Multiple light scattering: mean number of scatterings and related problems |
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Authors: | V V Ivanov |
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Institution: | (1) V. V. Sobolev Institute of Astronomy, St. Petersburg State University, St. Petersburg, Russia |
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Abstract: | This is a discussion of V. A. Ambartsumyan’s studies of the mean number of scatterings for photons in scattering media and
of further work and development in this area, especially at Ambartsumyan’s St. Petersburg school. The following questions
are discussed briefly: (a) the traditional method for calculating the number of scatterings from the source function and critiques
of this method. (b) The equation for the number N(τ; τ0 ) of scatterings for a photon born at optical depth τ in a plane layer of optical thickness τ0 and its use for calculating the number of scatterings, averaged over the entire ensemble of photons for a medium with arbitrary internal sources. These questions
are first considered for the case of monochromatic scattering, and then for scattering in a spectral line with complete frequency
redistribution (CFR). (c) The mean path length for a resonance line photon in a scattering medium with CFR and continuum absorption: the basic equations and asymptotic
behavior of an optically thick layer. (d) A review of calculations of and in media that are so thick that the CFR approximation breaks down and the effects of partial frequency redistribution (PFR)
become dominant. The presentation is at a semiquantitative level in many parts of this paper, with stress on physical significance
rather than the mathematics, through the use of approximate and asymptotic solutions.
Translated from Astrofizika, Vol. 52, No. 1, pp. 29–45 (February 2009). |
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Keywords: | multiple scattering of light mean number of scatterings mean photon path length ![](/content/y8561617v38k0321/10511_2009_9054_Article_IEq5) law" target="_blank">gif" alt="$\sqrt \varepsilon$" align="middle" border="0"> law |
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