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Development of the small angle approximation of the radiative transfer theory taking into account the photon path distribution function

Abstract

The development of the small angle approximation of the radiative transfer equation (RTE) solution for the slab taking into account the photon path distribution function in the forward hemisphere of sighting directions is offered. The solution is based on the Taylor series expansion of the sighting angle cosine up to the 2nd order without the RTE conversion to the diffusion approximation. The obtained solution practically coincides with the exact solution in the forward hemisphere of directions up to the deep regime.

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References

  1. M. C. Wang and E. Guth, “On the Theory of Multiple Scattering, Particularly of Charged Particles,” Phys. Rev. 84(6), 1092–1111 (1951).

    MATH  Article  MathSciNet  ADS  Google Scholar 

  2. K. Stamnes and R. A. Swanson, “A New Look at the Discrete Ordinate Method for Radiative Transfer Calculation in Anisotropicaly Scattering Atmosphere,” J. Atmos. Sci. 38(2), 387–399 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  3. W. J. Wiscombe, “The Delta-M Method: Rapid Yet Accurate Radiative Flux Calculations for Strongly Asymmetric Phase Functions,” J. Atmos. Sci. 34, 1408–1422 (1977).

    Article  ADS  Google Scholar 

  4. T. Yokota, H. Oguma, I. Morino, and G. Inoue, “A Nadir-Looking FSWIR H Sensor to Monitor CO2 Column Density for Japanese FGOSAT H Project,” in Proc. of the 24th Intern. Symp. on Space Technol. and Sci. (Jpn. Soc. for Aeronaut. and Space Sci. and ISTS, Miyazaki, 2004), p. 887.

    Google Scholar 

  5. V. P. Budak and S. V. Korkin, “On the Solution of a Vectorial Radiative Transfer Equation in an Arbitrary Three-Dimensional Turbid Medium with Anisotropic Scattering,” J. Quant. Spectrosc. Radiat. Transfer. 109, 220–234 (2008).

    Article  ADS  Google Scholar 

  6. S. Goudsmith and J. L. Saunderson, “Multiple Scattering of Electrons,” Phys. Rev. Pt. I 57, 24–29 (1940); Pt. II 58, 36–42 (1940).

    ADS  Google Scholar 

  7. A. Isimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978; Mir, Moscow, 1981).

    Google Scholar 

  8. V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, “Propagation of a Light Signal in a Substance with Large-Scale Random Inhomogeneities with Photon Path-Length Fluctuations Due to Multiple Scattering Taken Into Account,” Izv. AN SSSR, Fiz. Atmosf. Okeana 18(6), 623–631 (1982).

    Google Scholar 

  9. L. S. Dolin, “Passage of a Pulsed Light Signal through an Absorbing Medium with Strongly Anisotropic Scattering,” Izv. Vyssh. Uchebn. Zaved., Ser. Radiofiz. 26, 300–309 (1983).

    ADS  Google Scholar 

  10. N. Ya. Vilenkin, Special Functions and Group Representation Theory (Nauka, Moscow, 1965) [in Russian].

    Google Scholar 

  11. L. S. Dolin, “Beam Description of Weakly-Inhomogeneous Wave Fields,” Izv. Vyssh. Uchebn. Zaved., Ser. Radiofiz. 7(3), 559–562 (1964).

    Google Scholar 

  12. N. N. Kalitkin, Numerical Methods (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  13. L. G. Henyey and J. L. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93(1), 70–83 (1941).

    Article  ADS  Google Scholar 

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Published in Russian in Optica Atmosfery i Okeana.

The article was translated by the author.

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Budak, V.P., Ilyushin, Y.A. Development of the small angle approximation of the radiative transfer theory taking into account the photon path distribution function. Atmos Ocean Opt 23, 181–185 (2010). https://doi.org/10.1134/S1024856010030048

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  • DOI: https://doi.org/10.1134/S1024856010030048

Key words

  • anisotropic scattering
  • small angle approximation
  • photon path distribution function