Liou and Schotland 1971
Liou, K.-N., and R.M. Schotland, 1971: Multiple backscattering and depolarization from water clouds for a pulsed lidar system. J. Atmos. Sci., 28, 772-784, doi:10.1175/1520-0469(1971)028<0772:MBADFW>2.0.CO;2.
A computational approach for the multiple backscattering from spherical cloud droplets for a collimated pulsed radar system has been developed, based on the geometry of the system. The radiative transfer relationships include a complete set of Stokes' parameters. The depolarization ratio of the multiple backscattering from a volume of spherically symmetrical and uniformly distributed water drops is obtained.
Calculations are performed for secondary backscattering from water clouds in terms of wavelength, cloud height, beam width and particle number density. It is found that the depolarization does not have a significant dependence on the wavelength in the visible and near visible, or on the distance between the target and receiver. However, the receiver beam width and particle number density significantly affect the depolarization as well as the returned power.
A small receiver beam width, on the order of 10-4 rad, is recommended for measurement of the depolarization due to ice crystals in clouds to avoid depolarization caused by multiple scattering from the liquid drops.