Double-scattering approximation of lidar equation for inhomogeneous atmosphere

The lidar equation in a double-scattering approximation, applicable for the case of an inhomogeneous atmosphere, has been derived. It is shown that a doubly scattered flux contains information on the microstructure of the medium investigated. Calculations of the intensity of doubly scattered radiation reflected from clouds are given as an illustrative example. It follows from these calculations that double scattering depends essentially on the distance from the lidar to the cloud sounded.