The ℐ-matrix method, as extended recently to randomly oriented scatterers [ J. Opt. Soc. Am. A 8, 871 ( 1991)], is used to calculate rigorously light scattering by size–shape distributions of randomly oriented axially symmetric particles. The computational scheme is described in detail along with a newly developed convergence procedure that enables one to substantially reduce computer time and storage requirements. It is demonstrated that the elements of the Stokes scattering matrix for a power law size distribution of randomly oriented moderately aspherical spheroids are much smoother than and differ substantially from those of equivalent monodisperse spheroids, and thus averaging over orientations does not eliminate the necessity of averaging over particle sizes. Numerical calculations are reported for volume-equivalent polydispersions of spheres and size–shape distributions of moderately aspherical spheroids with the index of refraction 1.5 + 0.02 i, which is typical of some maritime aerosols. The angular-scattering behavior of the ensembles of nonspherical particles is found to be greatly different from that of the equivalent polydisperse spheres. The size–shape distributions of spheroids exhibit stronger side scattering near 120° and weaker backscattering, the ratio F22/F11 of the elements of the scattering matrix substantially deviates from unity, and the element F33 is greatly different from F44. For size distributions of oblate and prolate spheroids of the same aspect ratio, the ratios F22/F11, F33/F11, and F34/F11 can differ substantially and, thus, are indicators of particle shape, whereas the angular patterns of the intensity (F11) and linear polarization (−F12/F11) are similar. For the size–shape distributions of moderately aspherical spheroids, the optical cross sections, the single-scattering albedo, and the asymmetry parameter of the phase function do not differ substantially from those of equivalent spheres. In general, the elements of the scattering matrix and optical cross sections are more shape dependent for larger particles.
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