An Alternative Polynomial Representation of the Wavefront Error Function

Abstract

Abstract: : Purpose: Despite the good mathematical properties of Zernike polynomials, their fit to the wavefront error functions or height data from a videokeratoscope may not always be adequate. This occurs mainly because Zernike polynomials are global functions and are not suitable for characterizing local changes. A question arises whether a set of functions exists that would result in better modeling of the wavefront error function. Methods: We used our recently reported Bhatia-Wolf polynomial based method (IEEE Trans. on Biomed. Eng. Vol. 49, 2002, in press) as an alternative for modeling the wavefront error functions and compared it to the traditional Zernike polynomial based modeling. Results: The modeling error (RMS) of the Bhatia-Wolf polynomial based method is always smaller than that of the Zernike polynomials for a given radial order. For normal subjects it was observed that reduction in the modeling error was in the range of 30% to 50%. For subjects with significant aberrations (e.g. severe keratoconus), the decrease in the MSE was tenfold. Although some of the lower order terms of the Bhatia-Wolf polynomial expansion may not be directly recognized as a commonly known type of aberration, their use in fitting gives a significant improvement in wavefront estimation. We provide a physical explanation for these terms and introduce the concept of generalized defocus. Conclusion: The use of Bhatia-Wolf polynomial based modeling of the wavefront error function is a viable alternative to the Zernike polynomial representation. This is particularly important in areas such as customized refractive surgery, where the information from the Zernike polynomial fit may be directly used.

Keywords: 364 computational modeling • 542 refraction • 500 optical properties