### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 5aPA1. Eigenfunction and eigenvalue analysis of scattering operators.

**T. Douglas Mast
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Robert C. Waag
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*Dept. of Elec. Eng., Univ. of Rochester, Rochester, NY 14627
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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.