A theoretical framework to formulate and solve the problem of obtaining the objective refraction of an eye from aberrometric data is presented. Matrix formalism was applied to represent lens power and beam vergences in standard clinical, sphere+cylinder (S+C) refraction, and to describe the vergence error of a general aberrated skew ray. The vergence error matrix of each ray passing through the pupil is obtained, and the global refractive error is obtained by simple pupil average. The 2×2 vergence error matrix of a skew ray can be decomposed into the sum of two even-symmetric and odd-symmetric contributions. The even symmetric part corresponds to classic S+C refractive errors. The odd component can not be corrected with standard lenses. All odd components have zero mean over pupil, and do not contribute to the global refractive error, which is completely determined by S+C components. The contributions of wavefront Zernike modes to the global vergence error were obtained: The contributions of odd orders are zero, but all even HOA, but spherical aberration, contribute to refractive error. The matrix formulation of power and vergence errors provided a direct, simple way to use aberrometers as objective refractometers.
A multizone model for postsurgical corneal topography is presented and applied to a comparative analysis of the outcome of standard and customized myopic LASIK. The different zones are segmented automatically by a clustering algorithm. The algorithm uses a set of three local descriptors, which correspond to normalized physical magnitudes computed for each point of the corneal topography map: Gauss curvature, root-mean-square (RMS) fit error to an ellipsoid surface model, and distance to the center of the topographic map. Both presurgical and post-LASIK corneal topographies of 31 eyes were analyzed using monozone and multizone models. The patients were classified into three groups according to the different LASIK treatments applied: Allegretto, Zyoptix, and PlanoScan. For post-LASIK corneas, the multizone model provided a lower fit error, an average of 1.2±0.4 µm versus 2.4±0.7 µm (monozone). The comparative analysis of the three different LASIK treatments showed no improvement of custom over standard treatments. The outcomes of Zyoptix and PlanoScan were basically equivalent and consistent with previous findings: The higher-order aberration (HOA) increased by a factor of two. The increase in HOA was higher, by a factor of three, after the Allegretto treatment. The mutizone model shows a higher-fidelity representation and permits a deeper understanding of the postsurgical cornea.