A new method for improving the accuracy of wavefront fitting with Zernike polynomials

Zernike polynomials have been widely used to fit wavefront and, by their representation, calculate the deviation due to wavefront aberrations in an optical system. In order to obtain the coefficients of the Zernike polynomials, a set of discrete orthogonal polynomials needs to be constructed using the Gram-Schmidt method on a unitary circle, and the coefficients are then calculated by fitting the wavefront data and orthogonal polynomials by the least squares method. Through simulation, it is found there is a large deviation between the given coefficients and the calculated results because of limitations of the least squares method. This paper proposes a modified method to improve the accuracy of wavefront fitting.