Classification of wave phenomena and its relation to coherence theory

Various types of problems that arise within the framework of wave propagation through a medium are classified according to whether the medium or the source is random or nonrandom. When both medium and source are nonrandom, the applicable differential equation is of a deterministic nature; otherwise, it is stochastic. A representative case of a random medium and nonrandom source is the multiple scattering of a monochromatic wave by a randomly perturbed medium or by random scatterers. A case in which the medium is nonrandom and the source random is exemplified by the theory of partial coherence. Finally, when both medium and source are random we have the general case in which waves generated by random sources propagate through random media. The last case, which reduces under appropriate conditions to each one of the remaining types, is discussed in detail and its formal solution is obtained by the perturbation method.