Modified differential approximation for radiative transfer in a scattering medium with specularly reflecting boundaries

Hsien Hung Chien, Chih-Yang Wu

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A modified differential approximation proposed by Olfe is extended to the treatment of a scattering medium with specularly reflecting boundaries. The extension admits of direction-dependent reflectivities at boundaries. The reflectivity and transmissivity, which results from either diffuse or collimated incident radiation on a slab, are presented as a function of refractive index, optical thickness and scattering albedo. The apparent properties are obtained from the unmodified differential approximation, modified differential approximation and integral equation approach. Comparison of the approximate results with the correct results obtained from the integral equation approach shows that, in general, the modified differential approximation is superior to the unmodified differential approximation.

Original languageEnglish
Pages (from-to)439-446
Number of pages8
JournalJournal of Quantitative Spectroscopy and Radiative Transfer
Volume46
Issue number5
DOIs
Publication statusPublished - 1991 Jan 1

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Radiative transfer
radiative transfer
Integral equations
Scattering
approximation
scattering
Refractive index
integral equations
Radiation
reflectance
transmissivity
incident radiation
albedo
optical thickness
slabs
refractivity
Direction compound

All Science Journal Classification (ASJC) codes

  • Radiation
  • Atomic and Molecular Physics, and Optics
  • Spectroscopy

Cite this

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abstract = "A modified differential approximation proposed by Olfe is extended to the treatment of a scattering medium with specularly reflecting boundaries. The extension admits of direction-dependent reflectivities at boundaries. The reflectivity and transmissivity, which results from either diffuse or collimated incident radiation on a slab, are presented as a function of refractive index, optical thickness and scattering albedo. The apparent properties are obtained from the unmodified differential approximation, modified differential approximation and integral equation approach. Comparison of the approximate results with the correct results obtained from the integral equation approach shows that, in general, the modified differential approximation is superior to the unmodified differential approximation.",
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AU - Wu, Chih-Yang

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N2 - A modified differential approximation proposed by Olfe is extended to the treatment of a scattering medium with specularly reflecting boundaries. The extension admits of direction-dependent reflectivities at boundaries. The reflectivity and transmissivity, which results from either diffuse or collimated incident radiation on a slab, are presented as a function of refractive index, optical thickness and scattering albedo. The apparent properties are obtained from the unmodified differential approximation, modified differential approximation and integral equation approach. Comparison of the approximate results with the correct results obtained from the integral equation approach shows that, in general, the modified differential approximation is superior to the unmodified differential approximation.

AB - A modified differential approximation proposed by Olfe is extended to the treatment of a scattering medium with specularly reflecting boundaries. The extension admits of direction-dependent reflectivities at boundaries. The reflectivity and transmissivity, which results from either diffuse or collimated incident radiation on a slab, are presented as a function of refractive index, optical thickness and scattering albedo. The apparent properties are obtained from the unmodified differential approximation, modified differential approximation and integral equation approach. Comparison of the approximate results with the correct results obtained from the integral equation approach shows that, in general, the modified differential approximation is superior to the unmodified differential approximation.

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