PERSPECTIVE THE PRESENCE OF OPTICAL ABERRATIONS THAT BLUR. Making Sense Out of Wavefront Sensing

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1 PERSPECTIVE Making Sense Out of Wavefront Sensing JAY S. PEPOSE, MD, PHD AND RAYMOND A. APPLEGATE, OD, PHD THE PRESENCE OF OPTICAL ABERRATIONS THAT BLUR retinal images were the subject of popular lectures by Helmholtz in the 1860s, and led him to state: Now, it is not too much to say that if an optician wanted to sell me an instrument which had all these defects, I should think myself justified in blaming his carelessness in the strongest terms and giving him back his instrument. 1 Recently, the availability of wavefront aberrometers in the clinical setting and wavefront-guided vision correction has rekindled an intense interest in the optical aberrations of the eye and in particular those aberrations that cannot be corrected with traditional sphero-cylindrical lenses. In this Perspective, we will review the concept of optical aberration (wavefront error) of the eye, factors influencing retinal image quality, factors contributing to the visual percept, and evaluation of visual performance. We provide this review to set a common stage on which to examine a series of questions. It is our hope that the responses to these questions will facilitate the application of wavefront sensing to: (1) truly customize wavefront guided corrections to a patient s needs; and (2) understand the factors influencing visual performance and the measurement of visual performance in the age of wavefront guided corrections. REVIEW OF BASIC CONCEPTS: An optical aberration in an imaging system is any ray of light that is misdirected from its desired image point. As the number of rays that are Accepted for publication Nov 2, From the Pepose Vision Institute, St. Louis, Missouri and the Department of Ophthalmology and Visual Sciences, Washington University School of Medicine, St. Louis, Missouri (J.S.P.); and the College of Optometry, Visual Optics Institute, University of Houston, Houston, Texas (R.A.A.). This work was supported in part by NIH grant EY R (R.A.A.), CORE Grant NIH/NEI EY07551 to the College of Optometry, University of Houston, University of Houston HEAF funds, and The Visual Optics Institute at the College of Optometry, University of Houston, and The Midwest Cornea Research Foundation, St. Louis, Missouri. Raymond A. Applegate has proprietary interests in the development of single value metrics predictive of visual performance and consults for Alcon, Inc., and Sarver and Associates, Inc. Inquiries to Jay Pepose, MD, PHD, Pepose Vision Institute, Baxter Road, Suite 205, St. Louis, MO 6301Y; jpepose@ peposevision.com incorrectly directed increase, so do the optical aberrations of the eye. These errors can be classified in a number of ways. Commonly, as a first pass in evaluating the optics of the eye, these aberrations are broken into errors that are correctable with sphero-cylindrical corrections and those that are not. In the language of wavefront sensing the former is commonly referred to as low order wavefront errors and the latter higher order (HO) wavefront errors. Wavefront aberrometers quantify the eye s wavefront error. Wavefront error is defined as the difference between an unaberrated reference wavefront and the actual wavefront formed by the eye s optics. Wavefront error is one of the key components defining retinal image quality. Other key components include diffraction, chromatic aberration, and scatter. 2 The retinal image is the input to the neural pathways and is a key element in determining our visual percept. As such, it is a key element determining our visual percept, but it is not the only factor. The interpretation of the retinal image is also affected and limited by additional neural factors, including cone photoreceptor density, the orientation of the photoreceptors, visual memory, blur interpretation, and all other neural wiring throughout the central nervous system leading to the visual percept. 3 In an otherwise normal optical system (for example, no cataract or corneal scarring leading to forward scattering), wavefront error and diffraction effects fundamentally describe the appearance of the retinal image for any single wavelength or combinations of wavelengths of light. For example, it is possible by knowing the wavefront error to calculate how any given point is imaged onto the retina monochromatically or polychromatically. Since diffraction and wavefront error spread the image of a point, such an image is referred to as the point spread function (PSF). Knowing the PSF of an optical system allows one to reconstruct an image point by point using the mathematical process of convolution. It is important to remember that the effects of both aberration and diffraction are very pupil-size dependent. The adverse effects of diffraction increase with decreasing pupil size; whereas, the effects of optical aberrations (wavefront error) generally increase with increasing pupil /05/$ BY ELSEVIER INC. ALL RIGHTS RESERVED. 335 doi: /j.ajo

