Random processes in wave propagation

Part I. Transmission: For wave propagation through a randomly scattering medium, theory predicts statistical averages of certain measurements. Familiar theories are discussed in terms of the measurements to which they relate. For instance, the "extinction cross section" of a large opaque object is simply shown to be twice its geometric cross section; the relevant measurement is not one of transmitted power flux, but an interferometric measurement of the average phase and amplitude of a coherent wave passing through a cloud of such objects. A similar interferometric measurement relates to the attenuation currently calculated from the Booker-Gordon scattering formula. This is shown by two new derivations of the propagation constant of a "blobby" medium. The simpler measurement of average transmitted power-flux requires a complicated theory of photon transport. Theory and measurements relating to angle-of-arrival are intermediate between those relating to power-flux and propagation constant. Part II. Reflection: Similar considerations hold for reflection from a rough surface. Specular reflection is an interferometric concept. Lambert\´s law and backscatter are power-flux concepts. A theory of specular reflection is logically prior to a theory of backscatter. The requirements for such theories are discussed through simple examples.