Evaluation of optimal Zernike radial degree for representing corneal surfaces

Abstract

Tomography data of the cornea usually contain useful information for ophthalmologists. Zernike polynomials are often used to characterize and interpret these data. One of the major challenges facing researchers is finding the appropriate number of Zernike polynomials to model measured data from corneas. It is undeniable that a higher number of coefficients reduces the fit error. However, utilizing too many coefficients consumes computational power and time and bears the risk of overfitting as a result of including unnecessary components. The main objective of the current study is to analyse the accuracy of corneal surface data modelled with Zernike polynomials of various degrees in order to estimate a reasonable number of coefficients. The process of fitting the Zernike polynomials to height data for corneal anterior and posterior surfaces is presented and results are shown for normal and pathological corneas. These results indicate that polynomials of a higher degree are required for fitting corneas of patients with corneal ectasia than for normal corneas.