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

The far-field acoustic scattering amplitudes for the scattering of plane waves by targets having inversion symmetry obey a generalized optical theorem in the absence of dissipation. The theorem allows a component of the complex scattering amplitude in an arbitrary direction to be expressed in terms of an angular integration involving scattering amplitudes evaluated at different angles. The result reduces to the usual optical theorem in the case of forward scattering. The theorem is applied to the backscattering by a perfectly soft sphere as a numerical example. The relevant integrand is shown to be oscillatory. Some potential applications to inverse problems, multiple scattering, and the verification of numerical algorithms are noted.