A solution of LIDAR problem in double scattering approximation

TL;DR

This paper develops an analytical approach to model monoenergetic particle pulse reflection in stratified media considering elastic scattering and absorption, using multiple scattering series solutions of the Kolmogorov equation.

Contribution

It provides a compact analytical representation for the first two terms of the scattering series for a point source and cylindric detector, advancing LIDAR problem modeling.

Findings

Analytical expressions for first two scattering terms derived.

Framework applicable to LIDAR and environmental sensing.

Future work includes n-fold scattering and polarization effects.

Abstract

A problem of monoenergetic particles pulse reflection from half-infinite stratified medium is considered in conditions of elastic scattering with absorbtion account. The theory is based on multiple scattering series solution of Kolmogorov equation for one-particle distribution function. The analytical representation for first two terms are given in compact form for a point impulse source and cylindric symmetrical detector. Reading recent articles on the LIDAR sounding of environment (e.g. Atmospheric and Oceanic Optics (2010) 23: 389-395, Kaul, B. V.; Samokhvalov, I. V. http://www.springerlink.com/content/k3p2p3582674xt21/) one recovers standing interest to the related direct and inverse problems. A development of the result fo the case of n-fold scattering and polarization account as well as correspondent convergence series problem solution of the Kolmogorov equation will be published in nearest future.