article · Journal of the Optical Society of America A · 1992
Spectral methods in edge-diffraction theories
Cited by 6Abstract and details only
Abstract
Spectral methods for the construction of uniform asymptotic representations of the field diffracted by an aperture in a plane screen are reviewed. These are separated into contrasting approaches, roughly described as physical and geometrical. It is concluded that the geometrical methods provide a direct route to the construction of uniform representations that are formally identical to the equivalent-edge-current concept. Some interpretive and analytical difficulties that complicate the physical methods of obtaining uniform representations are analyzed. Spectral synthesis proceeds directly from the ray geometry and diffraction coefficients, without any intervening current representation, and the representation is uniform at shadow boundaries and caustics of the diffracted field. The physical theory of diffraction postulates currents on the diffracting screen that give rise to the diffracted field. The difficulties encountered in evaluating the current integrals are thoroughly examined, and it is concluded that the additional data provided by the physical theory of diffraction (diffraction coefficients off the Keller diffraction cone) are not actually required for obtaining uniform asymptotics at the leading order. A new diffraction representation that generalizes to arbitrary plane-convex apertures a formula given by Knott and Senior [ Proc. IEEE62, 1468 ( 1974)] for circular apertures is deduced.
Cite this paper
Arnold, J. M. (1992). Spectral methods in edge-diffraction theories. Journal of the Optical Society of America A, 9(12), 2192. https://doi.org/10.1364/josaa.9.002192
Arnold, John M. “Spectral methods in edge-diffraction theories.” Journal of the Optical Society of America A, vol. 9, no. 12, 1992, p. 2192, https://doi.org/10.1364/josaa.9.002192.
Arnold, John M. 1992. “Spectral methods in edge-diffraction theories.” Journal of the Optical Society of America A 9 (12): 2192. https://doi.org/10.1364/josaa.9.002192.
Arnold, J.M. (1992) ‘Spectral methods in edge-diffraction theories’, Journal of the Optical Society of America A, 9(12), p. 2192. Available at: https://doi.org/10.1364/josaa.9.002192.
@article{arnold1992spectral,
title = {{Spectral methods in edge-diffraction theories}},
author = {Arnold, John M.},
journal = {Journal of the Optical Society of America A},
volume = {9},
number = {12},
pages = {2192},
year = {1992},
doi = {10.1364/josaa.9.002192}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.