Optical Diffraction in Close Proximity to Plane Apertures. III. Modified, Self-Consistent Theory

Published

September 1, 2004

Author(s)

Klaus Mielenz

Abstract

The classical theory of diffraction by plane apertures illuminated by normally incident light is modified so that the diffraction on the source side of the screen is taken in to consideration and the optical field is continuous as well as continuously differentiable in the aperture plane. The modified field expressions involve the sums and differences of the Rayleigh-Sommerfeld diffraction integrals as descriptors of a bi-directional flow of energy in the near zones on either side of the aperture plane. The modified theory is valid for unpolarized fields and can be applied to metallic as well as black screens. In the mid zone it is reduced to the Fresnel approximation, and here the latter may be used with confidence. The modified field expressions are used for numerical near-field computations of the diffraction profiles and transmission coefficients of circular apertures and slits.

Citation

Journal of Research (NIST JRES) -

Volume

109 No. 5

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

Keywords

bidirectional scalar fields, boundary-value theory, circular apertures, diffraction, irradiance, Kirchhoff, near zone, optics, polarization

Citation

Mielenz, K. (2004), Optical Diffraction in Close Proximity to Plane Apertures. III. Modified, Self-Consistent Theory, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed October 15, 2025)