Estimation of scatterer volume density near a concentration gradient

A general formulation of the echo received from a random scatterer ensemble illuminated by a short electromagnetic or sonic signal is developed. It is shown theoretically and confirmed experimentally with ultrasound, that a gradient in scatterer density will return an echo which is partially spatially coherent (i.e. specular). The surface of a random ensemble of uniform scatterers is shown to produce an echo from whose degree of coherence, the scatterer density and cross section can be calculated.