Polarized Radiative Transfer in Optically Active Light Scattering Media

  • Margarita G. KuzminaEmail author
  • Leonid P. Bass
  • Olga V. Nikolaeva
Part of the Springer Series in Light Scattering book series (SSLS)


The disperse media composed of non-spherical particles (say, dust aerosols layers, and ice crystal clouds) can appear both optically isotropic and optically anisotropic, depending on local optical characteristics of turbid medium in question and also on the orientation of particles.



The work has been supported by the Fund of Fundamental Research RAS, the Department of Mathematical Sciences, Project 1.3.2, the Program #3.

Our heartfelt thanks to A.A Kokhanovsky for his kind suggestion to prepare this review. Our great thanks also to three anonymous reviewers for their helpful remarks and comments on the manuscript.

One of the authors (M.G.K) is greatly thankful for many remarkable researchers on radiation transport theory for interesting and helpful discussions on various aspects of polarized radiation transfer in due time. These are M.V. Maslennikov (who for a long time was the chief of the Department of kinetic equations of Keldysh Institute of Applied Mathematics, RAS (KIAM RAS), and also the organizer and the head of regularly running seminar on kinetic equations at KIAM RAS), T.A. Germogenova, N.V. Konovalov (KIAM RAS), G.V. Rosenberg, V.I. Tatarsky, Yu.N. Barabanenkov, Yu.N. Gnedin, N.A. Silant’ev, H. Domke, E.P. Zege, L.I. Chaikovskaya, and many others. It is also a great pleasure to thank T. Nishida, K. Asano and the participants of the seminar on nonlinear equations of the Department of Mathematics, Kyoto University, for interesting and helpful discussion on the VRTE properties for optically anisotropic media (1989).


  1. Ablitt BP, Hopcraft KI, Turpin KD, Chang PCY, Walker CG, Jakeman E (2006) Imaging and multiple scattering through media containing optically active particles. Google Scholar
  2. Alexandrov MD, Rogozkin DB, Remizovich VS (1993) Multiple light scattering in a two-dimensional medium with large scatterers. J Opt Soc Am A 10:2602–2610CrossRefADSGoogle Scholar
  3. Alonova MV, Angelsky OV, Ermolenko SB, Zimnyakov DA, Isaeva EA, Sina JS, Skurlov ID, Tverdova AA, Ushakova OV (2013) Optical properties of densely packed dispersive systems: effective medium approximation, Vestnik SGP 3:72 (in Russian) Google Scholar
  4. Apresyan LA, Kravtsov YuA (1996) Radiation transfer. statistical and wave aspects. Basel, Gordon and Breach 1996. (Original Russian edition: Nauka, Moscow, 1979.)Google Scholar
  5. Arsenova EA (2009) Correlation functions and the features of transfer and scattering of waves in liquid crystals, Doct. Thesis, S.-Petersburg, (in Russian)Google Scholar
  6. Astrov DN (1960) The magnetoelectric effect in antiferromagnetics. Zh Eksp Teor Fiuz 38:984–985 (in Russian)Google Scholar
  7. Azzam RM (1978) Propagation of partially polarized light through anisotropic media with without depolarization: a differential 4 4· matrix calculus. J Opt Soc Am 68:1756–1767CrossRefADSGoogle Scholar
  8. Azzam RM, Bashara NM (1989) Ellipsometry and polarized light. North Holland PC, NYGoogle Scholar
  9. Barabanenkov YuN (1973) Wave corrections to the transfer equation for “back” scattering. Radiophys Quantum Electron 16:65–71 (in Russian)MathSciNetCrossRefADSGoogle Scholar
