The degree of polarization as well as the direction of the polarization are calculated by a Monte Carlo method for homogeneous layers. Two solar zenith angles and a range of optical thicknesses up to 10 are considered. The results are compared with calculations for single scattered photons. For a given pair of incident and scattered directions, there are only two possible values for the direction of the polarization for single scattering: it must be within or perpendicular to the scattering plane. The choice between these two values depends only on the sign of the element M(-) in the first row and second column of the scattering matrix in the I, Q, U, V representation. In most cases there is little change in the direction of the polarization when multiple scattering is taken into account, so that this quantity with respect to a meridian plane can usually be predicted from a very simple trigonometric relationship to good accuracy. The partial scattering angles at which M- changes sign are unique for a particular aerosol model. Thus different size distributions and indices of refraction can be distinguished by measurements of the direction of polarization.
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Kattawar et al. (1972) studied this question.