T. Douglas Mast
Robert C. Waag
Dept. of Elec. Eng., Univ. of Rochester, Rochester, NY 14627
Acoustic scattering by a given inhomogeneity can be compactly described by a scattering operator. This operator acts on the transmitted acoustic field to yield the scattered acoustic field on a measurement surface. For scattering at fixed frequency, the operator is known to admit a basis of eigenfunctions. When a finite number of transmit angles and receiving points is considered, the scattering operator can be represented as a matrix with an associated basis of eigenvectors. The present paper reports an investigation of the relationship between these eigenfunctions, eigenvectors, and associated eigenvalues and the characteristics of scattering objects, including their location, size, shape, orientation, and strength. Scattering operators are derived analytically for axisymmetric scatterers such as cylinders; in this case, the eigenfunctions of the operators take on simple trigonometric forms. Connections are noted between the eigenvalues and eigenfunctions of the scattering operators and the basis functions that appear in orthogonal function representations of the scattered fields. Scattering matrices for arbitrary scatterers are calculated using a coupled finite-element/integral equation method due to Kirsch and Monk [IMA J. Num. Anal. (to appear)]. Examples of the relationship between scatterer properties and eigenvalues and eigenvectors of the scattering matrix are presented.