Interocular high-order corneal wavefront aberration symmetry - Vision ...

Lombardo et al.

Vol. 23, No. 4 / April 2006 / J. Opt. Soc. Am. A

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Interocular high-order corneal wavefront aberration symmetry Marco Lombardo Department of Experimental and Clinical Medicine, University Magna Græcia, Viale Europa, 88100 Catanzaro, Italy

Giuseppe Lombardo Excellence Center CEMIF. CAL, INFM-Licryl Laboratory, Department of Physics, University of Calabria, Ponte P. Bucci, 87036 Rende (Cs), Italy

Sebastiano Serrao Serraolaser, Via Nizza 46, 00198 Rome, Italy Received July 27, 2005; revised October 7, 2005; accepted October 11, 2005; posted October 25, 2005 (Doc. ID 63576) The interocular symmetry of the high-order corneal wavefront aberration (WA) in a population of myopic eyes was analyzed before and after photorefractive keratectomy (PRK). The preoperative and one-year postoperative corneal aberration data (from third to seventh Zernike orders) for 4- and 7-mm pupils from right and left eyes were averaged after correcting for the effects of enantiomorphism to test for mirror symmetry. Also, the mean corneal point-spread function (PSF) for right and left eyes was calculated. Preoperatively, a moderate and high degree of correlation in the high-order corneal WA between eyes was found for 4- and 7-mm pupils, respectively. Myopic PRK did not significantly change the interocular symmetry of corneal high-order aberrations. No discernible differences in the orientation PSF between eyes were observed one year after surgery in comparison with the preoperative state over the two analyzed pupils. © 2006 Optical Society of America OCIS codes: 170.4470, 170.1020, 330.4460, 330.7310.

1. INTRODUCTION During the past years, the possibility that ocular optical aberrations could be corrected beyond spherocylindrical error using excimer laser systems1,2 and that minimizing high-order aberrations (HOAs) can improve the optical quality of the eye3 have given rise to increasing research on the knowledge, significance, and treatment of highorder optical aberrations.4 Efforts from many researchers are establishing an aberration standard of normal individuals to understand the nature and effect of each aberration and also to evaluate the optical and visual outcomes in refractive surgery.5,6 It is known that the form of the ocular wavefront aberration (WA) varies substantially with the individual, presumably depending upon the surface asymmetries and surface tilts between the optical components of the particular eye and their relative locations with respect to the pupil.7 The optical performance of the normal eye is governed by the combination of aberrations in the corneal and intraocular optics, and it has been shown that there is a significant correlation between these elements.8 Since the ablation alters the natural optical balance of the eye, it is now suggested that both corneal and ocular aberration measurements are needed to plan a reliable customized treatment.9 Accordingly, the influence of standard corneal ablation on the combination effect for the most significant aberrations between the cornea and the lens has been studied in detail.9–12 Less attention has been paid to the interocular balance of optical aberrations. It is well known that the corneal 1084-7529/06/040777-11/$15.00

topography of right and left eyes exhibits mirror-image symmetry13–16 with respect to the vertical plane of the body. Recent works17–20 demonstrated a mirror symmetry of the high-order WA maps of the anterior cornea as well as the whole eye optics between eyes, especially for thirdand fourth-order terms over a dilated pupil. Therefore, even though there appears to be a random variation in the eye aberration from subject to subject, many aberrations in the right eye are significantly correlated with their counterparts in the left eye of the same person. Nevertheless, few clinical studies21,22 have investigated the effect of standard laser refractive surgery on the native mirror symmetry of HOA between the eyes. As thousands of people yearly undergo corneal laser refractive correction, and considering the expected longevity of these patients, it is a main point of interest to investigate whether these procedures may induce an unbalanced change of the interocular optical properties. To date, a single identical ablation pattern has been employed to treat both the right as well as the left eye. The assumption is to treat the cornea as a symmetric lens, subtracting tissue with the widest ablation zone possible.23 In previous works, we showed that the epithelial healing and the mechanical response of the cornea to photorefractive keratectomy (PRK) are mirror symmetric and highly regional dependent with a significant difference of the response between the nasal and the temporal regions of the corneal periphery,24,25 leading to an asymmetrical remodeling of the corneal profile between the eyes. In the present work, © 2006 Optical Society of America

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we evaluate the prevalence of interocular symmetry of high-order corneal WA in a population of myopic eyes that undergo bilateral PRK.

