Simple Scaling Relationships for Calculation of Lidar Returns from Turbid Media in Multiple Scattering Regime

Abstract

Calculations for back-scattered radiation from a turbid medium, for situations such as lidar sounding of a cloud, or in general of measurements aimed at deducing the optical properties of the medium, can involve long-time operation of computers, especially in the cases of dense media, where multiple scattering has to be considered. This paper presents some simple scaling relationships that allow the results obtained for a particular situation to be used to obtain results for situations with different optical or geometrical parameters. The effect of multiple scattering on the polarization of the returns is taken into account. Some numerical examples are presented to check these relationships. In the Appendix some details are given of the Monte Carlo code used to deal with polarization of the returns, as well as comparisons of Monte Carlo results for double scattering with the results of analytical formulas that were presented in an earlier paper.