Abstract

An algorithm for fast numerical integration of near-field scalar diffraction formulas is presented, based on the local approximation of the integrand of the diffraction equation by a variant of the Fresnel kernel. The two-dimensional local propagation integral is solved analytically for an integration domain enclosed between two mutually perpendicular line segments and a parabolic arc. We show that, by combining rectangular and arched elements, one can achieve accurate computation of the field diffracted at complicated aperture shapes without having to resort to time-consuming numerical quadrature techniques. The numerical accuracy and the computational speed of the algorithm are assessed and compared with the performance of the linear-phase approximation method developed by Hopkins and Yzuel [ Opt. Acta 17, 157 ( 1970)].

© 1994 Optical Society of America

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