RefractiveRefractive SurgerySurgery andand OpticalOptical AberrationsAberrations Susana Marcos

or more than a century there Measuring refractive- has been awareness of the fact surgery-induced change F that the eye is not a perfect of corneal aberrations optical system and that it suffers Computerized videokeratography from defects or optical aberrations — which measures the shape of the other than defocus and . , typically by analysis of the Attempts to measure the wave aber- distortion of concentric rings pro- ration of the , i.e., phase jected on it—is routinely used in distortions at the plane of the pupil, clinics to evaluate surgical results date back to 1894. In recent years, (i.e., centration and location of the new terminology and new technolo- treatment zone and characteristic gy have invaded the field of refrac- patterns of what is known in clini- tive surgery and changed the way cal terms as irregular corneal astig- 2 ophthalmologists and optometrists matism). Applegate et al. and 3 look at the image-forming capabili- Oliver et al. used corneal elevation ties of ocular optics. Wave-front- Courtesy of Jesús Merayo and Raúl Martín. maps from commercial corneal sensing, aberrometers, high-order aberra- topographers to measure the changes tions, and Zernike polynomials are only a induced in the cornea by different types of few of the novelties that have recently optical quality of the human eye.1 Only refractive surgery; their findings show that entered the field. recently, however, as these procedures refractive surgery is generally followed by an Over the past two decades, several new have begun reaching a clinical population, increase in the amount of and an alteration methods have been developed to assess the has the instrumentation involved captured in the distribution of aberrations. the attention of refractive surgeons. For The corneal surface and the pattern of the compensation of refractive errors aberrations associated with any optical sys- (, hyperopia, and astigmatism), tem are typically described as a polynomi- corneal refractive surgery has become a al expansion. The first-order terms corre- spond to a prismatic error; the second- popular alternative to wearing or order terms to defocus and astigmatic contact lenses: the operation and recovery errors; third-order aberrations include are rapid and the procedures are constant- coma, in which a point source appears as a ly being perfected. The surgery alters the comatic shape; fourth-order aberrations curvature of the central area of the cornea, include spherical aberration, or increased reducing it in myopes and increasing it in focusing error as the pupil dilates. Studies hyperopes. From the lens designer’s point based on show that, of view, it is clear that a change in only part for large pupils, corneal aberrations of the front surface of the cornea (the most increase by approximately a factor of 3. In refractive element of the ocular optical sys- addition, the distribution of aberrations tem) must modify the aberration pattern shifts from third-order dominance (coma- of the entire optical system. Particularly like) to fourth-order dominance (spheri- in the case of large pupils, an increase in cal). The dramatic increase in spherical Asymmetric optical aberrations—despite the correc- aberration is caused by a surgery-induced Symmetric tion of defocus and astigmatism—can change in corneal asphericity. Figure 1 frequently be associated with complaints shows the distribution of aberrations (in of halos and visual loss at night. Under- Figure 1. Distribution of corneal aberrations terms of variance) in normal eyes, and (symmetric versus asymmetric) for eyes before standing the change in aberrations in- one-year after (RK), (pre-op) and one year after myopic RK, PRK and duced by standard refractive surgical pro- photorefractive keratectomy (PRK) , and LASIK. (Adapted from R. A. Applegate, H. C. cedures is important for assessment of in situ (LASIK). In Howland, and S. D. Klyce, Corneal Aberrations and how vision can be compromised after general, there is an increase in both third- Refractive Surgery in Customized Corneal : The surgery. It is essential to develop new abla- and fourth-order aberrations, and the Quest for Super Vision, Slack, Inc., N.J., in press. tion algorithms to overcome such prob- increase is correlated to a decrease in con- Courtesy of R.A. Applegate.) lems, and perhaps even improve vision. trast sensitivity.

