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
Original Manuscript: October 29, 1993
Revised Manuscript: April 4, 1994
Manuscript Accepted: May 2, 1994
Published: October 1, 1994
Luigi A. D’Arcio, Joseph J. M. Braat, and Hans J. Frankena, "Numerical evaluation of diffraction integrals for apertures of complicated shape," J. Opt. Soc. Am. A 11, 2664-2674 (1994)