  10. Barabanenkov YuN (1975) Multiple scattering of waves by the ensembles of particles and the theory of radiation transport. Sov Phys—Uspekhi 18:673–689 (in Russian)Google Scholar
  11. Barabanenkov YuN, Kravtsov YuA, Ozrin VD, Saichev AI (1991) Enhanced backscattering in optics. Prog Opt 29:65–197CrossRefGoogle Scholar
  12. Barabanenkov YuN, Zurk LM, Barabanenkov MYu (1995) Poynting’s theorem and electromagnetic wave multiple scattering in dense media near resonance: modified radiative transfer equation. J Electromag Waves and Appl 9:1393–1420CrossRefGoogle Scholar
  13. Bass LP, Nikolaeva OV, Kuznetsov VS, Bykov AV, Priezzhev AV, Dergachev AA (2009) Modeling of optical radiation propagation in bio-tissue phantom with using of the supercomputer MBC1000, Mathem. Modelirovanie 21:3–14 (in Russian)zbMATHGoogle Scholar
  14. Bass LP, Nikolaeva OV, Kuznetsov VS, Bykov AV, Priezzhev AV (2010) Parallel algorithms for simulation of ultrashort pulse propagation in turbid media, IL NUOVO CIMENTO 33 C, n. 1Google Scholar
  15. Bautin NN, Leontovich EL (1976) Methods of qualitative analysis of dynamical systems in the plane, M. Nauka (in Russian)Google Scholar
  16. Bolgov DI, Remizovich VS, Rogozkin DB (1998) Multiple scattering of light in a 2-D medium with large-scale inhomogeneities: an exactly solvable model and approximate methods of calculation. Laser Phys 8:462–470Google Scholar
  17. Born M, Wolf E. (1975). Principles of optics, 5th Ed, PergamonGoogle Scholar
  18. Borovoi AG (1966a) Iteration method in multiple scattering. Izv Vyssh Ucheb Zaved Fiz 2:175–177Google Scholar
  19. Borovoi AG (1966b) Iteration method in multiple scattering: radiative transfer equation. Izv Vyssh Ucheb Zaved Fizika 6:50–54Google Scholar
  20. Borovoi AG (1967a) Multiple scattering of short waves by a system of correlated particles. I. Averaged field. Izv Vyssh Ucheb Zaved Fizika n 4:97–101Google Scholar
  21. Borovoi AG (1967b) Multiple scattering of short waves by a system of correlated particles. II. Kinetic equation. Izv Vyssh Ucheb Zaved Fizika n 5:7–11Google Scholar
  22. Borovoi AG (1983) Light propagation in media with closely packed particles. Optics and Spectrosc 54:449–450ADSGoogle Scholar
  23. Borovoi AG, Grishin IA, Oppel UG, (2000) Mueller matrix for oriented hexagonal ice crystals of cirrus clouds. In: Eleventh international workshop on multiple scattering LIDAR experiments (MUSCLE 11), November 1–3, 2000, Williamsburg, Virginia, USA, 2000Google Scholar
  24. Borovoi A, Grishin I, Naats E, Oppel U (2002) Light backscattering by hexagonal ice crystals. J Quant Spectrosc Radiat Transfer 72(4):403–417CrossRefADSGoogle Scholar
  25. Borovoi AG (2005) Multiple scattering of optical waves in media containing discrete scatterers. Doct. Thesis., TomskGoogle Scholar
  26. Borovoi AG (2006) Multiple scattering of short waves by uncorrelated and correlated scatterers. Light Scattering Rev 1:181–252CrossRefGoogle Scholar
  27. Borovoi A, Kustova N (2006) Statistical approach to light scattering by convex ice crystals. Opt Lett 31:1747–1749CrossRefADSGoogle Scholar
  28. Borovoi AG, Burnashov AV, Cheng AYS (2007) Light scattering by horizontally oriented ice crystal plates. J Quant Spectrosc Radiat Transfer 106(1):11–20CrossRefADSGoogle Scholar
