By definition, a discrete random medium (DRM) is a scattering object in the form of an imaginary volume V populated by a large number N of particles in such a way that the spatial distribution of the particles throughout the volume is statistically uniform or quasi-uniform. Over time, particle positions and states change randomly, thereby resulting in random changes of the state ψ of the entire object (Section 10.4). Classical examples of a DRM are clouds and particle suspensions (Plates 1.1b—1.1d). In many cases a particulate surface (Plates 1.1e and 1.1f) can also be modeled as a DRM, since even minute changes of the source-of-light → object → detector configuration during the measurement are equivalent to multi-wavelength shifts in particle positions and, in essence, result in a stochastic scattering object. The volume packing density of a DRM can vary from almost zero for a cloud to more than 50% for a particulate surface.

Given their specific morphological traits and ubiquitous presence, scattering objects in the form of a DRM deserve a detailed study. As always, the desirable way to model electromagnetic scattering by an ergodic DRM is to solve the MMEs numerically for a representative set of realizable states ψ of the object and then average the relevant optical observables or energy-budget characteristics using an appropriate probability density function ρ(ψ) (Section 10.4).