retinal ganglion cells located within 1-11 degrees of the centre of the area centralis showed neither loss of grating resolution nor any abnormal orientation bias. Furthermore, the astigmatic rearing had minimal effect on the development of the cat's natural optics to the emmetropic state. The experiments indicate that the amblyopic defect induced by the cylindrical lenses occurs in the brain rather than the eye Vaney DI, Levick WR, Thibos LN. Rabbit retinal ganglion cells. Receptive field classification and axonal conduction properties. Exp Brain Res. 1981;44(1): PMID: [PubMed - indexed for MEDLINE] The classification of concentrically organized receptive fields of rabbit retinal ganglion cells was extended along similar lines to that in the cat by distinguishing brisk and sluggish classes and then sustained and transient types of each. Quantitative measures of responsiveness to stationary and to moving stimuli revealed characteristic features which distinguished these classes. Brisk-transient and brisk-sustained classes are not as distinct from each other as in the cat: centre size distributions overlapped almost completely and there was also substantial overlap of axonal conduction properties whether expressed in terms of latency or conduction velocity between two central stimulus sites. Representatives of every class of rabbit ganglion cells sent axons to the superior colliculus Levick WR, Thibos LN. Orientation bias of cat retinal ganglion cells. Nature Jul 24;286(5771): PMID: [PubMed - indexed for MEDLINE] Kuffler described the receptive fields of cat retinal ganglion cells as having a concentric arrangement. This has usually been taken to mean that they are approximately circular in form (see, for example, ref. 2). Hammond tested the circularity of the centre component of receptive fields by plotting a contour of isosensitivity to a small flashed spot. He concluded that centres were often ellipitical (average ratio of major to minor axis 1.23) and that more than 50% of the recorded cells had the major axis oriented 52

53 within /+- 20 degrees of the horizontal. Such data are important for discussions of the neurophysiological basis of the 'oblique effect' (reduced visibility for periodic grating patterns when oriented away from the vertical or horizontal) observed in psychophysical experiments on humans because subcortical units are often assumed to be orientationally unbiased. Orientation selectivity is a prominent attribute of visual cortical neurones so analysis has usually emphasized the distribution of orientation selectivity at that level. The results presented here redirect attention to the retinal level since they reveal a previously unsuspected systematic relation between orientation bias of ganglion cells and their location relative to the area centralis Thibos LN, Levick WR, Morstyn R. Ocular pigmentation in white and Siamese cats. Invest Ophthalmol Vis Sci May;19(5): PMID: [PubMed - indexed for MEDLINE] Free full text Ocular pigmentation in white cats with blue and yellow eyes and in Siamese cats was examined ophthalmoscopically and histologically. Yellow-eyed white cats had entirely normal ocular pigmentation. Blue eyes of white cats had normal pigmentation of the iridial and retinal pigment epithelia but no stromal pigmentation of the iris or choroid. This deficit is apparently due to the absence of stromal pigment cells, certainly in the iris. As a general rule, the blue eye of white cats had no tapetum. Siamese cats had reduced pigmentation of the iridial and retinal pigment epithelia and no stromal pigmentation of the iris or choroid. The lack of pigmentation is apparently due to the inability of stromal pigment cells to produce pigment, certainly in the iris. We conclude that the abnormality of visual pathways previously described in the Siamese cat is not due simply to a deficiency of pigment of cells of neural crest origin Levick WR, Thibos LN, Morstyn R.Retinal ganglion cells and optic decussation of white cats. Vision Res. 1980;20(11): No abstract available. PMID: [PubMed - indexed for MEDLINE] 131. Thibos LN, Werblin FS. The response properties of the steady antagonistic surround in the mudpuppy retina. J Physiol May;278: PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article 1. The graded response of bipolar and ganglion cells to test flashes at the receptive field centre, spans only a limited portion of the test intensity domain: more than 90% of the graded response range can be elicited by test flashes differing by less than 100 to In the presence of steady illumination of the receptive field surround, the absolute levels of log test intensities required to elicit 90% of the graded response are increased (reset), but the relation in (1) still applies. 3. Each point in the receptive field surround, when illuminated, contributes to the resetting of the required centre test flash intensities by a weighing that decreases exponentially with distance from the centre. The space constant is 0.25 mm. 4. When the receptive field surround is fully covered with illumination, the centre test flash intensities required to elicit 90% of the response range must be increased by about tenfold for each tenfold increase in surround intensity over a surround intensity domain of about 1000 to The absolute levels of surround and required centre test intensities are inter-related: when the receptive field surround is 53

