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Proceedings Paper

Classical scattering theory of waves from the viewpoint of an eigenvalue problem and application to target identification
Author(s): Chris Bottcher; M. R. Strayer; Michael F. Werby
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Paper Abstract

The Helmholtz-Poincare Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWEs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a biorthogonal expansion of the Green function. However some freedom of choice in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermition operator. The methodology is explained in detail and examples are presented.

Paper Details

Date Published: 15 October 1993
PDF: 9 pages
Proc. SPIE 1960, Automatic Object Recognition III, (15 October 1993); doi: 10.1117/12.160612
Show Author Affiliations
Chris Bottcher, Oak Ridge National Lab. (United States)
M. R. Strayer, Oak Ridge National Lab. (United States)
Michael F. Werby, Naval Research Lab. (United States)


Published in SPIE Proceedings Vol. 1960:
Automatic Object Recognition III
Firooz A. Sadjadi, Editor(s)

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