15 December 2004 About the precision and application range of the small-angle approximation in the theory of radiative transfer
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Proceedings Volume 5743, Eleventh International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics; (2004) https://doi.org/10.1117/12.606342
Event: Eleventh International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics, 2004, Tomsk, Russian Federation
Abstract
The analytical complexities of the radiative transfer equation (RTE) have allowed formulating only superficial, qualitative estimations of the precision and application range of the small angle approximation (SAA). Another approach based on the comparison of the calculations in SAA with the similar numerical solutions of RTE is possible. However numerical methods of the RTE solution in media with strong anisotropic scattering are ineffective. The numerical solution of RTE for turbid media with the arbitrary anisotropy of scattering irradiated by a plane monodirectional (PM) source suggested in3 gives the opportunity of solving this problem. SAA was offered in paper4 and is based on the approximate equality of the trajectory path of photons by the anisotropic scattering to the nonscattered path. The analytical complexities of the RTE solution have established three forms of SAA. Comparisons with the numerical solution3 have shown, that all three forms use extra assumptions to4 except the case of normal irradiation by PM source in8. The analysis of SAA has allowed offering the development8 completely relevant to the ideas of4, from which all three forms follow at various assumptions. The generalization of this approach for cases of arbitrary boundary conditions doesn’t present any troubles.
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Vladimir P. Boudak, Vladimir P. Boudak, Alexis V. Kozelsky, Alexis V. Kozelsky, } "About the precision and application range of the small-angle approximation in the theory of radiative transfer", Proc. SPIE 5743, Eleventh International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics, (15 December 2004); doi: 10.1117/12.606342; https://doi.org/10.1117/12.606342
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