Edwin J. Sarver

Interaction between aberrations to improve or reduce visual performance

Purpose: To investigate how pairs of Zernike modes interact to increase or decrease visual acuity. Setting: Visual Optics Institute, College of Optometry, University of Houston, Houston, Texas, USA. Methods: Subjects read aberrated and unaberrated visual acuity charts 3 times. Each aberrated chart was produced by convolving an aberrated point‐spread function with an unaberrated acuity chart. Point‐spread functions were defined by 4 pairs of Zernike modes. For each pair, 9 combinations were used, ranging from all aberration being loaded into the first mode to all aberration being loaded into the second mode. The root mean square (RMS) wavefront error always totaled 0.25 &mgr;m (6.0 mm pupil), a level similar to the aberration induced by traditional flying small‐spot laser refractive surgeries. Results: For all conditions (except the unaberrated charts), visual acuity decreased. Acuity varied significantly depending on which modes were mixed and the relative contribution of each mode. Modes 2 radial orders apart and having the same sign and angular frequency tended to combine to increase visual acuity. Modes within the same radial order tended to combine to decrease acuity. Conclusions: For low levels of aberration, the RMS wavefront error is not a good predictor of visual acuity. Clinically, it is important to define how aberrations interact to optimize visual performance. New metrics of optical/neural performance that correlate better with clinical measures of visual performance need to be adopted or developed, as well as new clinically viable measures of visual performance that are sensitive to subtle changes in optical performance.

Are All Aberrations Equal

PURPOSE To determine for a fixed RMS error (25 microm, over a 6-mm pupil) how each mode of the normalized Zernike polynomial (second through the fourth radial order) affects high and low contrast logMAR visual acuity. METHODS Three healthy volunteers served as subjects. CTView was used to generate optically aberrated logMAR charts. Accommodation was paralyzed and pupils dilated. The foveal achromatic axis of the eye was aligned to a 3-mm pupil and the eye was optimally refracted. Aberrated acuity charts were read until five letters were missed. Data were normalized for each subject to the acuity obtained by reading unaberrated charts and plotted as letters lost as a function of Zernike mode. RESULTS Defocus (Z2(0)) decreased letter acuity more than astigmatism (Z2(2), Z2(-2)). Coma (Z3(1), Z3(-1)) decreased acuity more than trefoil (Z3(3), Z3(-3)). Spherical aberration (Z4(0)) and secondary astigmatism (Z2(2), Z4(-2)) decreased acuity much more than quadrafoil (Z4(4), Z4(-4)). CONCLUSIONS 1. For an equal amount of RMS error not all coefficients of the Zernike polynomial induce equivalent losses in high and low contrast logMAR acuity. 2. Wavefront error concentrated near the center of the pyramid adversely affects visual acuity more than modes near the edge of the pyramid. 3. Large changes in chart appearance are not reflected in equally large decreases in visual performance (ie, subjects could correctly identify highly aberrated letters). 4. Interactions between modes complicate weighting each Zernike mode for visual impact.

Visual Acuity as a Function of Zernike Mode and Level of Root Mean Square Error

Background. The coefficients of normalized Zernike expansion are orthogonal and reflect the relative contribution of each mode to the total root mean square (RMS) wavefront error. The relationship between the level of RMS wavefront error within a mode and its effect on visual performance is unknown. Purpose. To determine for various levels of RMS wavefront error how each mode of the normalized Zernike expansion for the second, third, and fourth orders affect high- and low-contrast acuity. Methods. Three healthy optimally corrected cyclopleged subjects read aberrated and unaberrated high- and low-contrast logarithm of the minimum angle of resolution acuity charts monocularly through a 3-mm artificial pupil. Acuity was defined by the total number of letters read correctly up to the fifth miss. Aberrated and unaberrated charts were generated using a program called CTView. Six levels of RMS wavefront error were used (0.00, 0.05, 0.10, 0.15, 0.20, and 0.25 &mgr;m). Each level of RMS error was loaded into each mode of the second, third, and fourth radial orders individually for a total of 72 charts. Data were normalized by subject, and the normalized data were averaged across subjects. Results. Across modes and within each mode as the level of RMS wavefront error increased above 0.05 &mgr;m of RMS wavefront error, visual acuity decreased in a linear fashion. Slopes of the linear fits varied depending on the mode. Modes near the center of the Zernike pyramid had steeper slopes than those near the edge. Conclusions. Increasing the RMS error within any single mode of the normalized Zernike expansion decreases visual acuity in a linear fashion. The slope of the best fitting linear equation varies with Zernike mode. Slopes near the center of the Zernike pyramid are steeper than those near the edge. Although the normalized Zernike expansion parcels RMS error orthogonally, the resulting effects on visual performance as measured by visual acuity are not orthogonal. New metrics of the combined effects of the optical and the neural transfer functions that are predictive of visual performance need to be developed.

