An Approximate Equation For The Multiply Scattered Contribution to A Lidar Return

An approximate equation is developed which describes the contribution of Nth order scattering to a lidar return. This development assumes a homogeneous scattering medium characterized by a scattering function sharply peaked in the forward direction and relatively insensitive to angle near the backscatter direction. The derivation includes the effects of finite divergence of the transmitted laser beam, finite receiver field of view, finite separation between the laser and the receiver and nonparallel system alignment. The derivation presented uses small angle approximations to reduce the time dependent multiple scattering problem to a time independent form which is then solved with techniques previously developed for multiple small angle nuclear scattering.