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 astigmatism. cornea, typically by analysis of the Attempts to measure the wave aber- distortion of concentric rings pro- ration of the human eye, 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- (myopia, 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 glasses 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 corneal topography 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 radial keratotomy (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 laser in situ keratomileusis (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 Ablation: 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 I 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 retina 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.