Wavelet Methods for the Representation, Analysis and Simulation of Optical Surfaces

In this paper, we introduce a wavelet method for the description, approximation, analysis and simulation of optical surfaces. We describe the new method and show results of several numerical experiments for relevant applications in optics. We focus on three main aspects. First, we describe a highly accurate representation of smooth optical surfaces in terms of a B-spline quasi-interpolant. This representation is used in a ray trace algorithm for the analysis of optical systems and is particularly suited for a wavelet decomposition. The Fast Wavelet Transform gives access to the use of wavelets for the separation of low and mid spatial frequency errors modeled by Zernike polynomials and Power Spectral Density functions, as well as the localization and correction of errors. We compare our results with the classical representation in terms of Zernike polynomials.