The reflection of light pulses from clouds is calculated by a Monte Carlo technique for all orders of multiple scattering. The photons are emitted within a narrow cone, scattered by water droplets and ice crystals in clouds as well as by Rayleigh scattering centers and aerosols, and finally detected at the source position. The returned flux is determined as a function of the photon path length for: (1) three different size distributions for the cloud particles (haze C, nimbostratus, ice crystal); (2) two different variations of the number density with height of the scattering centers within the cloud; (3) six different zenith angles of the source. The influence of detector half-width and of the atmosphere on the returned flux is studied. The returned flux as a function of the photon path length depends on both the size distribution of the particles within the cloud and on the density of scattering centers as a function of height.
Gilbert N. Plass and George W. Kattawar, "Reflection of Light Pulses from Clouds," Appl. Opt. 10, 2304-2310 (1971)