Multiple light scattering in aerosol media

Abstract

The average sizes of most aerosol particles are of the order of the visible light wavelength. This means that optical methods are very suitable for studies of atmospheric aerosol. However, apart from the nonsphericity and also inhomogeneity of particles yet another problem arises. One needs to account for multiple light scattering to characterize processes of light transmission, reflection and diffusion in aerosol layers. This problem is quite complex in mathematical terms (Mishchenko et al., 2002). It is treated usually in the simplified framework of radiative transfer theory. It means that instead of manipulating with electromagnetic fields $\overrightarrow E$ , one considers the transformation of the Stokes vector of the incident light by an aerosol medium. This enables the description of almost all possible experimental measurements in the field of aerosol optics. We start from the consideration of the scalar radiative transfer equation for the intensity of light field ignoring polarization effects. Also it is assumed that the scattering medium is isotropic, that scatterers are situated at large distances one from another and that there are no nonlinear effects (e.g. dependencies k_ext(I_t), I_t is the light intensity), time-dependent effects (e.g., propagation of laser pulses) and frequency change in the scattering processes. Also the possible effects of stimulated emission (e.g., lasing in aerosol media) are omitted. Even with so many simplified assumptions, the radiative transfer equation (RTE) has the following complicated form:

$$ \left( {\overrightarrow n gr\overrightarrow a d} \right)I_t \left( {\overrightarrow r ,\overrightarrow n } \right) = - k_{{\text{ext}}} I_t \left( {\overrightarrow r ,\overrightarrow n } \right) + \frac{{k_{{\text{sca}}} }} {{4\pi }}\mathop \smallint \limits_{4\pi } p\left( {\overrightarrow n ,\overrightarrow n } \right)I_t \left( {\overrightarrow r ,\overrightarrow n } \right)d\overrightarrow n + B_0 \left( {\overrightarrow r ,\overrightarrow n } \right) $$

((1))

where $\overrightarrow r = x\overrightarrow l _x + y\overrightarrow l _y + z\overrightarrow l _z$ is the radius-vector of the observation point, the vector $\overrightarrow n = l\overrightarrow e _x + m\overrightarrow e _y + n\overrightarrow e _z$ determines the direction of beam with the intensity I_t, $B_0 \left( {\overrightarrow r ,\overrightarrow n } \right)$ is the internal source function.