2. METHODS A. Subjects and Procedure Thirty patients, 10 males and 20 females, were enrolled for this prospective, randomized study. The mean age was 31.7± 6.71 years (range, 24 to 52 years) for a total of 60 eyes. The preoperative spherical equivalent (SE) refraction was −4.46± 2.05 diopters (D) (range, −1.75 to −8.75 D) with a mean (± standard deviation) of −4.40± 2.12 D for the right eye and −4.52± 2.01 D for the left eye. Subjects were considered eligible for the study if they were at least 21 years old and had at least one year of refractive stability, were free of ocular disease and had no previous ocular surgery, their SE refraction was myopic, and the manifest refractive cylinder was less than 1.50 D. Patients wearing contact lenses were asked to discontinue their use for at least four weeks prior to surgery. An institutional review board approval was not required for this study. The PRK procedure was performed with a Technolas Keracor 217C excimer laser (Bausch & Lomb Chiron Technolas, Dornach, Germany) after removing the corneal epithelium with an Amoils brush. Photoablation was applied to a 6-mm optical zone, with a transition zone of 9 mm. PTK was performed using a viscous masking 0.25% sodium hyaluronate solution (smoothing technique) at the end of the procedure, as previously described.25 B. Data Analysis All patients underwent complete ocular evaluation, including corneal topography (Keratron Scout; Optikon 2000, Rome, Italy) both preoperatively as well as postoperatively. For each eye, measurements were repeated at least three times to assess the repeatability and accuracy of the topography. One of three good images of each eye was used for analysis. Reproducibility and accuracy of videokeratoscopic measurements were also tested using an artificial spherical cornea provided by the manufacturer and calculated from three independent measurements. The standard deviation for the high-order rms surface error was ±0.007 and ±0.04 ␮m at 4 and 7 mm in diameter, respectively. To analyze corneal aberrations, we exported the aberration data output (that were represented with a Zernike polynomial expansion, calculated with respect to the reference axis of topography, i.e., the line of sight26,27) from the Keratron topographer. The preoperative and one-year postoperative high-order Zernike coefficients (from third to Seventh Zernike orders) for 4and 7-mm pupils of all the corneas treated were processed in a custom software written in MATLAB (software version 7.0, The Math Works, Inc.) for analysis. First and second orders were not considered in this study. The sign of odd symmetric terms about the y axis (i.e., terms having positive m values when the orders n are odd numbered and negative m values when the orders n are even) was flipped in the right eye to combine data in a single database and also to test for mirror symmetry.28,29 This approach was applied to correct for enantiomorphism in the

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wavefront error maps of eyes30 that would make W共x , y兲 for the left eye the same as W共−x , y兲 for the right eye. The recommended Optical Society of America notation is used to describe individual Zernike terms with a two-index scheme and with a single-index scheme for bar plot coefficients.31 Optical quality corneal maps were obtained by computing the point-spread function (PSF) for 4- and 7-mm pupils. The PSF was calculated using the corneal wavefront data with the following formulas: PSF = 兩FT共PF共x,y兲兲兩2 ,

共1兲

where FT is the two-dimensional Fourier transform and PF is the pupil function. The pupil function has two components, an amplitude component A共x , y兲 and a phase component that contains the wave aberration W共x , y兲. The amplitude component A共x , y兲 defines the shape, size, and transmission of the optical system; for A共x , y兲 we have used a circ function that defines a circular aperture, with rays of 2 and 3.5 mm, and transmission unitary inside the circ and zero outside:

冋

PF共x,y兲 = A共x,y兲exp − i

2␲ ␭

册

W共x,y兲 ,

共2兲

where ␭ is the wavelength of light used (555 nm). The Stiles–Crawford effect was not incorporated in our computation, as it was outside the scope of this work (only the role of the anterior cornea on image quality was investigated). Paired Student’s t-test was used to compare the oneyear postoperative and the preoperative Zernike coefficient values. Correlation analysis (Pearson correlation coefficient r) was performed to analyze the HOA symmetry between right and left eyes. The significance level was 0.05 for all the tests performed. Statistical comparison of the preoperative data (SE refraction and HOA) revealed no significant differences (Fischer test, p ⬎ 0.05) between the right and left eyes of the study group.

