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Optical Diffraction in Close Proximity to Plane Apertures. I. Boundary-Value Solutions for Circular Apertures and Slits

Published

Author(s)

Klaus Mielenz

Abstract

In this paper the classical Rayleigh-Sommerfeld and Kirchhoff boundary-value diffraction integrals are solved in closed form for circular apertures and slits illuminated by normally incident plane waves. The mathematical expressions obtained involve no simplifying approximations, are free of singularities, and were used for numerical computations in the near zone in which the Fresnel approximation does not apply. It was found that all of these solutions fail in the immediate vicinity of the aperture, in that they do not correctly describe the diffracted field as an analytical continuation of the incident geometrical field. This inconsistency appears to be confined to sub-wavelength distances from the aperture plane. At larger distances, the differences between the three solutions become imperceptibly small even before the Fresnel limit is reached.
Citation
Journal of Research (NIST JRES) -
Volume
107 No. 4

Keywords

circular apertures, diffraction, Kirchhoff, near zone, optics, polarization, Rayleigh-Sommerfeld, scalar wavefunctions, slits

Citation

Mielenz, K. (2002), Optical Diffraction in Close Proximity to Plane Apertures. I. Boundary-Value Solutions for Circular Apertures and Slits, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed May 28, 2024)

Issues

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Created August 1, 2002, Updated February 17, 2017