Extension of the method of the small angle approximation: open detector

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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 cross-section 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 ... continued below

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Pages: 14

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Chitanvis, S.M. & Gerstl, S.A.W. August 18, 1986.

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Description

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 cross-section 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/sup 0//sub d//sigma/sup 0//sub s/, the ratio of the diffusion scattering cross-section to the forward scattering cross-section. Thus our technique works well when small angle scattering dominates.

Physical Description

Pages: 14

Notes

NTIS, PC A02/MF A01.

Source

  • CRDEC conference on obscuration and aerosol research, Aberdeen, MD, USA, 23 Jun 1986

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  • Other: DE86015308
  • Report No.: LA-UR-86-2917
  • Report No.: CONF-8606202-2
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 5224361
  • Archival Resource Key: ark:/67531/metadc1072804

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • August 18, 1986

Added to The UNT Digital Library

  • Feb. 4, 2018, 10:51 a.m.

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  • March 23, 2018, 2:51 p.m.

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Chitanvis, S.M. & Gerstl, S.A.W. Extension of the method of the small angle approximation: open detector, article, August 18, 1986; United States. (digital.library.unt.edu/ark:/67531/metadc1072804/: accessed April 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.