Parametric fitting of corneal height data to a biconic surface

Abstract

As the average corneal shape can effectively be approximated by a conic section, a determination of the corneal shape by biconic parameters is desired. The purpose of the paper is to introduce a straightforward mathematical approach for extracting clinically relevant parameters of corneal surface, such as radii of curvature and conic constants for principle meridians and astigmatism. A general description for modeling the ocular surfaces in a biconic form is given, based on which an implicit parametric surface fitting algorithm is introduced. The solution of the biconic fitting is obtained by a two sequential least squares optimization approach with constrains. The data input can be raw information from any corneal topographer with not necessarily a uniform data distribution. Various simulated and clinical data are studied including surfaces with rotationally symmetric and non-symmetric geometries. The clinical data was obtained from the Pentacam (Oculus) for the patient having undergone a refractive surgery. A sub-micrometer fitting accuracy was obtained for all simulated surfaces: 0,08 μm RMS fitting error at max for rotationally symmetric and 0,125 μm for non-symmetric surfaces. The astigmatism was recovered in a sub-minutes resolution. The equality in rotational symmetric and the superiority in non-symmetric surfaces of the presented model over the widely used quadric fitting model is shown. The introduced biconic surface fitting algorithm is able to recover the apical radii of curvature and conic constants in principle meridians. This methodology could be a platform for advanced IOL calculations and enhanced contact lens fitting.

Keywords: Biconic fitting; Hornhaut-Topographie; Oberflächenfits; Optische Oberflächen; corneal topography; ocular surfaces.