3. RESULTS A. High-Order-Aberration Magnitude Values The mean one-year postoperative SE refraction was −0.02± 0.37 D (with a mean of −0.03± 0.31 D for the right eye and 0.00± 0.42 D for the left eye). No eyes lost one or more Snellen lines of the spectacle-corrected visual acuity. One patient (1 female, for a total of 2 eyes) did not complete the follow-up and hence was excluded from the computational analysis. Preoperative and postoperative average coefficient values are summarized in Fig. 1. The overall magnitude value of corneal HOA was almost confined to third and fourth orders both before as well as after surgery for the two analyzed pupils (Table 1). No discernible differences in the surgically induced increase of HOA between eyes were found, as shown in Table 1. Preoperatively, highorder aberrations showed average values that were near to zero over a 4-mm pupil. One year after surgery, the magnitude values of third and fourth corneal HOA did not significantly differ from the preoperative state, except for primary spherical aberration Z40 共p ⬍ 0.05兲. Preopera-

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Fig. 1. High-order Zernike coefficient values up to the seventh order before and one year after surgery over (a) 4- and (b) 7-mm pupils. The right and left eye WA data were averaged after converting the Zernike coefficients with odd symmetry about the y axis in the right eye. The numbers in the x axis represent the j index (single indexing scheme) related to each Zernike term. (a) Over the smaller pupil size, third-order terms (Z6 to Z9) were not significantly increased 共p ⬎ 0.05兲 after surgery, and primary spherical aberration (coefficient Z12) contained almost the overall magnitude value of corneal HOA. (b) Over a 7-mm pupil, most of the postoperative increase in the magnitude value of HOA was contained in the third and fourth orders. The inset shows an enlargement of the coefficient values with a different scale bar to emphasize the changes induced by photoablation for higher-order terms. Asterisks highlight high-order terms with a significant increase of the magnitude value induced by PRK 共p ⬍ 0.05兲.

tively, over a 7-mm pupil, the average values of all the Zernike terms were higher than those over the smaller pupil size, as expected. Six of nine Zernike terms of third and fourth orders were significantly increased 共p ⬍ 0.05兲 after surgery, including coma terms (Z31 and Z3−1) and primary spherical aberration Z40. B. High-Order-Aberration Symmetry between Eyes To determine the prevalence of bilateral symmetry of corneal HOAs in our population, for each patient we calculated correlation between the high-order corneal WA of right and left eyes both for 4- and 7-mm pupils. Postop-

erative values were also calculated to determine the effect of photoablation on mirror symmetry. Results are summarized in Tables 2 and 3. Over the smaller pupil size, the mean r for all the individuals (± one standard deviation) was 0.40± 0.35 and 0.42± 0.38 before and one year after surgery, respectively. This indicates a moderate degree of interocular symmetry between the anterior corneal highorder WA over the central pupil, with a large individual variability; also, PRK did not significantly influence the high-order corneal WA relationship between eyes within the ablation zone. Over a dilated pupil, the preoperative mean r for all the individuals was 0.81± 0.21, indicating

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clear mirror symmetry in the high-order WA between eyes. One year after surgery, the mean r was 0.80± 0.14 and the interocular symmetry of high-order WA appeared not to be altered by photoablation. The correlation between the high-order WA of right and left eyes was highly statistically significant 共p ⬍ 0.001兲 in all the patients, except for one, i.e., patient reference number 23, both before as well as after surgery. The scatter graphs between the left eye coefficients versus their corresponding value in

the right eye are shown in Fig. 2. Table 4 shows the interocular differences in total corneal rms HOA for each patient of the study group: Preoperative difference values ranged between 0.001 and 0.156 ␮m over a 4-mm pupil and between 0.006 and 0.238 ␮m over a 7-mm pupil. One year after surgery, there were no significant interocular differences in rms HOA compared with the preoperative state 共p ⬎ 0.05兲, with values ranging from 0.001 to 0.192 ␮m and from 0.001 to 0.779 ␮m for 4- and 7-mm

