Generalized optical theorem for scatterers having inversion symmetry: Applications to acoustic backscattering

The far-field acoustic scattering amplitudes for the scattering of plane wa ves by targets having inversion symmetry obey a generalized optical theorem in the absence of dissipation. The theorem allows a component of the compl ex scattering amplitude in an arbitrary direction to be expressed in terms of an angular integration involving scattering amplitudes evaluated at diff erent angles. The result reduces to the usual optical theorem in the case o f forward scattering. The theorem is applied to the backscattering by a per fectly soft sphere as a numerical example. The relevant integrand is shown to be oscillatory. Some potential applications to inverse problems, multipl e scattering, and the verification of numerical algorithms are noted. (C) 2 001 Acoustical Society of America.