Calculation of n-scattered lidar returns for large n in an idealized cloud

A simple formula is derived that approximates the time-dependent intensity of n-scattered lidar returns, when n ≫ 1, for a monostatic lidar immersed in an infinite cloud of isotropic scatterers. A primary motivation for deriving this approximate formula is to provide a special-case check of a more general but much more complicated exact formula that was derived in an earlier publication. The earlier analysis is corroborated, in that reasonable numerical agreement between the two formulas is found for larger n, whereas discrepancies for smaller n are consistent with the approximations made in the present analysis. In addition, for the idealized cloud model considered here we obtain some explicit results concerning the long-time convergence and truncation properties of the multiple-scattering-series expansion of the return signal.