ABSTRACT

Numerical techniques play an important role in investigations of the fluctuations of scattered waves. This chapter covers two aspects: generation of random processes, and simulation of wave propagation. The former allows one to produce a set of numbers which conform to a particular statistical model, a

realization

of the random process under consideration, and the latter to investigate the propagation of radiation after it has interacted with a scattering system. For example, one can generate a set of numbers corresponding to the phase shifts produced at different positions on a random phase screen and then simulate the propagation of electromagnetic radiation through the screen to investigate the development of intensity fluctuations. This approach complements the analytical techniques described in the rest of this book. Analytical techniques usually calculate averages or probability distributions. With numerical techniques one can observe single realizations, which will often give useful physical insight into the scattering process. Averages, and other statistical quantities, can also be calculated numerically by repeatedly generating realizations. These can be used to check the results of analytical calculations and to investigate regimes that are analytically intractable (this also works in the reverse direction; in fact, the first thing one should always try to do with a new numerical algorithm is to reproduce a known analytical result). There are, of course, limits to what can be achieved numerically, and numerical techniques will never replace analysis.