Table 1. Effect of Each Zernike Order on the Mean Total Corneal rms HOA for the Right and Left Eyes of the Study Group over 4- and 7-mm Pupils before As Well As after Surgery Right Eye Preoperative

Mean total rms HOA 共␮m兲 Third order (%) Fourth order (%) Fifth order (%) Sixth order (%) Seventh order (%)

Left Eye

One-Year Postoperative

Preoperative

One-Year Postoperative

4 mm

7 mm

4 mm

7 mm

4 mm

7 mm

4 mm

7 mm

0.159 63 27.8 4.7 2.8 1.7

0.727 43.2 53.2 2.2 0.9 0.5

0.273 44.5 52.3 1.5 1.1 0.6

1.254 29.5 69 0.9 0.4 0.2

0.146 60.2 29.1 5.3 3.4 1.8

0.732 43.9 53 2.1 0.6 0.4

0.271 41.6 55.3 1.7 0.8 0.6

1.262 34 64.6 0.8 0.4 0.2

Table 2. Correlation Coefficients for the High-Order Corneal WA between the Left and Right Eyes of Each Patient of the Study Group for 4-mm Pupil before As Well As after Surgery Significantly Correlated p ⬍ 0.001a

Correlation Coefficient r

a

Patient Reference Number

Preoperative

Postoperative

Preoperative

Postoperative

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

0.047 0.727 0.051 0.073 0.721 0.577 0.515 0.269 0.709 0.708 0.109 0.599 0.816 0.679 0.528 0.844 0.460 0.747 0.333 0.123 0.070 0.016 −0.530 −0.073 0.862 0.694 0.439 0.576 −0.125

0.463 −0,477 0.862 0.612 0.478 0.784 0.036 0.135 0.457 0.655 0.337 0.429 0.731 0.674 0.892 0.045 0.671 0.875 0.521 0.304 −0.679 0.333 −0.173 0.529 0.470 0.808 0.260 0.535 0.462

No Yes No No Yes Yes Yes No Yes Yes No Yes Yes Yes Yes Yes No Yes No No No No No No Yes Yes No Yes No

No No Yes Yes No Yes No No No Yes No No Yes Yes Yes No Yes Yes No No Yes No No No No Yes No Yes No

Bonferroni correction was applied to correct for multiple tests for the 30 Zernike high-order terms 共p ⬍ 0.05/ 30兲.

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Table 3. Correlation Coefficients for the High-Order Corneal WA between the Left and Right Eyes of Each Patient of the Study Group for 7-mm Pupil before As Well As after Surgery Significantly Correlated p ⬍ 0.001a

Correlation Coefficient r

a


Preoperative

Postoperative

Preoperative

Postoperative

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

0.792 0.888 0.932 0.823 0.896 0.869 0.665 0.965 0.848 0.869 0.871 0.855 0.953 0.783 0.889 0.922 0.844 0.916 0.709 0.682 0.779 0.903 −0.124 0.647 0.913 0.939 0.934 0.878 0.647

0.836 0.892 0.837 0.955 0.700 0.945 0.633 0.904 0.706 0.937 0.832 0.776 0.731 0.854 0.906 0.818 0.672 0.979 0.878 0.721 0.624 0.855 0.345 0.687 0.848 0.968 0.641 0.761 0.706

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes

Bonferroni correction was applied to correct for multiple tests for the 30 Zernike high-order terms 共p ⬍ 0.05/ 30兲.

