Extension of the method of the small angle approximation: Open detector
Abstract
We use the radiative transfer equation to study the multiple scattering undergone by a laser beam propagating through a turbid medium. During the propagation, we view the beam as first scattering into a narrow forward cone, and then into a diffuse pattern. To describe this process, we propose a systematic and practical method to combine the small angle approximation with the diffusion approximation. The method works when the scattering crosssection describing scattering from aerosols can be written as the sum of a Gaussian sigma sub s to describe scattering into small angles, and a term sigma sub d, that can be represented by the first two terms of a Legendre expansion to describe scattering into large/diffuse angles. We use a Green's function formalism to perform partial resummations and set up a hierarchy of approximations in the form of coupled radiative transfer equations to describe the scattering of radiation from small angles into large angles. The adjoint operator formalism then provides a simple way to obtain the net flux received by an open detector at any given point. Our approximations may be described rigorously as a power series expansion in sigma sub d/ sigma sub s, the ratio of the diffusion scattering crosssection to the forward scattering crosssection. Thus our technique works well when small angle scattering dominates.
 Publication:

Presented at the CRDEC Conference on Obscuration and Aerosol Research
 Pub Date:
 August 1986
 Bibcode:
 1986crde.confQ....C
 Keywords:

 Aerosols;
 Approximation;
 Beams (Radiation);
 Extensions;
 Forward Scattering;
 Green'S Functions;
 Lasers;
 Scattering Cross Sections;
 Transfer Functions;
 Diffusion;
 Power Series;
 Radiative Transfer;
 Series Expansion;
 Lasers and Masers