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An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance of photon direction and position. The result is that for an N-point profile thedoi:10.1364/ao.45.005984 pmid:16926887 fatcat:cn2ippewr5cldjyqyibyju6joy