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We present an analytical technique that solves exactly, and in closed form, for the first and second moments of the spatial and angular positions of photon distributions in a multiple-scattering medium. The analysis leads to simple analytic expressions for these moments, both conditioned on the number of scatterings and summed over all scattering events. The conventional results for small-angle forward scattering, and for the diffusion regime, are recovered in the appropriate limiting cases.

An analytic model for propagation of an optical pulse through an optically thick multiple-scattering medium such as a cloud is developed. Both a narrow collimated and a broad Gaussian beam are considered incident at the entrance of the medium, which is assumed to be a plane-parallel slab of infinite horizontal extent. Analytic expressions are derived for the radiance and power received by an on-axis receiver at any distance beyond the exit plane of the medium. Calculations with these expressions are compared with published Monte Carlo results for an infinite-plane, π/2-field-of-view receiver at the exit plane of the medium. Calculated and simulated results show excellent agreement for optical thickness beyond approximately 20.