pupils, respectively. Differences in total rms HOA between eyes showed to be predictive of no significant interocular symmetry of high-order corneal WA over a dilated pupil, where the greatest interocular differences were calculated for patient 23 both before as well as after surgery. This was not clearly demonstrated over a 4-mm pupil, probably dependent on the slight differences in total corneal rms HOA between eyes. Over the smaller pupil size, however, interocular differences greater than 0.100 ␮m correlated with no significant symmetry of high-order corneal WA between eyes. Average high-order WA color-coded maps of the study group over a 7-mm pupil were generated to emphasize mirror-image symmetry of HOA patterns between eyes and the effect of laser correction (Fig. 3). Mirror symmetry between HOA patterns of right and left anterior corneas was unchanged following PRK, however with an increased contribution of spherical aberration to overall high-order WA. As suggested by Thibos et al.,32 we used two different methods to compute the average image optical quality for our study population. The first uses the mean values of the Zernike coefficients to construct an average WA function, from which the PSF is computed. This method is

known to produce a modulation transfer function of high quality because aberration coefficients are equally likely to be positive or negative, so the average is near zero and may be representative of the upper bound on the optical quality achieved by individual eyes. In the latter method, instead of averaging the optical aberrations directly, we averaged the effect of those aberrations on image formation. It is as if we superimposed the PSFs for all the eyes in our study population, summed them, and divided by their total number to compute the mean. The result is a PSF that represents the lower bound to the optical quality of individual eyes. All of these calculations were performed for 4- and 7-mm pupils by using only the HOAs. Averages of the PSFs were calculated separately for the right and left eyes of the study group as well as bilaterally. By averaging Zernike coefficients, as performed in the first method, very-high-quality corneal PSFs were obtained over a 4-mm pupil both before and after surgery; slight differences between the image qualities of right and left corneas were also shown over a dilated pupil (Fig. 4). The binocular PSFs appeared not to be different from that computed for monocular corneal optics. The most significant information was the increased effect of spherical ab-

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erration following myopic ablation,33 as expected. On the other hand, the latter method of computation showed manifestly different orientation PSFs between eyes, despite their similar corneal HOA values (Figs. 5 and 6). The binocular PSFs smoothed the monocular effect of right and left corneal optics. One year after surgery, the interocular optical image quality balance was mainly affected by the increased contribution of spherical aberration to overall high-order corneal WA.

4. DISCUSSION It has been recently reported that the native ocular human optics show mirror symmetry between the HOA of right and left eyes of the same individual; however, this varyies from subject to subject. This was demonstrated both for the anterior cornea and the whole eye.17–20 In this study, we systematically analyzed the interocular symmetry between HOAs of the anterior cornea in a population of eyes that underwent bilateral PRK. The preoperative wavefront data from our statistics were similar to those reported in the literature on the distribution of corneal HOA in a young, healthy, myopic population: Magnitudes declined with order, except for spherical aberration, a positive value of Z40, and values near to zero over the central cornea, however with large individual variability.10–12,17 After surgery, the high-order terms were not significantly increased over a 4-mm pupil, except for primary spherical aberration.

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Possible explanations for the effect of ablation profile and parameters on central corneal asphericity were discussed in previous articles.34,35 On the other hand, a significant increase of the magnitude value of most of the third and fourth Zernike order terms was determined over a dilated pupil, as expected. Many works analyzed the effect of pupillary dilation and the role of ablation zone diameter on the amount of HOAs induced by laser correction,36–38 and our findings are in broad agreement with previous results. Preoperatively, a slight tendency toward the mirror symmetry of corneal HOA between eyes for a photopic pupil size was found. The low magnitude value of corneal HOA near to the center of the pupil in normal eyes, confirming the central tendency for human cornea (as also demonstrated for the whole eye optics) to be free of HOAs,10,12,18,32 may be an explanation for this observation. No significant interocular differences were observed one year after surgery. The smoothing technique following PRK induced less HOA within the optical zone and uncomplicated wound healing in comparison with PRK alone,25,39,40 thus maintaining low levels of anterior corneal HOA. Over a dilated pupil, a fair interocular correlation of anterior corneal HOA was demonstrated, as also reported by previous authors either for the corneal or the whole eye optics over 6- and 7-mm pupils.17,18,20,28,32 For only one patient in our population (3%) was a significant interocular correlation of corneal HOA not found over a 7-mm pupil, together with the highest interocular differences in total corneal rms HOA.

Fig. 2. Correlation of HOAs between the fellow eyes in our population for 4- and 7-mm pupils. (a) Preoperative data, (b) one-year postoperative data. Each symbol shows the value of aberration coefficients for a given Zernike mode determined for left and right eyes of the same individual. The sign of odd symmetric terms in the right eyes has been changed to test for mirror symmetry (bilateral symmetry predicts that data will fall along the positive diagonal). The solid lines represent a linear fit to the data.