2 FIGURE 1. Retinal image simulations of a normal eye with a spectacle correction simulated by setting the second order Zernike expansion coefficients to zero. (Left) Simulation using a 1 mm pupil - Diffraction effects dominate the retinal image quality (high order aberrations over the 1 mm pupil 0.01 m). (Center) Simulation usinga3mmpupil - In the typical normal eye, somewhere between 2.5 and 3 mm diameter pupil the balance between diffraction effects and aberration effects produce the best retinal image. In this example, the standard deviation of the high order aberration (commonly referred to as RMS error) is 0.04 m over the 3 mm diameter pupil. (Right) Simulations using a 7 mm pupil - In the typical normal eye when the pupil is large high order aberrations dominate over diffraction effects. In this example, the higher order aberrations have a relatively low RMS wavefront error of 0.33 m overa7mmpupil (typically the higher order RMS error is around 0.48 over a7mmpupil). When carefully measured, high contrast high luminance visual acuity for 3 and 7 mm pupils typically differ by only two to three letters, yielding essentially equivalent acuity as measured clinically, despite the difference in retinal image quality. Retinal image simulations were generated using the software package-visual Optics Laboratory v6.72, Sarver and Associates, Inc. size. 4 Consequently, the optical quality of the retinal image can vary significantly with pupil size. In the young adult normal eye with sphero-cylindrical errors corrected, the standard deviation of the wavefront error (higher order RMS wavefront error) over a3mmpupil for normal eyes between 20 and 40 is typically on the order of m(a dioptric equivalent of 0.17 diopters) and for a7mmpupil on the order of 0.48 m (a dioptric equivalent of 0.27 diopters), and it increases with age. As can be seen in Figure 1, the impact on image quality for a given individual varies noticeably with pupil size, despite high luminance high contrast acuity remaining stable within three letters, for the 3 mm and 7 mm pupil diameters. For the 1 mm pupil diameter, diffraction effects decrease acuity. The RMS wavefront error (the standard deviation of the wavefront across the pupil diameter) does not accurately predict the quality of vision particularly at low aberration levels. This is in part because: (1) light rays from the center of the pupil play a greater role in defining the visual percept attributable to photoreceptor orientation (the Stiles-Crawford effect); 5,6 (2) specific wavefront errors near the center of the Zernike pyramid (such as coma and spherical aberration) tend to affect retinal image quality more than ones along the edge of the Zernike pyramid (for example, trefoil, quadrafoil); 7,8 (3) various combinations of wavefront aberrations can either conspire to make retinal image quality better than the individual component aberrations by themselves or worse depending on how they are combined; 9 (4) the neural processing of specific aberration patterns may not be equal; 10 and (5) individuals have varying degrees of plasticity in their neural processing of new aberration patterns as they change slowly with age or more dramatically with refractive surgery. Better metrics of optical quality need to be developed that better predict visual performance. As a case in point, in this issue of THE JOURNAL, Levy and associates used a commercially available aberrometer to measure monochromatic higher order aberrations in subjects with uncorrected high contrast vision of 20/15 or better which they claim is super normal vision. They found that the standard deviation of the higher order aberration (RMS wavefront error) was not significantly different from published reports of higher order RMS wavefront error in ammetropes. They suggest that these results may prompt us to rethink the import of RMS wavefront error and even the value of trying to reduce or eliminate all of the eye s higher order aberrations using wavefront-guided laser ablation. This interesting and provocative article raises a number of important questions important to understanding wavefront sensing, quantification of aberrations, and the resulting impact on visual performance: WHAT IS NORMAL AND SUPER NORMAL VISION? Studies of healthy eyes of prepresbyopic subjects indicate that the mean best spectacle corrected high contrast high luminance vision is between 20/12.5 (logmar 0.2) and 20/16 (LogMAR 0.1). 11 Even with dilated pupils, average best corrected high contrast high luminance log- MAR acuity is approximately 20/16 for normal eyes with best sphero-clindrical correction between 20 and 60 years of age. 12 If average best corrected acuity under physiologic pupil conditions is better than 20/16, then how should super normal vision be defined? It surely has to be better than average visual acuity in the general population. It is, therefore, more reasonable, if high contrast visual acuity is even to be used, to define super normal vision as high 336 AMERICAN JOURNAL OF OPHTHALMOLOGY FEBRUARY 2005

