Wavefront fitting using Gaussian functions

Often the polynomial description of a wavefront shape is inaccurate because sharp local deformations are difficult to represent. In this case an analy tical representation in terms of Gaussians may give better results. We have made a study of properties of Gaussians in fitting wavefronts. We analyzed an specific array of Gaussian functions and show their easy Fourier transf ormation. In Fourier space some criteria are proposed for setting the Gauss ian width, the separation between these functions and making an estimation of the wavefront fitting error. Two simulated wavefronts are fitted and a c omparison with a Zernike polynomial is made. It is well known that when fit ting using Zernike polynomials one needs to find the optimal number of term s beyond which the errors in the approximation become larger. We show that using Gaussians the accuracy of the fit increases with the number of terms. We demonstrate some interesting properties, such as their facility to fit local deformations and fast parameter determination. (C) 1999 Published by Elsevier Science B.V. All rights reserved.