Raymond A. Applegate

Accuracy and precision of objective refraction from wavefront aberrations

We determined the accuracy and precision of 33 objective methods for predicting the results of conventional, sphero-cylindrical refraction from wavefront aberrations in a large population of 200 eyes. Accuracy for predicting defocus (as specified by the population mean error of prediction) varied from -0.50 D to +0.25 D across methods. Precision of these estimates (as specified by 95% limits of agreement) ranged from 0.5 to 1.0 D. All methods except one accurately predicted astigmatism to within +/-1/8D. Precision of astigmatism predictions was typically better than precision for predicting defocus and many methods were better than 0.5D. Paraxial curvature matching of the wavefront aberration map was the most accurate method for determining the spherical equivalent error whereas least-squares fitting of the wavefront was one of the least accurate methods. We argue that this result was obtained because curvature matching is a biased method that successfully predicts the biased endpoint stipulated by conventional refractions. Five methods emerged as reasonably accurate and among the most precise. Three of these were based on pupil plane metrics and two were based on image plane metrics. We argue that the accuracy of all methods might be improved by correcting for the systematic bias reported in this study. However, caution is advised because some tasks, including conventional refraction of defocus, require a biased metric whereas other tasks, such as refraction of astigmatism, are unbiased. We conclude that objective methods of refraction based on wavefront aberration maps can accurately predict the results of subjective refraction and may be more precise. If objective refractions are more precise than subjective refractions, then wavefront methods may become the new gold standard for specifying conventional and/or optimal corrections of refractive errors.

Comparison of corneal wavefront aberrations after photorefractive keratectomy and laser in situ keratomileusis.

PURPOSE To compare changes in the corneal wavefront aberrations after photorefractive keratectomy and laser in situ keratomileusis. METHODS In a prospective randomized study, 22 patients with bilateral myopia received photorefractive keratectomy on one eye and laser in situ keratomileusis on the other eye. The procedure assigned to each eye and the sequence of surgery for each patient were randomized. Corneal topography measurements were performed preoperatively, 2 and 6 weeks, 3, 6, and 12 months after surgery. The data were used to calculate the wavefront aberrations of the cornea for both small (3-mm) and large (7-mm) pupils. RESULTS Both photorefractive keratectomy and laser in situ keratomileusis significantly increased the total wavefront aberrations for 3- and 7-mm pupils, and values did not return to the preoperative level throughout the 12-month follow-up period. For a 3-mm pupil, there was no statistically significant difference between photorefractive keratectomy and laser in situ keratomileusis at any postoperative point. For a 7-mm pupil, the post-laser in situ keratomileusis eyes exhibited significantly larger total aberrations than the post-photorefractive keratectomy eyes, where a significant intergroup difference was observed for spherical-like aberration, but not for coma-like aberration. This discrepancy seemed to be attributable to the smaller transition zone of the laser ablation in the laser in situ keratomileusis procedure. Before surgery, simulated pupillary dilation from 3 to 7 mm caused a five- to six-fold increase in the total aberrations. After surgery, the same dilation resulted in a 25- to 32-fold increase in the photorefractive keratectomy group and a 28- to 46-fold increase in the laser in situ keratomileusis group. For a 3-mm pupil, the proportion of coma-like aberration increased after both photorefractive keratectomy and laser in situ keratomileusis. For a 7-mm pupil, coma-like aberration was dominant before surgery, but spherical-like aberration became dominant postoperatively. CONCLUSIONS Both photorefractive keratectomy and laser in situ keratomileusis increase the wavefront aberrations of the cornea and change the relative contribution of coma- and spherical-like aberrations. For a large pupil, laser in situ keratomileusis induces more spherical aberrations than photorefractive keratectomy. This finding could be attributable to the smaller transition zone of the laser ablation in the laser in situ keratomileusis procedure.

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.