3 contrast high luminance vision of at least 20/12.5 (Log- MAR 0.2) or by a statistical rule such as vision must be at least one standard deviation better than the mean acuity for the age. More importantly, in the age of wavefront guided optical corrections, it is imperative that we use tests of visual performance sensitive to subtle variations in retinal image quality. High contrast high luminance visual acuity is not such a test. DOES VISUAL FUNCTION IN NORMAL EYES VARY AS A FUNCTION OF HIGHER ORDER RMS ERROR? In lieu of assessing high contrast visual acuity (which is known to be insensitive to minor variations in aberration structure), 12 low contrast visual acuity testing under mesopic conditions is more sensitive to small differences in retinal image quality for principally two reasons. First, low contrast letters have less redundant spatial information than high contrast letters; and second, the physiologic pupil is large allowing optical aberrations to manifest themselves and degrade retinal image quality. As a consequence, mesopic low contrast acuity is more sensitive to minor variations in retinal image quality than photopic high contrast acuity. To see if visual function is in fact sensitive to minor variation in aberration structure, best corrected visual performance and aberration data were extracted from the ongoing Texas Investigation of Cataract Optics (TICO) of normal eyes (without cataract) with typical photopic (280 cd/m 2 ) high contrast acuity (20/15) 2 letters (20/16.6 to 20/13.8). For these eyes both the visual function and aberration were measured under dilated pupil conditions (that is, with undilated pupils one can expect acuities to be approximately two to three letters better or a mean acuity of 20/14.5). Figure 2 plots photopic high contrast acuity (280 cd/m 2 ) and mesopic (0.70 cd/m 2 ) low contrast acuity as a function of each eye s high order RMS wavefront error (aberration not correctable with sphero-cylindrical lenses). Notice that even over this very narrow range of acuity, photopic high contrast acuity decreases with increasing HO aberration accounting for approximately 12% of the variance in acuity. More importantly, notice that the mesopic low contrast acuity is more affected by subtle variations in higher order aberrations and that HO RMS error accounts for 26% of the variance in acuity. Even though RMS wavefront error is known to be less than an ideal indicator of retinal image quality, it accounts for a significant amount of the variance in acuity. IS CONTRAST SENSITIVITY TESTING WITH SINUSOI- DAL BAR PATTERNS MORE SENSITIVE TO CHANGES IN ABERRATION STRUCTURE THAN LOW CONTRAST ACU- ITY? While contrast sensitivity testing using sinusoidal gratings is an excellent way to measure how HO RMS wavefront error impacts contrast sensitivity, such measures are not sensitive to phase shifts and typically only measure contrast sensitivity to specific grating orientations. Why are phase shifts and grating orientation important? Phase FIGURE 2. Restricting the Texas Investigation of Cataract Optics (TICO) to normals without cataract which have photopic high contrast (PHC) acuities ranging between 20/13.8 and 20/16.6 through drug dilated pupils reveals that high order (HO) RMS error through a 7 mm pupil accounts for 12% of the variation in acuity (r 2.12). PHC acuity decreases by 2.5 letters for a 1 m increase in HO RMS wavefront error. If we use mesopic low contrast (MLC) acuity as the metric of visual performance, the high order wavefront error accounts for 26% of the variance. The slope of the best fitting line increases by over a factor of 3 ( 12 letter decrease in acuity for a 1 m increase in HO RMS wavefront error). shifts are often more important to image fidelity in recognition tasks (Figure 3) than a loss in contrast. 2 As can be seen in Figure 3, recognition tasks where a specific object has to be named, like the letter E, are sensitive to phase shifts, whereas, detection of the presence of sinusoidal bars of any given spatial frequency are not, by their very nature, sensitive to phase shifts. Conversely, if the visual performance task is a detection task ( I see as opposed to I recognize it ), object contrast will more likely be the critical factor. Further, contrast sensitivity varies with grating orientation particularly when the eye has uncorrected asymmetric aberrations which is typically the case in the normal eye and particularly following traditional laser refractive surgery. Thus, to properly measure contrast sensitivity, it is necessary to measure full contrast sensitivity functions for several different orientations of the grating pattern. Conversely, contrast sensitivity testing has an advantage over photopic high contrast acuity in that at the limit of acuity, the contrast sensitivity curve is steep and a large increase in contrast sensitivity may only be associated with a modest increase in high contrast letter acuity, if at all. WHAT CLINICALLY VIABLE TESTS ARE THE MOST SENSI- TIVE FOR EVALUATING VISUAL PERFORMANCE? The limitations of contrast sensitivity testing using sinusoidal bar VOL. 139, NO. 2 WAVEFRONT SENSING 337

4 FIGURE 3. Top and bottom a row of letter E decreasing in size in the presence of simple defocus. In the top row, both the contrast loss and the phase shifts as a function of spatial frequency are included in the images. In the bottom row, the contrast loss is the same as the top row; the only difference is that the phase shifts as a function of spatial frequency have been corrected. Notice that it is the phase shifts that are mostly responsible for lowering the letter recognition and not the loss of contrast. Figure reprinted with permission from Chapter 7, Assessment of Visual Performance in Customized Visual Correction: The Quest for Super Vision II, Slack, Inc. 4 patterns along with the time consuming nature of contrast sensitivity testing 13 and the observations presented immediately above make mesopic (large physiologic pupil) low contrast letter acuity the most sensitive readily available