The experimental-cum-theoretical investigation reported here explains a simple, practical, and efficient experimental method and its appropriate theory for measuring the size distribution n(r) of particles in a settling polydisperse aerosol, under such conditions of optical thickness (γ) that the multiple light scattering (MS) contribution cannot be neglected as compared to the single scattering (SS) contribution. The basis of the experimental technique is the measurement of the radiance (B) due to multiple light scattering (MS) alone; and the basis of the theoretical approach is (1) to treat MS radiance as the sum of contributions due to the various orders of scattering from the second order up, and (2) that the Nth order scattering is the result of N single scatterings. It is shown that below a certain value of γ (~1.5) the contributions due to the second and third orders of scattering suffice to explain the observed data for the MS radiance. For higher values of γ, the computation of higher orders of scattering is needed. A semiempirical expression which can accurately fit the observed data is given. The technique explained in this paper can be adapted for the determination of the particle size distribution of natural aerosols in a planetary atmosphere.
A. Deepak and A. E. S. Green, "Second and Higher Order Scattering of Light in a Settling Polydisperse Aerosol," Appl. Opt. 9, 2362-2371 (1970)