Usefulness of orthogonal basis sets for predicting optical performance of wavefronts with mid-spatial frequency error

Abstract

Mid-spatial frequency (MSF) texture on optical elements degrade their performance. A Zernike polynomial representation of the wavefront can be used to characterize the mid-spatial frequency and predict the optical performance. The ability to generate very large orders of Zernike polynomials enables fitting and describing optical wavefronts all the way from low order form errors to mid-spatial frequencies. Based on a filtering aspect of Zernike polynomials, we show how different fabrication signatures affect optical performance differently. We investigate the Strehl ratio and Modulation Transfer Function (MTF) as optical performance metrics for mid-spatial frequency. We then present how the orthogonality properties of Zernike polynomials along with linear systems theory of MTF can provide an effective tool in separating the optical performance degradation due to different mid-spatial frequency texture. We present an example of real mid-spatial frequency texture to examine the error in the approximation of MTF when using linear systems formulation.