clinically viable task for detecting small differences in retinal image quality that affect recognition tasks. Said differently, for individuals with low aberration and excellent acuity (20/12 and better), improved optical image quality will be difficult to detect with photopic high contrast acuity because the upper limit of acuity for pupil diameters greater than 3 mm is fundamentally limited by sampling of the cone mosaic (Figure 4) which provides a ceiling effect between 20/10 and 20/8. Further, and equally important using photopic high contrast acuity charts, gains in contrast are harder to detect. Therefore, it would be clinically interesting to perform low luminance (large physiologic pupil) low contrast acuity on the subjects in Levy s study and to correlate these data with each individual s monochromatic higher order aberrations measured at the same pupil size. It is inappropriate to measure aberrations at one pupil size and correlate the measured aberrations to visual performance measured at a different pupil size. Consider the fact that pinholes (small pupil diameter) can improve vision of the optically aberrated eye. Providing a patient with optical aberrations a pinhole, which allows them to see better, does not mean the aberrations of the eye (over the larger natural pupil) have been reduced. Pupil size plays an important role, particularly in the highly aberrated eye. We suspect that if aberrations and mesopic low contrast acuity are measured for the same pupil size, the data of the Levy study will more closely resemble the data presented in Figure 2, where small variations in aberration in eyes with 20/15 vision affect acuity. WHAT IS THE IMPORTANCE OF MEASURING ACUITY CAREFULLY? Acuity, as measured in the typical clinical practice, is generally measured poorly. The added time to measure and score acuity correctly is minimal and associated gains in sensitivity are large. 14 Generally, in clinical practice, a variation of the Snellen acuity chart is used (as opposed to a logmar chart with its inherent advantages) 15 and the point at which to end testing is loosely defined, and examiner and patient dependent. To optimize the sensitivity of acuity testing a logmar chart should be used with a fixed end point criterion (for example, five or seven letters missed with credit being given to all letters read up to the fifth or seventh miss (Figure 5). 16 Failing to measure acuity in consistent systematic manner increases the variability (to detect change may require a gain or loss of two lines or more as opposed to less than one line if acuity is measured carefully) thus decreasing the ability to detect differences between groups for any given sample size. WHAT METHODS ARE USED TO MEASURE THE EYE S ABERRATION AND ARE THEY ACCURATE? Liang, Bille, and associates 17 developed a fast objective measure of the wave aberration of the human eye by sampling a large number of localized points across the entire pupil using a Shack-Hartmann lenslet array. Using Shack-Hartmann wavefront sensing technology, Liang and Williams 18 and others 19,20 went on to provide what may be one of the most detailed and robust descriptions of the typical human eye s wave aberrations giving quantitative validation to the aberrations noted well over a century ago by Helmholtz. 1 In the report in this issue of THE JOURNAL, Levy and associates use a commercial instrument based upon a slit scanning technique that is similar to skiascopy (streak retinoscopy). It is not clear whether the slit scanning skiascopy technique that samples numerous rays across an entire meridian of the eye can accurately follow localized skew rays (Figure 6). Comparing data across aberrometers is inherently dangerous even within a specific type (for example, Shack- Hartmann) of aberrometer for a variety of reasons. For example, each system has to develop a centroiding algorithm to best locate the chief ray of each lenslet image and an algorithm to locate the pupil center. Depending on the 338 AMERICAN JOURNAL OF OPHTHALMOLOGY FEBRUARY 2005

5 FIGURE 4. If a letter E falls entirely within one photoreceptor the letter E cannot be differentiated from a period. To be recognized as a letter E, the individual components of the letter E must be equal to or greater than the diameter of an individual foveolar cone. This places the limit of visual acuity at between 20/8 and 20/10. Figure reprinted with permission from Chapter 7, Assessment of Visual Performance in Customized Visual Correction: The Quest for Super Vision II, Slack, Inc. 4 specific strategy employed to solve these and other calculation related issues the answers obtained would be slightly different. What is needed is a set of schematic eyes with known aberrations to calibrate systems. 