Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Numerical Evaluation of Diffraction Integrals

Published

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

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 April 15, 2024)
Created July 1, 2000, Updated February 17, 2017