Bessel Function Model for Corneal Topography

Abstract

In this paper we consider a new nonlinear mathematical model for corneal topography formulated as two-point boudary value problem. We derive it from first physical principles and provide some mathematical analysis. The existence and uniqeness theorems are proved as well as various estimates on exact solution. At the end we fit the simplified model based on Modified Bessel Function of the First Kind with the real corneal data consisting of matrix of 123x123 points and obtain an error of order of 1%.