Image Quality in Myopic Eyes Corrected With Laser in situ Keratomileusis and Phakic Intraocular Lens

PURPOSE To compare image quality due to higher-order aberrations following laser in situ keratomileusis (LASIK) or implantation of phakic intraocular lens (PIOL) to correct high myopia. METHODS Postoperative wavefront examinations, normalized to a pupil size of 5.5 mm, were obtained for 19 LASIK and 20 PIOL eyes for the same surgeon over the same time period. Higher-order aberrations and simulated retinal images were compared. RESULTS For this small sample, the LASIK eyes yielded an average three times more spherical aberration and two times more coma than PIOL eyes. The effects of these differences were visualized using the simulated retinal images. CONCLUSION Spherical aberration and coma are the major differences between postoperative LASIK and PIOL higher-order aberrations, and simulated retinal images can be used to visualize these effects.

Quantifying scatter in Shack-Hartmann images to evaluate nuclear cataract.

PURPOSE Quantify and localize lenticular forward scatter using Shack-Hartmann wavefront sensing (SHWS) as single-valued metrics and a scatter map, and to examine the relationships between forward scatter and backscatter metrics and visual acuity. METHODS We obtained SHWS images from 148 patients in the Texas Investigation of Cataract Optics study. Patient age was 22 to 84 years, with Lens Opacities Classification System III (LOCS III) nuclear opalescence (NO) scores ranging from 0.8 to 5.6. Visual acuities were measured at photopic (280 cd/m2) high (VA(PHC)) and low contrast (VA(PLC)) and mesopic (0.75 cd/m2) high (VA(MHC)) and low contrast (VA(MLC)). Scattering was described in a scatter map and by five single-valued metrics characterizing SHWS lenslet point spread functions. The relationships between scatter and visual acuity were tested using linear regression. RESULTS Visual acuities decreased proportional to both LOCS III NO (R2=up to 39%) and scatter metrics (R2=up to 21%). Stepwise multiple linear regression improved visual acuity prediction by including a backscatter and a forward scatter metric (R2 up to 51.2%). For the subjects over age 60 years (N=46, 68.8+/-6.12 years), the forward scatter metrics explain as much variance in visual acuities (R2=up to 29%) as LOCS III NO (R2=up to 26%). Combined they accounted for up to 48.8% of visual acuity variance. CONCLUSION Forward light scatter can be quantified using SHWS and the resulting metrics explain significant variance in visual acuity, especially in the aging eye. Together with a backscatter metric they explain approximately 50% of the variance in VA.

Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality

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 aberrometers measurement axis must coincide with the eyes line‐of‐sight (LoS). Second, the videokeratographers measurement axis (the vertex normal) must be parallel with the eyes 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 μm 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.

Astigmatic power calculations for intraocular lenses in the phakic and aphakic eye

PURPOSE To develop sets of equations employed in the power calculations for toric intraocular lenses (IOLs) in phakic or aphakic astigmatic eyes. METHODS Mathematical operations to convert from standard toric parameters of sphere, cylinder, and axis to astigmatic decomposition components, and vice versa, are presented. These operations are used to derive equations to calculate the ideal toric IOL power for a phakic or aphakic astigmatic eye, predict the postoperative spectacle correction for a selected toric IOL with power other than the ideal power, and back calculate a parameter to be used to optimize predictability of the calculations based on clinical data. RESULTS Two numerical examples are provided to show how the equations are used with clinical data. CONCLUSION The equations developed provide a method to perform toric IOL power calculations and supporting operations of predicted postoperative spectacle refraction and optimization of prediction error for phakic and aphakic eyes with astigmatism.

