Parameterized scattering matrices for small particles in planetary atmospheres

Parameterized matrices are discussed that may be used as (single) scattering matrices for interpretations of the brightness and polarization of planetary atmospheres containing randomly oriented small particles. A number of guidelines are developed for the construction of such matrices. These guidelines are based on (i) physical conditions for the elements of a natural scattering matrix, some holding for arbitrary scattering angles and some for the exact forward and backward scattering directions only, as well as (ii) theorems for the asymptotic behavior of coe$cients in expansions of the matrix elements in generalized spherical functions of the scattering angle. A set of parameterizedmatrices is introduced and assessed according to these guidelines. These particular parameterizations are especially useful for scattering by particles that are not large compared to the wavelength, particles in the Rayleigh}Gans domain and for a variety of irregularly shaped particles in the visible part of the spectrum. The use of parameterized matrices as scattering matrices is illustrated by deriving their elements as functions of the scattering angle from simulated measurements of the brightness and polarization of light re#ected by plane}parallel atmospheres containing aggregated or spheroidal particles. In both cases, the scattering angle dependences of the original elements are retrieved in fair approximation. 2001 Elsevier Science Ltd. All rights reserved. 0022-4073/01/$ see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 4 0 7 3 ( 0 0 ) 0 0 1 0 3 5 Fig. 1. Scheme showing di!erent approaches for analyzing photopolarimetric data of a multi-layered atmosphere bounded below by a surface in a trial-and-error formalism. (a) Analysis using single-scattering algorithms. (b) Analysis using parameterized matrices instead. Particle properties are properties describing shape, size, and refractive index; atmosphere properties are properties such as optical thickness, mixing ratio, and number of layers; surface properties refer to the re#ection properties of the surface.