21 Until then care must be employed when comparing data across measurement platforms. WHAT IS THE VALUE OF A ZERNIKE EXPANSION? The Zernike expansion was first applied to study the aberrations of the human eye by Howland and Howland in The Zernike expansion consists of an infinite number of fitting shapes called modes. Fitting the wavefront error to a Zernike expansion parcels the error into unique building blocks giving us a language to talk about the aberrations in an eye. For example, early traditional refractive surgery tends to induce significant amounts of spherical aberration. Fitting the wavefront error with a Zernike expansion allowed us to see that a large portion of the wavefront error induced by traditional refractive surgery was attributable to Zernike mode Z 0 4 (the spherical aberration term). Parceling the wavefront error into unique components facilitates our understanding and communication with colleagues and patients by giving us a way to identify, quantify, and talk about various types of aberrations. Practically, the number of Zernike modes that can justifiably be fit to a given data set is limited by the number of samples in the data set. Just as it takes two points to define a line, it takes a minimum of one new independent data point being sampled for each new mode of the Zernike expansion added to the analysis. To be able to estimate errors in the quality of the fit it is best to have at least two and preferably more independent samples for each mode in the Zernike expansion used to fit the wavefront error. Current Shack-Hartmann aberrometers meet this criterion easily, being able to fit up to the 10th order (65 individual modes) with sampling density to spare. The Zernike expansion is the Optical Society of America s (OSA) and the American National Standards Institute s (ANSI) recommended standard for documenting the optical defects of the eye. 21 It is an orthogonal smoothing function (each mode is mathematically independent of all other modes) that is generally well adapted for optical systems. Smoothing functions, when designed appropriately, reduce the noise inherent in each sampling point. However, no single smoothing function is perfect for all situations and for some very highly aberrated eyes the Zernike expansion may not be adequate. It is, therefore, imperative that manufacturers of wavefront sensors, as part of the standard output, provide metrics of the quality of the fit. This is true regardless of the fitting function used whether it is the Zernike expansion, a Taylor series, a Fourier series, or any other fitting function. It is also important to know the noise surrounding each data point. If a fitting function is chosen that better approximates each data point (which can generally be accomplished by adding more modes in a Zernike fit or more frequencies in a Fourier fit) and individual data point determination is noisy, such a fit can be following noise instead of the true aberration. This is a particularly difficult problem since the noise will vary with the complexity of the surface. It is not sufficient to measure the noise on a well-behaved system and conclude that highly aberrated systems will behave the same. Such an assumption could easily lead to extremely erroneous conclusions. For the normal eye and most abnormal eyes, the Zernike expansion is an excellent way to represent the wavefront error. For some extremely aberrated eyes (for example, advanced keratoconus, penetrating keratoplasty), even a 10th order Zernike fit is not adequate to accurately represent the wavefront error. In these cases, it is highly likely that the noise associated with each data point is also large because local variations in slopes are large. If so, the first step would be to reduce the noise in each individual pupil location sampled by taking numerous measurements, and averaging to get the best estimate of the wavefront error at a given location before fitting the data with a smoothing function (such an analysis applies equally to any shape where extreme variations are being measured; for example, pathologic corneal topographies). If the fitting error to the average wavefront error at each pupil location is still high, caution is advised in using the fitted function to design a corneal ablative procedure. It would be wiser to try such a correction in a stabilized contact lens when such designs become available in the near future 23 before implementing them in a corneal ablative refractive surgery that causes a permanent loss of tissue. VOL. 139, NO. 2 WAVEFRONT SENSING 339

6 FIGURE 5. To optimize the sensitivity of acuity testing, a logmar chart design should be used and the patient required to read the chart until five letters are missed. The acuity is then scored to the letter counting all letters read correctly up to the fifth miss. Here the patient read 42 letters correctly up to the fifth miss. For this chart, when used at the calibrated distance reading 40 letters correctly, is equivalent to reading 20/20. This patient read 42 letters before making a fifth error. Reading 42 letters makes the acuity 20/20 2 in Snellen notation or 0.04 in logmar notation. Scoring in this manner allows the detection of a significant change in acuity that is less than one line. WHAT SINGLE VALUE METRIC OF IMAGE QUALITY BEST CORRELATES WITH VISUAL PERFORMANCE? There are literally hundreds of metrics of image quality that are fundamentally based on knowledge of the wavefront error. Most are designed to meet specific application needs. What will likely happen as the field matures is that different metrics will be found that are predictive of visual performance on specific tasks (for example, face recognition, acuity, detection of a hostile incoming aircraft, a metric defining the best end point of a refraction, and so on). The most common metric in use today is root mean squared wavefront error (RMS wavefront error). RMS wavefront error is simply the standard deviation of the wavefront error over the pupil size of interest. RMS wavefront error commonly includes or excludes the wavefront error attributable to a traditional sphero-cylindrical error. If it includes the sphero-cylindrical error of the eye, it is called the total RMS wavefront error. If it does not include the RMS wavefront error attributable to the sphero-cylindrical wavefront error of the eye, it is referred to as higher order RMS wavefront error. Applegate and associates have found that a fixed level of wavefront error affects visual performance as measured by high luminance high contrast logmar acuity differently depending on how the error is distributed across the pupil. That is, each individual Zernike mode affects acuity differently. 