Although the far-field formulas derived in Chapter 13 for a stochastic scattering object are attractively simple, they have a rather limited range of applicability. Indeed, one of the criteria of the far zone, Eq. (5.14), becomes quite challenging for an object significantly greater than the wavelength (Problems 14.1 and 14.2) and often prohibits direct use of the far-field approximation. It turns out, however, that many aspects of the far-field formalism can be preserved if the stochastic scattering object belongs to a particular morphological type. Specfically, in this chapter we will assume that the object can be defined as a group of N distinct particles separated from each other and distributed throughout an imaginary volume element V. Accordingly, the starting point of the analysis of electromagnetic scattering by this object will be the FEs derived in Section 6.1 rather than the VIE. In addition, we will assume that:

1. • the total number of particles forming the object is sufficiently small and the average distance between them is sufficiently large that in the framework of the FEs (Section 6.1), each particle can be assumed to be “excited” only by the incident field;

2. • the N-particle object is observed from a distance much greater than any linear dimension of the volume element V;

3. • although the observation point is allowed to be in the near zone of the entire object, it is remote enough to be in the far zone of any of the N distinct particles forming the object; and

4. • the N particles are moving randomly and independently of each other throughout the volume element V.