Approximating ocular surfaces by generalised conic curves

Abstract

Most of the optical models of the human eye use simple conic functions to represent its individual components such as corneal surfaces and the surfaces of the crystalline lens. Although a conic function provides an acceptable approximation for most anatomical eye surfaces, it also leads to a simple optical analysis of the whole eye system. To fill the gap between the classical use of conic surfaces and the use of more sophisticated functions that often invoke numerically expensive procedures in the optical analysis, a functional generalisation of the conic curve is proposed. A detailed derivation of the generalised conic function is presented for a two-dimensional (meridional) case. This is followed by a three-dimensional surface approximation. Examples are given in which the superiority of the proposed approximation over a classical conic function as well as the hyperbolic cosine approximation is evident. In particular, it is shown that for an average total corneal profile, the proposed generalisation results in a residual height error that is of an order smaller than those achieved with the conic and hyperbolic cosine approximations. In conclusion, the proposed generalised conic function can be a useful tool in eye modelling, where the simplicity of expression is often desirable.