Starting with the most elementary multiple scattering problem, a symmetrically excited pair of monopoles, we use both “successive-scattering” and “self-consistent” procedures to obtain the closed-form multiply scattered amplitude in terms of the singly scattered value. Then we represent the field for an arbitrary configuration of arbitrary scatterers in terms of the individual, multiply scattered amplitudes, and specify these in terms of singly scattered amplitudes by a system of self-consistent integral equations. Applications are made to fixed configurations (two scatterers, and the diffraction grating), and to random distributions (models for rough surfaces, and for random media). Simple explicit results in terms of isolated scatterer functions are derived, and some of their essential features are given in graphs: the coupling effects for two dielectric rods (intensity and phase) are graphed versus spacing for both polarizations; for the diffraction grating, when a surface wave is “near grazing,” the spectral orders show essential features of the anomalies measured by Wood, Strong, and Palmer; for a lossless rough surface, the graphs for both polarizations for the coherently reflected intensity and phase are analogous to those obtained for reflection from a lossy interface (the corresponding results for the incoherent scattering accounting for the loss from the “main beam”); and for a slab region containing a random distribution of nearly transparent large scatterers, we graph the macroscopic parameters, and the coherent and incoherent, forward-scattered intensities versus the fractional volume.
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