On the Absolute Accuracy of Zernike Polynomials to Characterize the Corneal Surface and the Optical Aberrations of the Human Eye

摘要

Zernike Polynomials have been successfully used for many years in optics. Nevertheless there are some recent discussions regarding their accuracy when applied to surfaces such as the human cornea. A set of synthetic surfaces resembling several common corneal anomalies was sampled and was also used to compute the optical path difference using a simple ray-tracing procedure. The Root Mean Square Error between the Zernike Polynomials fit and the theoretical elevation and WF error surface was computed for both surfaces and for all number of Zernike terms. We have found that RMSE for the simplest, most symmetric corneal surface (spherical shape) and for the most complex shape (post-radial keratotomy) both the optical path difference and surface elevation, for 1 through 36 Zernike terms, range from: 421.4 to 0.8 microns, and 421.4 to 8.2 microns, respectively; mean RMSE for maximum Zernike terms for both surfaces were 4.5 microns. Computations in this work suggest that, for surfaces such as post-RK, keratoconus or post-keratoplasty, even more than 36 terms may be necessary in order to obtain minimum precision requirements. We suggest that the number of Zernike Polynomial should not be a global fixed conventional value but rather based on specific surface properties.