Abstract: A new precise algorithm for computing the fitting coefficients of the Zernike polynomial was presented. The new algorithm orthogonalized and triangulated the matrix of inconsistent equation group by using improved Gram-Schmidt orthogonalization method. The Zernike coefficients were worked out directly. The algorithm was verified by fitting the given coefficients and normal mathematical surface respectively. The new algorithm has equivalent computational precision to the algorithm of constructing normal equation group. By avoiding constructing normal equation group, the computational error introduced by constructing normal equation group is eliminated. The new algorithm is easy to be programmed and proved to be an efficacious algorithm.

Key words: nonlinear optics, wave-front aberration fitting coefficients, improved Gram-Schmidt orthogonalization method, Zernike polynomial