8 As mentioned above, modes near the center of the Zernike tree (for example, coma, spherical aberration) tend to affect acuity more than those near the edge of the tree (for example, trefoil). 8 Further, although Zernike modes are considered orthogonal in terms of wavefront error, they are not orthogonal with respect to visual performance as measured by visual acuity. That is, for any fixed level of total RMS error, Zernike modes interact to either increase or decrease acuity depending on how the modes are combined and their relative contributions to the fixed level of RMS error. In experiments conducted at the Visual Optics Institute, the total RMS error was held constant at 0.25 m over a 6 mm pupil (if all the wavefront error had been loaded into simple defocus, 0.25 m of RMS wavefront error over a 6 mm pupil in dioptric terms is less than 0.25 diopters of spherical refractive error), yet visual acuity varied by up to two lines (10 letters) depending on how the wavefront error was distributed across the pupil. 9 These experiments indicate that the distribution of the wavefront error across the pupil is a key factor in determining its effect on visual acuity and most likely most other measures of visual performance. Since the RMS wavefront error was held 340 AMERICAN JOURNAL OF OPHTHALMOLOGY FEBRUARY 2005

7 the eye s optical properties with aging, declining visual performance and loss of contrast sensitivity over time may also reflect age-related neural changes in visual processing. As we proceed forward, care will be required to determine whether a loss in visual performance in aging experiments is attributable to a loss in the optical transfer function and/or the neural transfer function. FIGURE 6. Three rays of light are refracted at a surface. Ray No. 1 strikes the surface along the normal and enters the new optical media unaltered in direction and serves as the reference ray for the system. Ray No. 2 and No. 3 are refracted at the surface and never cross the reference ray or each other. Rays that do not cross the reference ray are called skew rays. To accurately measure the aberrations of the eye without using simplifying assumptions, aberrometers should be able to measure the true path of skew rays. constant in these experiments, it could not account for any of the variance in visual acuity. Conversely, a single valued metric called the visual Strehl could account for nearly 80% of the variance in acuity in these experiments. 24 It is premature to conclude from this initial experiment that, therefore, we should be using the visual Strehl as our measure of optical quality. What is clear is that we need to be exploring metrics that are predictive of useful visual tasks. To this end and in an effort to explore which of several single valued metrics best predicts the end point of a subjective refraction, Thibos and associates recently tested 31 different single valued metrics of optical performance. Here too, the visual Strehl performed well 25 as did a few other metrics. ARE HIGHER ORDER ABERRATIONS STABLE OVER TIME AS WE AGE? Levy and coworkers did not find a statistically significant correlation between specific or total higher order aberrations and age. This is in direct contrast to the reports of a number of investigators using different measuring techniques, showing an increase in the monochromatic optical aberrations of the eye with age when compared at matched pupil diameters However, when RMS was measured at natural pupils, age-related miosis was a natural attenuating factor offsetting some of the increases in optical aberrations with age. 26 In evaluating why ocular aberrations increase over time, it appears that the compensation of corneal aberrations by the internal aberrations of the crystalline lens generally seen in youthful eyes decreases with age. 28 In addition to degradation of WHAT CAN ADAPTIVE OPTIC TECHNIQUES TEACH US ABOUT THE IMPACT OF REDUCING THE EYE S HIGHER ORDER ABERRATIONS? Guirao and associates 30 calculated the theoretical visual benefit of correcting the monochromatic higher order aberrations of a cohort of subjects with normal eyes over a range of spatial frequencies. Given the significant variation of higher order aberrations spanning the range of refractive errors and individuals, it is not surprising that selected subjects with larger pupils and greater amounts of higher order aberration showed an increase in contrast sensitivity of more than a factor of five when optical aberrations were reduced using adaptive optics, but for others where the optical aberrations were less, there was minimal improvement. Since retinal image quality does not directly translate into an individual s visual percept, perhaps