Beam domain formulation for wave propagation in weakly rough media

We present a novel strategy for tracking wavefields in weakly fluctuating medium as an extension of the phase-space beam summation method. In this method, which is based on the theory of overcomplete frames, the aperture source is expanded using a windowed Fourier transform frame, thus expressing the radiating field as a sum of beams emerging from a discrete set of points and directions in the source domain. We show that the set of propagating beams constitutes an overcomplete frame in the propagation zone, denoted as the propagating frame. This results in a new self consistent formulation for tracking wave fields in fluctuating medium, where the propagating field is described as a sum of beam fields, while the interaction of these beams with the medium is re-expanded using the same set of beams.