  29. Borovoi AG, Kustova NV (2010) Light scattering by large faceted particles. In: Polarimetric, Detection, and Remote Sensing. Springer, Dordrecht, The NetherlandsGoogle Scholar
  30. Borovoi AG (2013) Light scattering by large particles: physical optics and the shadow-forming field. Light Scattering Rev 8:115–138Google Scholar
  31. Brosseau C (1995) Evolution of the Stokes parameters in optically anisotropic media. Opt Lett 20:1221–1223CrossRefADSGoogle Scholar
  32. Cairns B, Waquet F, Knobelspiesse K, Chowdhary J, Deuze J- L (2010) Polarimetric remote sensing of aerosols over land surfaces. In: Satellite Aerosol Rmote Sensing Over Land, eds A. A. Kokhanovsky and G. de Leeuw (Chichester: pringer-Praxis), 295–325Google Scholar
  33. Chandrasekhar S (1960) Radiative transfer. Oxford University Press, OxfordzbMATHGoogle Scholar
  34. Chandrasekhar S (1977) Liquid crystals. Cambridge Univ Press, CambridgeGoogle Scholar
  35. Cheng TH, Gu XF, Xie DH, Li ZQ, Yu T, Chen XF (2011) Simultaneous retrieval of aerosol optical properties over the Pearl River Delta, China using multi-angular, multi-spectral, and polarized measurements. Remote Sens Env 115:1643–1652. CrossRefADSGoogle Scholar
  36. de Gennes PG (1974) The Physics of Liquid Crystals. Clarendon Press, OxfordzbMATHGoogle Scholar
  37. Dlugach JM, Mishchenko MI, Liu L, Mackowski DV (2011) Numerically exact computer simulations of light scattering by densely packed, random particulate media 112(13):2068–2078Google Scholar
  38. Dolginov AZ, Gnedin YuN Silant’ev NA (1970) J Quant Spectrosc Radiat Transfer 10:707Google Scholar
  39. Dolginov AZ, Gnedin YuN, Silant’ev NA (1975) Photon polarization and frequency change in multiple scattering. J Quant Spectrosc Radiat Transfer 10:707–754MathSciNetCrossRefADSGoogle Scholar
  40. Dolginov AZ, Gnedin YuN, Silant’ev NA (1995) Propagation and Polarization of Radiation in Cosmic Media (Gordon and Breach, Basel). (Original Russian edition: Nauka, Moscow, 1979.)Google Scholar
  41. Dubovik O, Herman M, Holdak A, Lapyonok T, Tanré D, Deuzé JL, et al (2011) Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations. Atmos Meas Tech 4:975–1018; doi:10.5194Google Scholar
  42. Dullemond K, Peeters K (1991–2010) Introduction to Tensor Calculus, Copyright 1991–2010, English translation 2008–2010;
  43. Dzyaloshinskii LE (1960) On the magnetoelectrical effect in antiferromagnetics. Soviet Phys JETP 10:628–669 (in Russian)MathSciNetGoogle Scholar
  44. Farrell R, Rouseff AD, McCally RL (2005) Propagation of polarized light through two- and three-layer anisotropic stacks. J Opt Soc Am A 22:1981–1992MathSciNetCrossRefADSGoogle Scholar
  45. Faure R, Kaufmann AM, Denis-Papin M (1964) Mathematiques Nouvelles. Dunod, ParisGoogle Scholar
  46. Fedorov FI (1976) Theory of the gyrotropy. Minsk, Nauka i Technika (in Russian)Google Scholar
  47. Fedorov FI, Philippov VV (1976) Reflection and refraction of light by transparent crystals. Minsk, Nauka i Tekhnika (in Russian)Google Scholar
  48. Foldy LL (1945) The multiple scattering of waves. Phys Rev 67:107–119MathSciNetCrossRefzbMATHADSGoogle Scholar
  49. Gao M, You Y, Yang P, Kattawar GW (2012) Backscattering properties of small layered plates: a model for iridosomes, OPTICS EXPRESS, 20(22)Google Scholar