54 fully covered, a test flash with intensity equal to that of the surround elicits a halfmaximal response. Thus, in the presence of a full field background, the bipolar potential is held near its half-maximum response potential. 6. The graded resetting of the required centre test flash intensities is well correlated with the graded increase in horizontal cell response as the surround intensity and area are varied. It is inferred that units with response and receptive field properties like those of the horizontal cells, when driven by surround illumination, act as interneurones to reset the relationship between required test flash intensity and response in bipolar and ganglion cells Thibos LN, Werblin FS. The properties of surround antagonism elicited by spinning windmill patterns in the mudpuppy retina. J Physiol May;278: PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article 1. A truncated spinning windmill pattern, illuminating only the receptive field surround, shown previously to activate amacrine cells, was used to elicit activity at the inner plexiform layer and to reduce the response of ganglion cells to test flashes at the receptive field centre. 2. The spinning windmill pattern reduced the ganglion cell response over its entire graded range by a fixed amount, and reduced the domain of test intensities required for graded activity. 3. The windmill effect was graded for windmill intensities over a domain of about 1000 to 1. The effect was constant for windmill velocities from about 0.05 to 0.5 rev/sec, and diminished beyond these velocities. 4. The windmill effect varied with windmill area as though each retinal point contributed to the reduction of ganglion cell response with a weighting which fell exponentially from the receptive field centre. The space constant was 0.35 mm. 5. The graded reduction in ganglion cell response was closely correlated with the graded increase in amacrine cell activity when the windmill intensity, area, and velocity were varied. It is inferred that amacrine cells, activated by the windmill, act to reduce the response range of the ganglion cells, primarily through a feed-forward pathway Freeman RD, Thibos LN. Visual evoked responses in humans with abnormal visual experience. J Physiol Jun;247(3): PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article 1. The visual evoked response to a grating target of varying spatial frequency was examined for normal subjects and for subjects with meridional amblyopia. This condition, reduced visual resolution for specific target orientations, is associated with, and thought to result from, marked ocular astigmatism. 2. For normal subjects, the general relation between spatial frequency and the evoked response is similar to psychophysical contrast sensitivity data. Evoked response amplitudes to oblique gratings are typically reduced and this is analogous to the lower acuity for oblique compared to horizontal and vertical detail. 3. In addition to the oblique effect, the magnitude of the evoked response for meridional amblyopes depends upon grating orientation over most of the spatial frequency range tested ( cycles/deg). The lowest evoked amplitude is found when stimulus grating orientation matches that for which acuity is reduced. 4. The evoked potentials spatial frequency response functions are qualitatively similar to contrast sensitivity functions determined with the same 54

55 abnormal subjects. 5. From these results, it may be concluded that the physiological locus of meridional amblyopia is confined primarily to structures at or prior to the site of evoked potential generation Freedman RD, Thibos LN. Contrast sensitivity in humans with abnormal visual experience. J Physiol Jun;247(3): PMID: [PubMed - indexed for MEDLINE] PMCID: PMC Free PMC Article 1. Grating contrast sensitivities have been determined over a range of spatial frequencies for a normal subject and for subjects who are visually biased in that they have a lower resolution capacity for targets of specific orientations. The bias si only found in astigmatic subjects and the grating orientation yielding poorest acuity coincides with the most defocused astigmatic meridian. However this resolution anisotropy remains when optical factors are accounted for. 2. For the normal subject, high and low frequency attenuation is found and a typical reduction in contrast sensitivity is exhibited for oblique target orientations. 3. The biased subjects, called meridional amblyopes because they have reduced acuity for a given grating orientation, show markedly abnormal contrast sensitivity functions. Their cut-off spatial frequencies are different for various target orientations and this difference applies also to contrast sensitivity over nearly the entire spatial frequency range tested ( cycles/deg). The differences are of about the same magnitude for most frequencies and they are found in all types of meridional amblyopes. 4. Optical explanations of these differences are ruled out by laser-interference fringe tests and by varying effective pupil size. 5. Theoretical effects of defocus have been calculated to compare predicted visual deprivation with performance. Results indicate that reduced contrast sensitivity functions can be equivalent to a small defocus effect. 6. To examine the results in the spatial domain, inverse Fourier transforms of representative contrast sensitivity functions have been computed. The optical portion of the resulting spatial weighting functions has been parcelled out to obtain neural spatial weighting functions Cohn TE, Thibos LN, Kleinstein RN. Detectability of a luminance increment. J Opt Soc Am Oct;64(10): No abstract available. PMID: [PubMed - indexed for MEDLINE] 136. Freeman RD, Thibos LN. Electrophysiological evidence that abnormal early visual experience can modify the human brain. Science Jun 15;180(4091):1216. PMID: [PubMed] In the caption of the cover photograph for 25 May 1973, the word "below" is misplaced; it should be deleted from the first sentence, and the second sentence should read: "(Below) Same view taken through a cylindrical lens..." Two errors occurred in the report by Freeman and Thibos in the same issue, p. 876: in column 2, line 4, "Freeman and co-workers" should be changed to "Freeman et al." in column 3, line 44, "the visual resolution" should be changed to "visual resolution"-ed. 55

56 137. Freeman RD, Thibos LN. Electrophysiological evidence that abnormal early visual experience can modify the human brain. Science May 25;180(88): PMID: [PubMed - indexed for MEDLINE] Visual resolution in humans is nearly equal for vertically and horizontally oriented detail, but for some subjects there is a substantial difference in resolving power for these orientations. Although subjects who exhibit this difference invariably have ocular astigmatism, optical explanations of the effect can be ruled out. Direct evidence has been found for an electrophysiological correlate to the psychophysical finding. Subjects who have reduced resolution for a pattern of a particular orientation also show a decreased evoked potential response elicited by a target of the same orientation. The results are consistent with the hypothesis that a deficiency of specific features in the early visual input can alter the organization of the visual pathways. 56