On the theory of scalar diffraction and its application to the prolate spheroid

doi:10.1016/0003-4916(59)90083-1

Annals of Physics

Volume 6, Issue 3, March 1959, Pages 277-299

https://doi.org/10.1016/0003-4916(59)90083-1 Get rights and content

Abstract

Scalar scattering of a plane wave by a perfectly reflecting body whose surface is a level surface in a coordinate system in which the scalar wave equation is separable is considered. A general method for the computation of the surface distribution is described. This method reduces the problem of finding the surface distribution to that of evaluating a certain contour integral. The distribution induced on a prolate spheroid by an axially-symmetric plane wave is specifically computed. The evaluation by residues of the contour integral, given by the general theory, leads to the expected “creeping wave” interpretation of the residue series in which the attenuation of the “creeping waves” depends, in first approximation, on the local radius of curvature. The asymptotic theory used is applicable for large values of cω, where 2c is the interfocal distance of the spheroid and ω is the wave number. The surface distribution is computed over the entire shadow region including the tip.

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^☆: The research reported in this paper has been sponsored by the Air Force Cambridge Research Center, Air Research and Development Command, Contract AF-19(604)-1949.

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On the theory of scalar diffraction and its application to the prolate spheroid☆

Abstract

Trans. I.R.E.

J. Math. and Mech.

New York University Research Report EM-42

University of Michigan Report No. 2591-4-T

Trans. Am. Math. Soc.

Trans. Am. Math. Soc.

J. Phys. (USSR)