Metrics of optical quality derived from wave aberrations predict visual performance

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

Corneal First Surface Optical Aberrations and Visual Performance

PURPOSE Wavefront analysis has demonstrated that refractive surgery-induced corneal first surface aberrations are large, are dominated by symmetric aberrations (spherical-like aberrations), and are correlated to measures of visual performance. It is not clear whether the correlation between corneal first surface aberrations and visual performance can be generalized to other corneal conditions where large asymmetric aberrations (coma-like aberrations) may dominate the aberration structure. The purpose of the research reported here was to determine the general utility of corneal first surface wavefront analysis in predicting visual performance. METHODS Patients were 13 normals and 78 patients with a variety of corneal conditions including surgically removed pterygia, penetrating keratoplasty, keratoconus, radial keratotomy, laser in situ keratomileusis, and others. Videokeratographs were taken for all patients and used to calculate corneal first surface wavefront variance for 3 and 7 mm pupils. Similarly, visual performance was quantified by measurements of contrast sensitivity and high and low contrast acuities through both 3 and 7 mm pupils. RESULTS Statistically significant correlations existed between all three measures of visual performance and the corneal wavefront variance. All relationships were stronger for the 7 mm diameter-pupil condition than the 3 mm pupil. CONCLUSION Regardless of the cause, corneas with increased wavefront variance showed a quantifiable decrease in visual performance that was pupil size dependent.

Corneal Aberrations and Visual Performance After Radial Keratotomy

BACKGROUND Refractive surgery and videokeratography have allowed us to study the effects on visual performance of relatively large changes in corneal aberration structure induced by surgical changes in corneal shape. METHODS We quantified in one eye of nine normal and 23 radial keratotomy patients, the area under the log contrast sensitivity function (AULCSF) and corneal first surface wavefront variance for two artificial pupil sizes (3 and 7 mm). Contrast sensitivity was measured with sine-wave gratings at six spacial frequencies. Wavefront variance was derived from videokeratographs using Zernike polynomials. RESULTS For normals eyes there were no significant changes over time. For eyes that had radial keratotomy, there were significant pupil size-dependent changes. For the 3 mm pupil, there were significant surgery-induced changes in the corneal wavefront variance which became large (approximately 30 times preoperative values) at 7 mm. Significant correlated changes in AULCSF for the 7 mm pupil but not for the 3 mm pupil occurred immediately following surgery and remained. CONCLUSIONS Radial keratotomy, like photorefractive keratectomy, shifts the distribution of aberrations from third order dominance (coma-like aberrations) to fourth order dominance (spherical-like aberrations). Radial keratotomy-induced aberrations and loss in contrast sensitivity are reduced with increasing clear zone diameter. Radial keratotomy induces an increase in the optical aberrations of the eye and the increase for large pupils (7 mm) but not small (3 mm) is correlated to a decrease in contrast sensitivity.

A population study on changes in wave aberrations with accomodation

Wave aberrations were measured with a Shack-Hartmann wavefront sensor (SHWS) in the right eye of a large young adult population when accommodative demands of 0, 3, and 6 D were presented to the tested eye through a Badal system. Three SHWS images were recorded at each accommodative demand and wave aberrations were computed over a 5-mm pupil (through 6th order Zernike polynomials). The accommodative response was calculated from the Zernike defocus over the central 3-mm diameter zone. Among all individual Zernike terms, spherical aberration showed the greatest change with accommodation. The change of spherical aberration was always negative, and was proportional to the change in accommodative response. Coma and astigmatism also changed with accommodation, but the direction of the change was variable. Despite the large inter-subject variability, the population average of the root mean square for all aberrations (excluding defocus) remained constant for accommodative levels up to 3.0 D. Even though aberrations change with accommodation, the magnitude of the aberration change remains less than the magnitude of the uncorrected aberrations, even at high accommodative levels. Therefore, a typical eye will benefit over the entire accommodative range (0-6 D) if aberrations are corrected for distance viewing.

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.

Parametric representation of Stiles-Crawford functions: normal variation of peak location and directionality

Evidence suggests that the psychophysically determined Stiles-Crawford effect of the first kind (SCE) reflects waveguide properties of human photoreceptors. The peak of the SCE data set is assumed to reflect the principal alignment tendencies, and the spread (e.g., rho value, the curvature or width at half-height) is assumed to reflect the directionality (i.e., interreceptor differences in alignment) of the population of photoreceptors being tested. As such, disruption of the normal SCE can be used and/or has been used (1) to document early natural history of retinal pathology involving the photoreceptors, (2) to provide a firm rationale for therapeutic intervention, and (3) to provide a method for monitoring therapies designed to alter the natural course of retinal-disease processes. We report large-sample norms for foveal SCE peak location and spread (horizontal peak location, nasal 0.51 +/- 0.72, horizontal rho value 0.047 +/- 0.013, vertical peak location, superior 0.20 +/- 0.64, vertical rho value 0.053 +/- 0.012), compare these norms with values determined in other laboratories, and discuss the various mathematical forms used for the empirical description of SCE data sets.

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.