Optimal modeling of corneal surfaces with Zernike polynomials

Zernike polynomials are often used as an expansion of corneal height data and for analysis of optical wavefronts. Accurate modeling of corneal surfaces with Zernike polynomials involves selecting the order of the polynomial expansion based on the measured data. We have compared the efficacy of various classical model order selection techniques that can be utilized for this purpose, and propose an approach based on the bootstrap. First, it is shown in simulations that the bootstrap method outperforms the classical model order selection techniques. Then, it is proved that the bootstrap technique is the most appropriate method in the context of fitting Zernike polynomials to corneal elevation data, allowing objective selection of the optimal number of Zernike terms. The process of optimal fitting of Zernike polynomials to corneal elevation data is discussed and examples are given for normal corneas and for abnormal corneas with significant distortion. The optimal model order varies as a function of the diameter of the cornea.