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Accuracy of Zernike Polynomials in Characterizing Optical Aberrations and the Corneal Surface of the Eye

From the Grupo de Óptica, Instituto de Física de São Carlos, Universidade de São Paulo (IFSC-USP), São Paulo, Brazil; and the Departamento de Oftalmologia, Escola Paulista de Medicina, Universidade Federal de São Paulo (UNIFESP), São Paulo, Brazil.

PURPOSE. Zernike polynomials have been successfully used for approximately 70 years in many different fields of optics. Nevertheless, there are some recent discussions regarding the precision and accuracy of these polynomials when applied to surfaces such as the human cornea. The main objective of this work was to investigate the absolute accuracy of Zernike polynomials of different orders when fitting several types of theoretical corneal and wave-front surface data.

METHODS. A set of synthetic surfaces resembling several common corneal anomalies was sampled by using cylindrical coordinates to simulate the height output files of commercial videokeratography systems. The same surfaces were used to compute the optical path difference (wave-front [WF] error), by using a simple ray-tracing procedure. Corneal surface and WF error was fit by using a least-squares algorithm and Zernike polynomials of different orders, varying from 1 to 36 OSA-VSIA convention terms.

RESULTS. The root mean square error (RMSE) ranged—from the most symmetric corneal surface (spherical shape) through the most complex shape (after radial keratotomy [RK]) for both the optical path difference and the surface elevation for 1 through 36 Zernike terms—from 421.4 to 0.8 µm and 421.4 to 8.2 µm, respectively. The mean RMSE for the maximum Zernike terms for both surfaces was 4.5 µm.

CONCLUSIONS. These results suggest that, for surfaces such as that present after RK, in keratoconus, or after keratoplasty, even more than 36 terms may be necessary to obtain minimum accuracy requirements. The author suggests that the number of Zernike polynomials should not be a global fixed conventional or generally accepted value but rather a number based on specific surface properties and desired accuracy.