Diffractal echoes

Abstract

Studies the dependence on time delay tau of the average echo power I( tau ) resulting from the reflection of a quasi-monochromatic outgoing pulse of radiation by a multiscale random surface, modelled as a fractal with Hausdorff-Besicovitch dimension D+1 between 2 and 3. In the 'weak fractal' limit where the fractal height variations are small, the reflection is paraxial and I( tau ) decays as tau ^-(3-D), for both statistically isotropic and 'corrugated' surfaces. This behaviour contrasts with a smooth random surface, for which I( tau ) decays exponentially.