Optical Diffraction in Close Proximity to Plane Apertures. II. Comparison of Half-Plane Diffraction Theories

Published

January 1, 2003

Author(s)

Klaus Mielenz

Abstract

The accuracy and physical significance of the classical Rayleigh-Sommerfield and Kirchhoff diffraction integrals are assessed in the context of Sommerfield s rigorous theory of half-plane diffraction and Maxwell s equations. It Is shown that the Rayleigh-Sommerfield integrals are in satisfactory agreement with Sommerfield s theory in most of the positive near zone, except at sub-wavelength distances from the screen.. On account of the bidirectionalnature of diffraction by metallic screens the Rayleigh-Sommerfield integrals themselves cannot be used for irradiance calculations, but must be resolved into forward and reverse components and it is found that Kirchhoff s integral is the appropriate measure of the forward irradiance. Because of the inadequate boundary conditions assumed in their derivation the Rayleigh-Sommerfeld and Kirchhoff integrals do not correctly describe the flow of energy through the aperture.

Citation

Journal of Research (NIST JRES) -

Volume

108 No. 1

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

Keywords

bidirectional fields, diffraction, half plane, irradiance, Kirchhoff, Maxwell, metallic screen, near zone, optics

Citation

Mielenz, K. (2003), Optical Diffraction in Close Proximity to Plane Apertures. II. Comparison of Half-Plane Diffraction Theories, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed October 14, 2025)