Classical Scattering Theory of Waves from the View Point of an Eigenvalue Problem and Application to Target Identification
NAVAL RESEARCH LAB STENNIS SPACE CENTER MS
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The Helmholtz Poincare Wave Equation HPWE 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 form objects. The extended boundary integral equations EBIE method is derived from considering both the exterior and interior solutions of the HPWEs. 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 and eigenvalue problem of a related Hermition operator. The methodology will be explained in detail and examples will be presented. Acoustic scattering, shallow water, Waveguide propagation.