the strongest evidence we have for the negative impact of both monochromatic and polychromatic higher order aberrations come from adaptive optics studies of Hofer 31 and associates. Using an optical system with a deformable mirror and 97 micropistons (that is, actuators), visual benefit was demonstrated by decreasing the eye s monochromatic aberrations (and to a lesser, but significant extent, the chromatic aberrations). These findings, coupled with the increased contrast sensitivity found in many patients with customized laser vision correction compared with standard treatment, argues in favor of keeping the eye s higher order aberrations at presurgical levels or reducing them to an optimal amount. SHOULD THE GOAL BE TO ELIMINATE THE MONO- CHROMATIC ABERRATIONS OF THE EYE? If we could totally correct the monochromatic aberrations of the eye (which is impossible for a variety of reasons), the depth of field for any given pupil size will decrease. Consequently, the eye will have to be more critically focused on task of interest. Interestingly, cross-sectional population studies indicate that higher order aberrations tend to average to zero, except for a small amount of positive spherical aberration suggesting evolutionary pressure to have a small amount of positive spherical aberration. A small amount of spherical aberration increases the depth of field providing acceptable vision over a greater depth of field. Said differently, some sacrifice in retinal image quality may in fact increase overall visual performance by increasing the depth of field. Currently, it is unclear what or if there is an optimal set of residual aberrations. More likely than not, there will be several sets of residual aberrations that VOL. 139, NO. 2 WAVEFRONT SENSING 341

8 optimize visual performance dependent on the visual task of interest and idiosyncrasies of the patient. Nonetheless, it is clear that traditional laser refractive surgery is inducing an increase in aberrations, which can lead to patient complaints of poor image quality. Further, wavefront guided corrections are reducing the amount of induced aberrations and decreasing the number of patients with complaints by improving postsurgical visual performance. The first goal of wavefront guided refractive surgery should be to correct the second order aberrations (sphere and cylinder) without inducing a new set of higher order aberrations in the vast majority of cases. The second goal would be to determine the ideal residual set of aberrations for the needs and lifestyle of the patient. WHAT CAN ADAPTIVE OPTIC TECHNIQUES TEACH US ABOUT CENTRAL NEURAL PROCESSING OF RETINAL IMAGES? Experiments by Artal and associates 32 reveal the plasticity of neural processing of the retinal image. Using adaptive optics, they rotated an individuals higher order aberrations. That is, the aberration was the same except for the orientation. While the objective blur remained constant, people subjectively reported sharper images with their own aberration orientation. The time and ability needed to adapt to new patterns of higher order aberration varies across individuals and as a function of age. There are similar reports of gradual adaptation to prismatic aberration and to progressive-power lenses. 29 The brain is capable of maintaining a number of adaptive states which can be called upon as needed, 32 as can be easily seen when individuals switch between distance glasses and readers, or look down the segments of a trifocal or progressive bifocal. ARE SPECIFIC HIGHER ORDER ABERRATION PATTERNS USEFUL TO RETAIN AND IS ELIMINATION OF ALL OF THE EYE S HIGHER ORDER ABERRATIONS BY CUSTOMIZED LA- SER VISION CORRECTION, CUSTOMIZED CONTACT LENSES, OR CUSTOMIZED INTRAOCULAR LENSES AN IMPORTANT OR REALISTIC FUTURE GOAL? Because of numerous factors, including corneal biomechanics, hydration, fluctuating accommodative states, fluctuating pupil size, variations in wound healing, changes in aberration structure as incoming vergence changes, problems inherent to wavefront acquisition and registration, and slow changes in the eye s wavefront error with age, elimination of all monochromatic higher order aberrations with corneal excimer laser surgery is impossible as it is for other modes of wavefront guided corrections. The key question is, how good is good enough for any given individual. SUMMARY AS LEVY NOTES, FOR SOME INDIVIDUALS THERE MAY BE AN advantage to keeping a general pattern of wavefront aberrations to which the brain has already adapted, just as we may need to make subtle changes in astigmatism axis and magnitude in adjusting glasses prescriptions. As we learn more about how to achieve specific desired corrections, understand differences in visual processing, define the visual requirements for different tasks, use sensitive tests capable of measuring the effects of small changes in aberration structure, and match these to our patients visual needs, we will reach the goal of truly customizing optical corrections to the individual. REFERENCES 1. von Helmholtz H. Popular scientific lectures. New Dover edition. New York: Dover Publications, 1962: Applegate RA. Glenn Fry award lecture 2002: wavefront sensing, ideal corrections, and visual performance. Optom Vis Sci 2004;81: Applegate R, Hilmantel G, Thibos L. Assessment of visual performance (Chapter 7). In: Krueger R, Applegate RA, MacRae S, editors. Wavefront customized visual correction: the quest for super vision. 