Light-scattering properties of very thin or flat dielectric particles are approximately calculated by means of a method which combines Rayleigh-Gans and Rayleigh scattering. For the approximation to be valid the shortest diameter of the particle, Rmin, must be small compared to the longest diameter Rmax and to the wavelength λ of the incident radiation. The method is applied to needles and circular disks and yields the scattering matrix and the differential and total scattering cross section in the lowest order of Rmin/Rmax and Rmin/λ. For the disks the total cross section is calculated only in the limiting cases of long and short wavelengths.

The total integrated reflectivity of a slightly rough dielectric surface is studied by the Rayleigh-Rice method. Special emphasis is laid on the correct second-order terms of the perturbation expansion; this is important for correlation lengths of the surface structure comparable to the wavelength. The main effects of a surface roughness of this kind are reflection loss, shift of the Brewster angle to smaller values, and slight reddening of the scattered light.

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The average scattering cross section for reflection of electromagnetic waves by an ensemble of randomly oriented convex particles is calculated. The particles are assumed to be large compared to the incident wavelength and to have a slightly rough surface such that the deviations from a smooth surface are smaller than wavelength. A perturbation expansion resulting from the Rayleigh–Rice approach leads to incoherent and coherent corrections to the zero-order specularly reflected light. The quantity that in this limit completely determines the scattering behavior of the particles is the two-point correlation function ρ(r) of the roughness structure. The main effect of roughness is a diminution of the reflected intensity for a wide range of the scattering angle θ and a shifting of the maximum of the polarization curve to larger θ. It turns out that measurements of the backscattered intensity in some wavelength limits provide information on the correlation function ρ(r). For conducting material, knowledge of the cross-polarized backscatter intensity over a wide frequency range even enables one, at least in principle, to calculate the complete shape of the correlation function.

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