Physics
Scientific paper
Aug 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998jqsrt..60..181p&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 60, issue 2, pp. 181-197
Physics
8
Radiative Transfer: Rayleigh Scattering
Scientific paper
The author considers a certain asymptotic limit of the Rayleigh scattering vector equation of transfer describing the Stokes parameters of light. This limit corresponds to near thermodynamic equilibrium. By introducing appropriate scalings in the vector equation to describe this limit, a renormalized scalar equation of transfer is derived for the total specific intensity of radiation. This equation is both the leading order result as well as the next higher order result of an asymptotic analysis. Numerical testing of this renormalized equation for the exponential decay rate in diffuse reflection halfspace problems demonstrates the very good accuracy of this scalar description. This good accuracy is extant for conditions even far from the asymptotic limit under consideration, thus establishing the robustness of this treatment. In particular, this equation is more accurate than the scalar equation of transfer commonly used to describe light transport through a Rayleigh scattering medium. This asymptotic analysis also yields simple estimates of the state of polarization of the light. Carrying the analysis to still one higher order leads to a fundamentally different scalar equation for the total intensity. This equation can also be cast into the form of a renormalized equation of transfer, but only formally.
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