A new deformable mirror influence function based on a Gaussian function is introduced to analyze the fitting capability of a deformable mirror. The modified expressions for both azimuthal and radial directions are presented based on the analysis of the residual error between a measured influence function and a Gaussian influence function. With a simplex search method, we further compare the fitting capability of our proposed influence function to fit the data produced by a Zygo interferometer with that of a Gaussian influence function. The result indicates that the modified Gaussian influence function provides much better performance in data fitting. (c) 2008 Optical Society of America.