Scattering of electromagnetic radiation near the backward direction is more sensitive to particle shape than scattering near the forward direction. Mie theory is therefore of dubious applicability to predicting backscattering by atmospheric particles known to be irregular or to inverting measurements on such particles. An irregular particle is one with an uncertain shape. In the face of uncertainty one must adopt a statistical approach in which scattering properties of ensembles are determined. To obtain ensemble averages, a basis is needed for averaging over a set of electromagnetic microstates. Ensemble averages based on the Rayleigh theory for small ellipsoids and on the T matrix method for spheroids agree better with measurements than Mie theory does. The coupled‐dipole method also provides a basis for ensemble averaging. This method also leads to a simple physical interpretation of why backscattering is so sensitive to particle shape and can be used to calculate scattering by one‐ and two‐dimensional analogs to three‐dimensional irregular particles.

The field scattered by an arbitrary particle modeled as an array of coupled dipoles can be expressed as an infinite series in terms of scattering orders. The fields of a given scattering order can be calculated from those of the previous order. When the series converge, the approximate method agrees well with the exact theory for a sphere. The maximum size of the dipolar array that can be used with the method as well as the number of terms required for convergence depends on the relative refractive index and the shape of the particle.

Longwave properties of the orientation averaged Mueller scattering matrix for particles of arbitrary shape. I. Dependence on wavelength and scattering angleThe coupled dipole approximation is applied to the calculation of the scattering matrix of an arbitrary particle. Both isotropic and anisotropic dipoles are used in the calculations. The forms of the matrices obtained for several types of scatterers are found to be in exact agreement with those predicted by symmetry. The method is tested quantitatively by comparison with Mie predictions for solid and coated spheres and good agreement is observed. This comparison is also used to establish appropriate magnitudes for anisotropic dipolar polarizabilities.

The coupled dipole model of scattering by an arbitrary particle has been reformulated in terms of internal scattering processes of all orders. This formalism readily permits physical interpretation of observables and provides a rational basis for making computations more efficient. The calculation of scattering parameters can be simplified by appropriately terminating the infinite series at any order as well as by restricting the summations over the dipolar interaction terms within each order. Large particles can be partitioned into segments so that the scattered field is a superposition of the fields from the segments together with fields due to interactions among dipoles in different segments.

An efficient numerical method is derived for evaluation of the scattering properties of randomly distributed particles described by the coupled dipole approximation. An exact analytic average for these properties is also derived. All elements of the scattering matrix for a collection of randomly oriented particles can be obtained by either method. The results are applicable to model calculations of the scattering matrix for realistic particles. The analytic average also allows qualitative interpretation of the dependence of the matrix elements on dipolar interactions.