Abstract
The paper presents a Monte Carlo algorithm for the study of bidirectional angular characteristics of a scattered polarized radiation based on projection expansion of the density of the corresponding angular distribution over hemispherical harmonics. The results of numerical estimation of two-dimensional angular distributions of the intensity and the polarization degree of the radiation passed through and reflected from optically thick layers of scattering and absorbing substance are presented.
Funding: The work was supported by the Russian Foundation for Basic Research (projects 17–01–00823-a, 18–01–00356-a, 18–31–00213-mol_a).
References
[1] V. Ambarzumian, A new method for computing light scattering in turbid media. Izv. Akad. Nauk SSSR. (1942) 3, 97–104 (in Russian).Suche in Google Scholar
[2] S. Chandrasekhar, Radiative Transfer. Oxford University Press, London, 1950.Suche in Google Scholar
[3] N. N. Centsov, Statistical Decision Rules and Optimal Inference. American Math. Soc., Providence, R.I., 1982.Suche in Google Scholar
[4] P. Gautron, J. Krivanek, S. Pattanaik, and K. Bouatouch, A Novel Hemispherical Basis for Accurate and Efficient Rendering. In Proc. of the Fifteenth Eurographics Conf. on Rendering Techniques. ISBN 3-905673-12-6. Eurographics Association Aire-la-Ville, Switzerland, 2004, pp. 321–330. URL: https://dx.doi.org/10.2312/EGWR/EGSR04/321-330.Suche in Google Scholar
[5] J. F. de Haan, P. B. Bosma, and J. W. Hovenier, The adding method for multiple scattering calculations of polarized light. Astron. Astrophys. 183 (1987), 371–391.Suche in Google Scholar
[6] H. C. van de Hulst, Light Scattering by Small Particles. John Wiley & Sons, New York, 1957.10.1063/1.3060205Suche in Google Scholar
[7] H. C. van de Hulst and F. Terhoeve, The escape of radiation from a semi-infinite non-conservative atmosphere. Bull. Astron. Inst. Neth. 18 (1966), 377–386.Suche in Google Scholar
[8] G. W. Kattawar and G. N. Plass, Asymptotic radiance and polarization in optically thick media: ocean and clouds. Appl. Opt. 15 (1976), 3166–3178.Suche in Google Scholar
[9] O. A. Machotkin, Analysis of radiative transfer between surfaces by hemispherical harmonics. J. Quant. Spetrosc. Radiat. Transfer56 (1996), No. 6, 869–879.10.1016/S0022-4073(96)00040-4Suche in Google Scholar
[10] G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics. Springer-Verlag, Heidelberg, 1980.10.1007/978-3-540-35237-2Suche in Google Scholar
[11] G. A. Mikhailov, N. V. Tracheva, and S. A. Ukhinov, Randomized projection method for estimating angular distributions of polarized radiation based on numerical statistical modelling. Comp. Math. Math. Phys. 56 (2016), No. 9, 1540–1550.Suche in Google Scholar
[12] G. V. Rozenberg, Light ray (contribution to the theory of the light field). Uspekhi Fiz. Nauk (Advances in Physical Sciences)20 (1977), No. 1, 55–80.10.1070/PU1977v020n01ABEH005317Suche in Google Scholar
[13] V. V. Smelov, On completeness of hemispherical harmonics system. Sib. J. Numer. Math. 1 (1998), No. 4, 391–395.Suche in Google Scholar
[14] T. A. Sushkevich, Mathematical Models of Radiation Transfer. BINOM, Moscow, 2005 (in Russian).Suche in Google Scholar
[15] Siberian Supercomputer Center SB RAS. URL: http://www.sscc.icmmg.nsc.ru/.Suche in Google Scholar
[16] N. V. Tracheva and S. A. Ukhinov, Numerical statistical study of the angular distribution of the polarized radiation scattered by medium. Russ. J. Numer. Anal. Math. Modelling32 (2017), No. 6, 135–146.10.1515/rnam-2017-0012Suche in Google Scholar
[17] S. S. Wilks, Mathematical Statistics. Wiley, New York, 1962.Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Variational assimilation with covariance matrices of observation data errors for the model of the Baltic Sea dynamics
- Numerically statistical simulation of the intensity field of the radiation transmitted through a random medium
- Modelling the Azov Sea circulation and extreme surges in 2013-2014 using the regularized shallow water equations
- Two-dimensional projection Monte Carlo estimators for the study of angular characteristics of polarized radiation
- On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier–Stokes equations in polar coordinates
Artikel in diesem Heft
- Frontmatter
- Variational assimilation with covariance matrices of observation data errors for the model of the Baltic Sea dynamics
- Numerically statistical simulation of the intensity field of the radiation transmitted through a random medium
- Modelling the Azov Sea circulation and extreme surges in 2013-2014 using the regularized shallow water equations
- Two-dimensional projection Monte Carlo estimators for the study of angular characteristics of polarized radiation
- On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier–Stokes equations in polar coordinates