  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%.

Analysis of PDEs