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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 11, Iss. 10 — Oct. 1, 1994
  • pp: 2664–2674

Numerical evaluation of diffraction integrals for apertures of complicated shape

Luigi A. D’Arcio, Joseph J. M. Braat, and Hans J. Frankena  »View Author Affiliations


JOSA A, Vol. 11, Issue 10, pp. 2664-2674 (1994)
http://dx.doi.org/10.1364/JOSAA.11.002664


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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

History
Original Manuscript: October 29, 1993
Revised Manuscript: April 4, 1994
Manuscript Accepted: May 2, 1994
Published: October 1, 1994

Citation
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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-10-2664

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