22 Optics & Photonics News January 2001 1047-6938/01/01/0022/4-$0015.00 © Optical Society of America REFRACTIVE SURGERY

Measuring the aberrations point source are imaged sequentially Figure 2. In an ideal aberration-free eye, rays of the entire optical system as a laser beam scans the pupil through any pupil location would converge onto the same retinal location. The wave aberration Although refractive-surgery-induced opti- through different positions, and the would be flat, and the image of a point source cal changes occur on the cornea and the deviations of each image from the viewed through a large pupil would be an Airy 4-6 anterior corneal surface provides the main principal ray are analyzed ; disk. Real eyes are aberrated. Therefore, rays that contribution to refraction, corneal aberra- • Dresden wave-front analyzer (DWA), enter the eye through different pupil locations will tions are not sufficient to describe the in which the distortions of an array of hit the at different locations. The deviations overall optical quality of the eye. points projected in the pupil are ana- from the ideal are proportional to the local slope Experimental measurement of total lyzed7-9; of the wave aberration, which is distorted. The ocular aberrations is the most direct and • Spatially resolved refractometer (SRR), retinal image of a point source, (which can be sim- accurate way to evaluate the effects of a sequential procedure like the LRT, ulated from the wave aberration), is in general refractive surgery on global image quality, which differs from it in that the retinal asymmetric. Most instruments that measure the aberrations of the living human eye measure these and it can be more directly related to visu- displacements are assessed psychophys- al performance. Figure 2 shows the under- deviations by projecting light beams through the ically by the subject, who aligns the pupil and by analyzing the light returned from the 10 lying principle of most methods for mea- spots to a reference cross ; retina, or by psychophysical methods. surement of the wave aberration of the eye. • Hartmann–Shack wave-front sensor, in If the eye were perfect, or in other words which the wave front is sampled as it (a) only limited by diffraction (Fig. 2, upper exits the eye by a microlens array conju- (b) panel), rays that enter the eye through any gate to the pupil, and the deviations of pupil position would converge on the same the multiple images from the ideal focal retinal location. But in the presence of points are analyzed.11-13 aberrations, rays that enter the eye through different pupil positions deviate from the Figure 4 shows some examples of ideal location (or principal ray), as indicat- overall wave aberrations (third- through ed in Fig. 2, lower panel. These deviations seventh-order in the Zernike polynomial are proportional to the local derivatives of expansion) from a recent study by 6 (c) (d) the wave aberration; in other words, the Moreno-Barriuso et al. The results are rays are normal to the wave front that trav- for the same patients before and approx- els toward the retina. A perfect eye would imately one month after myopic LASIK have a wave aberration of zero; for an aber- surgery. The measurements were made rated eye, the wave aberration is the devia- with a laser ray-tracing system developed tion of the distorted wave front from the by Rafael Navarro and colleagues at the ideal sphere (see Fig. 2). With knowledge Consejo Superior de Investigaciones of the wave aberration, and therefore also Cientificas (CSIC) in Madrid, Spain. For of the pupil function of the entire optical each patient, the scale used to plot the wave Figure 3. Raw data using different methods to system, we can compute the point- aberration is the same before and after assess aberrations following refractive surgery. (a) spread-function (an Airy disk for the ideal surgery, and in all cases pupil diameter is LRT: series of retinal images of a point source system, but in general, an asymmetric 6.5-mm. Preoperative myopia ranged through different entry locations. This is a one- shape for the eye) and simulate the degra- between -13 and -2 diopters (D), and pre- month post-LASIK eye (Moreno-Barriuso et al.). dation of any visual scene projected on operative astigmatism was less than 2.5 D. (b) DWA: image of a grid distorted by the ocular the retina (Fig. 2). Preoperative aberration patterns showed a aberrations (courtesy of M. Mrochen). (c) large intersubject variability in terms of Hartmann–Shack wave-front sensor: image of a Several wave-front-sensing methods point source projected on the retina through a have been used to measure the ocular aber- both amount and distribution, but in gen- lenslet array in a two-month post-LASIK patient rations associated with refractive surgery. eral no deep valleys or high peaks were (courtesy of X. Hong and L. Thibos). (d) Spatially Figure 3 shows raw data from four of them: found. After surgery, a typical central resolved refractometer: sets of alignments (in the • Laser ray tracing (LRT) system, in island (associated with the ablation pat- form of a retinal spot diagram) from a post-LASIK which a series of aerial images of a tern) appears in all cases, with variable patient (courtesy of K. Thompson and S. A. Burns).