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Table 4. Interocular Differences in Total Corneal rms HOA „␮m… of Each Patient of the Study Group over 4- and 7-mm Pupils before As Well As after Surgery 4-mm Pupila

a

7-mm Pupila


Preoperative

Postoperative

Preoperative

Postoperative

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

0.050 0.027 0.045 0.043 0.065 0.003 0.020 0.031 0.015 0.030 0.017 0.060 0.002 0.058 0.024 0.030 0.001 0.091 0.044 0.070 0.036 0.053 0.018 0.156 0.056 0.026 0.013 0.026 0.004

0.011 0.062 0.047 0.012 0.047 0.032 0.017 0.010 0.050 0.041 0.088 0.107 0.040 0.063 0.072 0.024 0.096 0.016 0.001 0.068 0.004 0.096 0.192 0.083 0.026 0.091 0.102 0.051 0.056

0.032 0.208 0.186 0.151 0.215 0.095 0.049 0.145 0.119 0.107 0.006 0.186 0.056 0.212 0.051 0.034 0.043 0.116 0.100 0.159 0.119 0.005 0.238 0.093 0.061 0.007 0.006 0.010 0.022

0.072 0.001 0.051 0.082 0.194 0.034 0.024 0.009 0.344 0.053 0.146 0.433 0.040 0.297 0.293 0.037 0.174 0.170 0.189 0.136 0.353 0.478 0.779 0.244 0.516 0.574 0.167 0.192 0.198

Student’s t-test: p ⬎ 0.05 共between preoperative and postoperative differences兲.

This tendency for the HOAs to be symmetric between right and left fellow corneas suggests that are some anatomical developmental factors underlying the control of the aberrations in eye optics. The bilateral symmetry of aberrations may be produced during the earlier stages of the development of the eye to improve optical quality and then to remain stable during adulthood. A recent work has demonstrated a significant correlation of third- and fourth-order Zernike terms between left and right eyes in a population of children.41 Moreover, symmetry is usually indicative of a systematic instead of a random process controlling the distribution of HOAs between eyes.28,42 Since the pupil is often mirror symmetrically decentered between eyes within the same individual, a balanced distribution of the aberrations may follow a mirror path in the right and left eyes with the best optical quality near the center of the pupil, as demonstrated with analysis of two pupil sizes. Also, authors have demonstrated that HOAs in the periphery are on average greater than those measured in the central optics of the eye and that they are symmetrically higher in the nasal visual field than in the temporal one.43,44 The alignment of ablation on pupil center45 and the wide optical zone used for myopic correction did not alter the native mirror symmetry of corneal

HOA between eyes. Average high-order corneal WA maps exhibited mirror-image symmetry between right and left eyes,30 and the interocular balance was unmodified one year after surgery, although there was an increased contribution of spherical aberration to overall corneal highorder WA. Present results correlate with our previous work on the differences in local response of the cornea to photoablation, where significant interocular changes occurred outside the optical zone (from 6 to 9 mm in diameter)24 and changes inside the ablation zone were comparable between right and left fellow corneas. Data cannot be extrapolated for LASIK, in which the effect of the flap creation on corneal aberrations needs to be considered. A difference in the orientation of the induced coma as a function of hinge position has been demonstrated,46 and this may greatly influence the interocular symmetry of the high-order corneal WA over a dilated pupil after surgery. To demonstrate the effect of interocular symmetry of HOA on the optical quality of the anterior cornea, we calculated average corneal PSFs for right and left eyes separately as well as for both eyes together. The role of the intraocular optics has not been taken into account in our computation PSF. In recent years, a great deal of work

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has been devoted to accurately measure the optical quality of human eye optics.47,48 The development of promising methods to correct optical HOAs (i.e., adaptive optics or customized laser surgery) represents a great stimulus to research for an adequate representation of the aberrations and their effect on vision. In this work, we computed corneal PSF using two different methods representing the upper and lower limits to the mean optical quality in our population to emphasize the complexity of interaction between aberrations and their relation with image quality. By averaging the Zernike terms, as performed in the first method, it was shown that the role of paracentral asymmetrical aberration (i.e., coma terms) was markedly underestimated both in monocular and in binocular averaging. For coma terms, the sign of the coefficient determines the direction of smearing of the image; when Zernike terms with positive or negative values are averaged in a

