Classical scattering theory of waves from the viewpoint of an eigenvalue problem and application to target identification

Chris Bottcher; M. R. Strayer; Michael F. Werby

doi:10.1117/12.160612

15 October 1993 Classical scattering theory of waves from the viewpoint of an eigenvalue problem and application to target identification

Chris Bottcher, M. R. Strayer, Michael F. Werby

Author Affiliations +

Proceedings Volume 1960, Automatic Object Recognition III; (1993) https://doi.org/10.1117/12.160612
Event: Optical Engineering and Photonics in Aerospace Sensing, 1993, Orlando, FL, United States

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.

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Chris Bottcher, M. R. Strayer, and Michael F. Werby "Classical scattering theory of waves from the viewpoint of an eigenvalue problem and application to target identification", Proc. SPIE 1960, Automatic Object Recognition III, (15 October 1993); https://doi.org/10.1117/12.160612

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