Schematic Eye Models for Simulation of Patient Visual Performance

PURPOSE To determine if model eyes can simulate the visual performance of normal human eyes under conditions of varying low myopic blur, pupil size, and contrast. METHODS High and low contrast Bailey-Lovie logMAR visual acuity (VA) of three normal eyes of three subjects were measured for four artificial pupil sizes and ten levels of myopic defocus. Simulated visual acuities were then determined for three model eyes--the Indiana Eye with no spherical aberration, the Indiana Eye with average spherical aberration, and the Kooijman Eye--by generating optically aberrated VA charts for each testing condition using Visual Optics Lab software by Sarver and Associates, Inc, and having the subjects read high resolution printouts of these charts using a 3-mm pupil and optimal spectacle correction. The correlation between real VA and simulated VA was then plotted and a regression line calculated. RESULTS Slopes for the Indiana Eye, Indiana Eye with spherical aberration, and Kooijman Eye were 0.98, 0.98, and 1.01 for high contrast, and 0.92, 0.67, and 0.75 for low contrast, respectively. The r2 values were 0.73, 0.74, and 0.77, for high contrast, and 0.69, 0.40, and 0.50 for low contrast, respectively. Under low contrast conditions the Indiana Eye VA was significantly closer to the real VA than that of the other two models (P<.0003). CONCLUSION Visual performance can be simulated by eye models. The simple single surface Indiana Eye with no spherical aberration best modeled both high and low contrast visual acuity.

Change in visual acuity is highly correlated with change in six image quality metrics independent of wavefront error and/or pupil diameter

It is well known that the wavefront error (WFE) of the eye varies from individual to individual with pupil diameter (PD) and age. Numerous studies have been proposed evaluating the relationship between visual acuity and WFE, but all these studies were performed with either a fixed or natural PD. It is still not clear if metrics of image quality correlate well with visual acuity independent of PD. Here we investigate the correlation between the change in visual acuity and the change in 30 image quality metrics for a range of optical quality typically established in normal eyes that varies both with age and PD. Visual acuity was recorded for 4 normal subjects using simulated blurred logMAR acuity charts generated from the point spread functions of different scaled WFEs for 6 different PDs (2-7 mm in 1 mm steps). Six image quality metrics (log neural sharpness, log visual Strehl [spatial domain], log visual Strehl [MTF method], log pupil fraction [tessellated], log pupil fraction [concentric area], and log root mean square of WFE slope) accounted for over 80% of variance in change in acuity across all WFEs and all PDs. Multiple regression analysis did not significantly increase the R(2). Simple metrics derived from WFE could potentially act as an objective surrogate to visual acuity without the need for complex models.

Modeling and predicting visual outcomes with VOL-3D.

odeling the optics of the eye, and in particular the optics of an individual patients eye, and predicting the resulting visual performance are major goals of visual optics and clinical researchers. The benefits of obtaining these goals include designing new optical corrections, selecting the best available correction to meet a particular patients needs, and demonstrating to the patient likely outcomes of various interventions. We report here our progress in developing a program called Visual Optics Lab – 3D (VOL-3D). The overall goal of the project is to develop for clinical and research use, a user-friendly software program that models and evaluates the optics of a real and/or user defined eye and stores analysis outcomes in a relational database. In developing the program, we followed the same fundamental analysis path as Greivenkamp and colleagues 1 , by constructing an optical model for an individual eye and applying ray-tracing analysis to the composite model. Our techniques go further in that we integrate all the various software functions required to construct a model and analyze its performance into a single program using units and terms familiar to the oph-thalmic and visual optics community. In this paper we demonstrate the methods employed by VOL-3D by building an eye model using a combination of clinical and schematic eye data. We then optically correct the eye using various modes of correction and evaluate and compare the optical performance of each correction mode. MATERIALS AND METHODS For demonstration purposes we constructed a model eye using clinical examination data derived from corneal topography and fill in missing or unavailable data with the parameters of a state-of-the-art schematic eye. To correct the optical defects of the eye, we incorporated into the model, one at a time, a variety of different compensating optics including: a spectacle lens, contact lens, a modified corneal surface, and a phakic intraocular lens (IOL). Forms for the compensating optic included sphere, sphero-cylinder, and higher-order surfaces such as a b-spline or Zernike polynomial expansion. To simulate visual performance and evaluate the optical quality of each model eye and its correction, we generated simulated retinal images, wavefront aberration maps and tables, point spread functions, spot diagrams, modulation transfer functions, and merit function values (eg, Stiles-Crawford root mean square [RMS] spot size (SC-RMS), Strehl ratio, area under the two-dimensional modulation transfer function [MTF], etc.). In this manner several different modes of correction were tested and compared to determine …