BEYOND DIFFUSION TO DIFFRACTION

Transport in random multiple-scattering systems in which the wave fiel d is delocalized is often described using the diffusion equation. In c ontrast, we examine the propagation of amplitude-amplitude correlation s in such a system from first principles: the summation of random mult iple-scattering series. We use generalized transfer matrices to sum th e series corresponding to the conventional ladder diagrams of perturba tion theory. The method is applied to correlations in both the Fourier space and the frequency domains. Using a specific model, the scalar w ave equation, we show how to diagonalize analytically these generalize d transfer matrices. Diffusive behaviour arises in the appropriate lim its of long length and long time, while over shorter length and time-s cales the diffusion equation breaks down and there is a transition to a more wave-like behaviour. Our results have applications to image rec onstruction and signalling. In particular there is a 'quantum' limit t o the amount of detail that can be reconstructed from an image blurred by passage through a random scattering region.