Statistical generalizations of the optical cross-section theorem with application to inverse scattering

A fundamental result of scattering theory, the so-called optical theorem, applies to situations where the field incident on the scatterer is a monochromatic plane wave and the scatterer is deterministic. We present generalizations of the theorem to situations where either the incident field or the scatterer or both are spatially random. By using these generalizations we demonstrate the possibility of determining the structure of some random scatterers from the knowledge of the power absorbed from two plane waves incident on it.