January 2001 Optics & Photonics News 23 REFRACTIVE SURGERY amounts of decentration. Root-mean- nonconventional terms (third order and retinal image results after standard LASIK square (rms) wave-front error is used as a higher) increases on average by a factor of because of an increase in third- and higher- global image quality metric. We observed 2. Data are also classified by orders: third- order aberrations. The image quality dete- that the rms increased in all cases after and fourth-order terms increase signifi- rioration occurs for both small (3-mm) standard LASIK surgery. cantly after surgery, whereas the higher- and large (6-mm) pupil sizes, but is more Figure 5 shows the average results for 22 order terms do not show a significant dramatic for dilated pupils. Along with a eyes (6.5-mm pupil) from the study by increase. The largest increase occurred for decrease in contrast, halos and ghost Moreno-Barriuso et al.: the green bars rep- spherical aberration (the main contributor images appear after surgery because of the resent data before surgery and the red bars to the fourth-order terms), which in this presence of asymmetric aberrations that represent data after surgery. The rms for all group of subjects increased by a factor of 4. affect phase information. Although these The spherical aberration simulations represent only those images induced is correlated with projected on the retina and cannot be con- the attempted myopic sidered by any means as an exact rendition correction, indicating that of what the patient actually perceives after the larger the decrease in processing by the entire visual system, they central corneal curvature are indicative of the blur caused by high- needed and the more tis- order aberrations, not obvious to practi- sue removed, the more tioners until recently. dramatic the change in asphericity and spherical Toward a perfect ablation aberration. The genera- To compensate for ametropias refractive tion of third-order terms surgery has improved over the years, with is associated with decen- the result that these operations are fast tered ablation zones. and generally uneventful. Visual out- These results agree with comes have been improved by the com- the findings from the bined effects of experience accumulated study by Seiler et al.8 of by practitioners and the incorporation of patients following stan- technical improvements such as active dard PRK surgery. By use eye-tracking systems to ensure proper of the Dresden wave- centration. Until recently, because the front analyzer, they main goal has been to compensate for found an even larger refractive errors, little attention has been increase in the amount of paid to retinal image degradation caused overall aberrations, prob- by nonconventional aberrations. We have ably because of differ- already shown that, when we compensate ences in the ablation for myopia with current techniques, the algorithms and the fact amount of aberrations increase, particular- that an eye-tracker sys- ly spherical ones. To avoid causing spheri- tem was not used during cal aberration, new ablation profiles are surgery. needed. Schwiegerling and Snyder14 pro- With knowledge of the posed ideal aimed at reducing the wave aberration, it is pos- amount of induced spherical aberration, sible to simulate how any although a caveat with this model is the visual scene looks on the requirement of a deeper ablation pattern subject’s retina by con- and a more abrupt transition zone. volving the point-spread Until recently, excitement about and function with the original interest in refractive surgery have over- image. Figure 6 shows the shadowed the problem of new aberrations effect of aberrations on in the eye; now, however, attention is turn- the retinal image of a ing toward compensating for individual Snellen card (a test com- preoperative high-order aberrations, as monly used by doctors to well as for conventional refractive errors. assess ). In The idea is to apply a customized corneal this chart, the bottom line ablation during the surgical procedure, Figure 4. Wave aberration of five eyes before corresponds to a visual acuity of 20/20 which has been adapted to the patient’s and after standard myopic LASIK surgery (assumed to be the highest resolving own aberration pattern. Several compa- (Moreno-Barriuso et al.), with a laser ray-tracing power of a normal eye, equivalent to 30 nies have started incorporating aberrome- method. Only third-order and higher terms are c/deg). Preoperative and postoperative ters (either based on corneal topography or shown (i.e., best correction for defocus and astig- results for one patient are shown, assum- overall wave aberration measurements) matism is assumed). Root-mean-square wave- 15 front error is taken as an image quality metric. ing best correction for defocus and astig- into their laser systems to guide ablation. matism in all cases. A degradation of the The first results of wave-front-guided

24 Optics & Photonics News January 2001 REFRACTIVE SURGERY

Figure 5. Root-mean-square wave-front error in a group of 22 patients before and after standard LASIK surgery. Average data from Moreno-Barriuso et al. Data are shown for all nonconventional (third-order and higher) aberrations together and by orders of a Zernike polynomial expansion. All terms (except the highest orders) register a significant increase following surgery. The largest increase (by a factor of 4) occurs for spherical aberration.