2nd ed. New Jersey: Slack, Inc., 2004: Applegate RA, Gansel KA. The importance of pupil size in optical quality measurements following radial keratotomy. Refract Corneal Surg 1990;6: Applegate RA, Lakshminarayanan V. Parametric representation of Stiles-Crawford functions: normal variation of peak location and directionality. J Opt Soc Am A 1993;10: Stiles WCB. The luminous efficiency of rays entering the eye pupil at different points. Proc Roy Soc Lond B 1933;112B: Applegate RA, Ballentine C, Gross H, Sarver EJ, Sarver CA. Visual acuity as a function of Zernike mode and level of root mean square error. Optom Vis Sci 2003;80: Applegate RA, Sarver EJ, Khemsara V. Are all aberrations equal? J Refract Surg 2002;18:S Applegate RA, Marsack JD, Ramos R, Sarver EJ. Interaction between aberrations to improve or reduce visual performance. J Cataract Refract Surg 2003;29: Artal P, Chen L, Fernandez EJ, Singer B, Manzanera S, Williams DR. Adaptive optics for vision: the eye s adaptation to point spread function. J Refract Surg 2003;19:S585 S Elliott DB, Yang KC, Whitaker D. Visual acuity changes throughout adulthood in normal, healthy eyes: seeing beyond 6/6. Optom Vis Sci 1995;72: Pesudovs K, Marsack J, Donnelly III W, Applegate R. Measuring visual acuity mesopic or photopic conditions, and high or low contrast letters? J Refract Surg 2004;20: S538 S Pesudovs K, Hazel CA, Doran RM, Elliott DB. The usefulness of Vistech and FACT contrast sensitivity charts for cataract and refractive surgery outcomes research. Br J Ophthalmol 2004;88: Bailey IL, Bullimore MA, Raasch TW, Taylor HR. Clinical grading and the effects of scaling. Invest Ophthalmol Vis Sci 1991;32: Bailey IL, Lovie JE. New design principles for visual acuity letter charts. Am J Optom Physiol Opt 1976;53: AMERICAN JOURNAL OF OPHTHALMOLOGY FEBRUARY 2005

9 16. Applegate RA, Howland HC, Sharp RP, Cottingham AJ, Yee RW. Corneal aberrations and visual performance after radial keratotomy. J Refract Surg 1998;14: Liang J, Grimm B, Goelz S, Bille JF. Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor. J Opt Soc Am A 1994; 11: Liang J, Williams DR. Aberrations and retinal image quality of the normal human eye. J Opt Soc Am A 1997;14: Porter J, Guirao A, Cox IG, Williams DR. Monochromatic aberrations of the human eye in a large population. J Opt Soc Am A Opt Image Sci Vis 2001;18: 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 2002;19: 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 2000;16:S654 S Howland HC, Howland B. A subjective method for the measurement of monochromatic aberrations of the eye. J Opt Soc Am 1977;67: Cox I, Lagana M. Feasibility of wavefront customized contact lenses. In: Krueger R, Applegate RA, MacRae S, editors. Wavefront customized visual correction: the quest for super vision. 2nd ed. New Jersey: Slack, Inc., 2004: Marsack JD, Thibos LN, Applegate RA. Metrics of optical quality derived from wave aberrations predict visual performance. J Vis 2004;4: Thibos LN, Hong X, Bradley A, Applegate RA. Accuracy and precision of objective refraction from wavefront aberrations. J Vis 2004;4: Calver RI, Cox MJ, Elliott DB. Effect of aging on the monochromatic aberrations of the human eye. J Opt Soc Am A Opt Image Sci Vis 1999;16: Smith G, Cox MJ, Calver R, Garner LF. The spherical aberration of the crystalline lens of the human eye. Vision Res 2001;41: Artal P, Berrio E, Guirao A, Piers P. Contribution of the cornea and internal surfaces to the change of ocular aberrations with age. J Opt Soc Am A Opt Image Sci Vis 2002;19: Villegas EA, Artal P. Spatially resolved wavefront aberrations of ophthalmic progressive-power lenses in normal viewing conditions. Optom Vis Sci 2003;80: Guirao A, Porter J, Williams DR, Cox IG. Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes. J Opt Soc Am A Opt Image Sci Vis 2002;19: Hofer H, Chen L, Yoon GL, Singer B, Yamauchi Y, Williams DR. Improvement in retinal image quality with dynamic correction of the eye s aberrations. Optics Express 2001;8: Artal P, Chen L, Fernandez EJ, Singer B, Manzanera S, Williams DR. Neural compensation for the eye s optical aberrations. J Vis 2004;4: VOL. 139, NO. 2 WAVEFRONT SENSING 343

10 Biosketch Jay S. Pepose, M.D., Ph.D., Professor of Clinical Ophthalmology, Washington University School of Medicine, St. Louis, Missouri and Medical Director, Pepose Vision Institute, is a recipient of the Cogan Award from the Association of Research in Vision and Ophthalmology and Senior Achievement Award from the American Academy of Ophthalmology. A clinician-investigator with interests in cornea and refractive surgery, Dr. Pepose serves as an Executive Editor of the American Journal of Ophthalmology and the Journal of Refractive Surgery. 343.e1 AMERICAN JOURNAL OF OPHTHALMOLOGY FEBRUARY 2005

11 Biosketch Raymond Applegate, O.D., Ph.D.: Dr. Applegate is professor, Borish Chair of Optometry, and Director of the Visual Optics Institute at the College of Optometry, University of Houston. His NIH funded research is focused on understanding the visual impact of optical aberrations and scatter in the normal and clinical eye and optimizing the visual outcomes of therapy designed to improve the visual performance of the normal and clinical eye. VOL. 139, NO. 2 WAVEFRONT SENSING 343.e2

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