New Monte Carlo Algorithm for Evaluation of Outgoing Polarized Radiation

  • Gennady A. Mikhailov
  • Natalya V. Tracheva
  • Sergey A. Ukhinov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)


This chapter is devoted to the discussion of a distinctive Monte Carlo method for evaluation of angular distribution of outgoing polarized radiation. The algorithm in consideration is based on the modification of N. N. Chentsov method for unknown probability density evaluation via the orthonormal polynomial expansion. A polarization was introduced into a mathematical model of radiation transfer with use of four-dimensional vector of Stokes parameters. Corresponding weighted Monte Carlo algorithm was constructed. Using this method and precise computer simulation, the angular distribution of outgoing radiation was investigated. Special attention was given to the value of polarization impact in the mathematical model of radiation. Algorithm in consideration allows us precisely estimate even a small effect of polarization as well as a deviation of the calculated angular distribution from the Lambertian one.


Statistical modeling Radiation transfer Polarization Stokes vector Orthogonal expansion Jacobi polynomials 



This work was partially supported by the Russian Foundation for Basic Research (no. 15-01-00894 a, no. 16-31-00123 mol_a, no. 17-01-00823 a) and the Presidium of Russian Academy of Science (program I.33II).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Gennady A. Mikhailov
    • 1
    • 2
  • Natalya V. Tracheva
    • 1
    • 2
  • Sergey A. Ukhinov
    • 1
    • 2
  1. 1.Institute of Computational Mathematics and Mathematical Geophysics SB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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