Numerical Evaluation of Diffraction Integrals

Published

July 1, 2000

Author(s)

Klaus Mielenz

Abstract

This paper describes a simple numerical integration method for diffraction integrals which is based on elementary geometrical considerations of the manner in which different portions of the incident wavefront contribute to the diffracted field. The method is applicable in a wide range of cases as the assumptions regarding the type of integral are minimal, and the results are accurate even when the wavefront is divided into only a relatively small number of summation elements. Higher accuracies are can be achieved by increasing the number of summation elements and/or incorporating Simpson's rule into the basic integration formula. The use of the method is illustrated by numerical examples based on Fresnel's diffraction formulas for circular apertures and apertures bounded by infinite straight lines (slits, half planes). In the latter cases, the numerical integration formula is reduced to a simple recursion formula, so that there is no need to perform repetitive summations for every point of the diffraction profile.

Citation

Journal of Research (NIST JRES) -

Volume

105 No. 4

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

Keywords

circular aperture, diffraction, half plane, numerical integration, recursion formula, slit

Citation

Mielenz, K. (2000), Numerical Evaluation of Diffraction Integrals, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed May 3, 2026)

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