LASIK show improvements in some eyes Applegate, Michael Mrochen, Xin Hong, Figure 6. Retinal image of a visual acuity card for 9, 16 over standard LASIK. and Keith Thompson for providing fig- an eye before and after standard LASIK surgery, There are still several limits to the ures; Esther Moreno-Barriuso for ines- obtained by convolution of the original card with achievement of an aberration-free eye: timable contributions at all stages of the the ocular point-spread-function. This simulation study; Lourdes Llorente and Sergio does not represent what the subject really per- • the wound healing process can modi- Barbero for their enormous help in the lab- ceives, but the appearance of the image projected fy the final corneal thickness and oratory; and Jesús Merayo and Raúl on the retina. Contrast loss, halos and ghost images shape; Martín (Instituto de Oftalmobiología (frequent complaints for night vision after surgery) • overall aberrations depend on the Aplicada, Universidad de Valladolid, appear particularly for a large (6-mm) pupil. patient’s accommodative state (near Spain) for patient selection and screening. or far vision) because of a change of 11. J. Liang et al., “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, the aberrations of the crystalline 2873 (1997). lens17; References 12. M. C. W. Campbell et al., "Dependence of optical 18, 19 1. W.N. Charman, “Wave front aberrations of the image quality on : eyes after • aberrations change with age ; eye: a review,” Optom. Vision Sci. 68, 574 (1991). photorefractive keratectomy (PRK) • compensation is attempted for a single 2. R.A. Applegate et al., “Corneal aberrations and versus controls," Invest. Ophthalmol. Visual Sci. visual performance after radial keratotomy,” J. (Suppl.) 40, 7 (1999). wavelength, although polychromatic Refract. Surg. 14, 397 (1998). 20 13. X. Hong et al., “Longitudinal evaluation of optical aberrations are equally important. 3. K.M. Oliver et al., “Corneal optical aberrations aberrations following laser in situ keratomileusis induced by photorefractive surgery,” J. Refract. Surg. 16, 647 (2000). On the other hand, the final limit to keratectomy,” J. Refract. Surg. 13, 246 (1997). 14. J. Schwiegerling et al., “Corneal ablation patterns to spatial resolution is imposed by retinal 4. R. Navarro et al., “Aberrations and relative effi- correct for spherical aberration in photorefractive ciency of light pencils in the living human eye,” keratectomy,” J. Cataract Refract. Surg. 26 (2), 214 and neural factors, even if the optics are Optom. and Vision Sci. 74, 540 (1997). (2000). perfectly corrected. All these aspects need 5. E. Moreno-Barriuso et al., "Ocular aberrations 15. S.M. MacRae et al., “Customized corneal ablation after refractive surgery measured with a laser ray and super vision,” J. Refract. Surg. 16, 230 (2000). to be taken into account to achieve a per- tracing technique," Invest. Ophthalmol. Visual Sci. 16. M. McDonald, “Summit-autonomous custom cornea fect correction and can be used to deter- (Suppl.) 41, 303 (2000). laser in situ keratomileusis outcomes,” J. Refract. mine whether other approaches (such as 6. E. Moreno-Barriuso et al., “Ocular aberrations Surg. 16, 617 (2000). before and after corneal refractive surgery: LASIK- 17. J.C. He et al., “Monochromatic aberrations in the custom-made intraocular lenses) would induced changes measured with Laser Ray accommodated human eye,” Vision Res. 40, 41 be better alternatives than corneal refrac- Tracing,” Invest. Ophthalmol. Visual Sci. (to be (2000). tive surgery. It is extremely significant, published). 18. J. S. McLellan et al., “Age-related changes in mono- 7. P. Mierdel et al., “Measuring device for determining chromatic wave aberrations in the human eye,” however, that contributions from differ- monochromatic aberration of the human eye,” Invest. Ophthalmol. Visual Sci. (to be published). ent fields including optics and astronomy Ophthalmologe 94 (6), 441 (1997). 19. A. Guirao et al., “Optical aberrations of the human 8. T. Seiler et al., “Ocular optical aberrations after cornea as a function of age,” J. Opt. Soc. Am. A 17, are providing new insights into refractive photorefractive keratectomy for myopia and 1697 (2000). surgical procedures. Patient care will myopic astigmatism,” Arch. Ophthalmol. (Chicago) 20. S. Marcos et al., “A new approach to the study of undoubtedly benefit. 118, 17 (2000). ocular chromatic aberrations,” Vision Res. 39, 4309 9. M. Mrochen et al., “Wave front-guided Laser in (1999). situ Keratomileusis: early results in three eyes,” J. Acknowledgments Refract. Surg. 16, 116 (2000). Susana Marcos is a faculty research scientist at the The author thanks Stephen A. Burns for a 10. J.C. He et al., “Measurement of the wave-front Instituto de Optica, Consejo Superior de Investi- aberration of the eye by a fast psychophysical pro- gaciones Científicas, Madrid, Spain. She can be critical review of the manuscript; Ray cedure,” J. Opt. Soc. Am. A 15, 2449 (1998). reached at [email protected].

January 2001 Optics & Photonics News 25