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population study, the net result tends to be a lower aberration value, near to zero, depending on the relative magnitude of the terms, thus minimizing the real effect of paracentral aberrations on the quality of the anterior corneal optics. Summing the effect of aberrations, as performed in the second method, could better represent the image optical quality in a study population. However, the separate effect for right and left eyes needs to be represented due to the smoothing effect calculated in binocular summation without allowing for enantiomorphism. In addition, this method is still imperfect because of the random variations in spatial symmetry of the PSF in computing population means.32 The main difference between the preoperative and postoperative optical quality maps of right and left corneas in our population was the increased contribution of spherical aberration to overall high-order WA. No discern-

Fig. 3. (Color online) High-order corneal WAs for the average right and left eye in the study group both properatively as well as one year postoperatively for a 7-mm pupil. The software allowed precise overlapping of the wavefront data for averaging with respect to the reference axis of topography (i.e., the line of sight). A fixed color scale, visually similar to that of commercial videokeratoscopes, was developed for easy interpretation (scale bar in micrometers). Myopic PRK did not appear to significantly influence the mirror-image symmetry of high-order corneal WA between eyes, although there was a large induced increase in spherical aberration.

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Fig. 4. Average PSFs for the right and left eyes as well as for all the eyes of the study group computed from the high-order WA for a 7-mm pupil. PSFs subtend to a visual angle of 30 arc min. Preoperatively (upper row), the combination of all determined high-order Zernike coefficients showed a similar orientation PSF between the right and left eyes. One year after surgery (lower row), spherical aberration dominated the optical image quality of the anterior cornea. There were no significant differences in the orientation PSF between eyes. Also, bilateral PSF was marked similar to monocular PSFs. Over a 7-mm pupil, the preoperative and postoperative mean high-order rms errors were comparable between eyes in our population, as summarized in Table 1.

Fig. 5. Average PSFs computed over a 4-mm pupil using the second method defined in the text. Before surgery, third-order terms dominated the optical image quality of the central corneal optics; after surgery the effect of spherical aberration largely increased (see Table 1). The preoperative and postoperative mean high-order rms errors were comparable between eyes over a 4-mm pupil (as reported in Table 1).

ible changes in orientation PSFs between eyes were observed one year after surgery in comparison with the preoperative state. Previous researchers analyzed the possible role of interocular differences on visual perfor-

mance with regard to laser refractive correction.17,24,49 It was found that an interocular relationship in corneal asphericity can positively influence visual function.50 Authors concluded suggesting that interocular differences

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Fig. 6. Average PSFs for the right and left eyes as well as for all the eyes of the study group computed over a 7-mm pupil using the second method defined in the text. The optical quality appeared to be worst in comparison with that computed in Fig. 4. Differences between the optical quality of right and left anterior corneas are also highlighted with this method of computation. The binocular PSFs smoothed the monoptical effect of right and left corneas, resulting in an improved image quality in comparison with monocular PSFs both before as well as after surgery.

have to be taken into account to improve the personalized correction of ocular aberration in refractive laser surgery. Further psychophysical studies are needed to elucidate the exact influence of aberration symmetry between eyes on visual performance, in which more parameters have to be investigated, such as the relationship between aberrations and cone directionality,28 the effect of combinations of HOAs on binocular vision, and the role of neural processing in vision. Indeed, the effect of HOA on binocular summation and binocular visual acuity may be less significant than that on monocular performance of the eye.49 This positive enhancement may be due to a mechanism of neural and psychophysical adaptation.51 Also, the role of internal WAs will be subsequently considered. A planned wavefront-guided procedure necessitates that both the corneal and the total WAs be taken into consideration to optimize the visual performance of the individual.8,9 The authors have no financial interest in the materials described herein.

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Marco Lombardo can be reached as follows: Via Adda 7, 00198 Rome, Italy; e-mail, [email protected]. 12.

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