The discussion in the preceding chapter was limited to the far field of a random particulate volume comprising a moderate number of particles. However, one is often interested in the near field in order to compute the energy budget of a volume element of a DRM rather than of the entire DRM. Furthermore, in the majority of actual applications the detector of light is located in the near zone of the entire DRM, including the cases of being inside the particulate volume. Although numerically exact solvers of the MMEs such as the MSM (Section 16.1.3) can be used to compute the near field of a DRM (see, e.g., Mackowski and Mishchenko 2013), the applicability of this direct approach is still limited in terms of the number of constituent particles and the overall size of the particulate volume relative to the wavelength.

This implies that the near-field solution of the MMEs for stochastic multi-particle objects such as those shown in Plates 1.1b—1.1f has to be based on a number of simplifying assumptions such as ergodicity, the sparsity and statistical uniformity of the particles' spatial distribution, and the asymptotic limit N → ∞, where N is the number of particles in a DRM. The main objective of the following analysis is to show that this methodology can indeed be used to derive analytically a set of closed-form equations that can be solved numerically with relative ease.