  50. Gao M, Yang P, Kattawar GW (2013) Polarized extinction properties of plates with large aspect ratios. J Quant Spectrosc Radiat Transfer 131:72–81CrossRefADSGoogle Scholar
  51. Germogenova TA (1985) On the inverse problems of atmosphere optics. Sov Dokl 285:5 (in Russian)Google Scholar
  52. Germogenova TA, Konovalov NV, Kuzmina MG (1989) The mathematical foundations of polarized radiation transport theory (strict results). In the issue Invariance Principle and Its Applications, Proceedings of the Symposium, Oct. 26–30, 1981, Buarakan., Erevan, Armenia; 271–284Google Scholar
  53. Ghosh N, Wood MFG, Vitkin IA (2008) Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence. J Biomed Opt 13(4):044036CrossRefGoogle Scholar
  54. Giden IH, Turduev M, Kurt H (2014) Reduced symmetry and analogy to chirality in periodic dielectric media. Opt Soc J Europ Opt Soc Public 9:14045iGoogle Scholar
  55. Ginzburg VL, Rukhadze AA (1975) Waves in magneto-active plasma. Nauka, Moscow, 1975 (in Russian)Google Scholar
  56. Grishin IA (2004) Light scattering on ice crystals typical for cirrus. Doctor Thesis. (150 p), (in Russian)Google Scholar
  57. Hasekamp OP, Litvinov P, Butz A (2011) Aerosol properties over the ocean from PARASOL multiangle photopolarimetric measurements. J Geophys Res 116:D14204; doi:
  58. Hovenier JW (Ed) (1996) Light scattering by non-spherical particles. J Quant Spectrosc Radiat Transf 55:535–694Google Scholar
  59. Hovenier JW, van der Mee C, Domke H (2004) Transfer of polarized light in planetary atmospheres. Kluwer, DordrechtCrossRefGoogle Scholar
  60. Van de Hulst HC (1957) Light scattering by small particles. Wiley, New YorkGoogle Scholar
  61. Van de Hulst HC (1980) Multiple light scattering. Academic Press, New YorkGoogle Scholar
  62. Ishimaru A (1978) Wave Propagation and Scattering in Random Media, vol. 1 and 2, N Y, Acad. Prèss (574 p)Google Scholar
  63. Ishimaru A, Lesselier D, Yeh C (1984) Multiple scattering calculations for nonspherical particles based on the vector radiative transfer theory. Radio Sci. 19:1356–1366CrossRefADSGoogle Scholar
  64. Katsev IL, Prikhach AS, Zege EP, Ivanov AP, Kokhanovsky AA (2009) Iterative procedure for retrieval of spectral aerosol optical thickness and surface reflectance from satellite data using fast radiative transfer code and ts application to MERIS measurements. In: Kokhanovsky AA, de Leeuw G. (Eds), Satellite Aerosol Remote Sensing ver L. Springer-Praxis, Berlin, pp 101–134Google Scholar
  65. Kiasat Y, Szabo Z, Chen X, Li E (2011) Light interaction with multilayer arbitrary anisotropic structure: an explicit analytical solution and application for subwavelength imaging. JQSABGoogle Scholar
  66. Knobelspiesse K, Cairns B, Redemann J, Bergstrom RW, Stohl A (2011) Simultaneous retrieval of aerosol and cloud properties during the MILAGRO field campaign. Atmos Chem Phys 11:6245–6263. CrossRefADSGoogle Scholar
  67. Kokhanovsky AA (1998) On light scattering in random media with large densely packed particles. J Geophys Res D 103:6089–6096CrossRefGoogle Scholar
  68. Kokhanovsky AA (1999a) Radiative transfer in chiral random media. Phys Rev E 60(4):4899–4907CrossRefADSGoogle Scholar
  69. Kokhanovsky AA (1999b) Light scattering media optics: problems and solutions. Wiley-Praxis, ChichesterGoogle Scholar
  70. Kokhanovsky AA (2000) The tensor radiative transfer equation. J Phys A: Math Gen 33:4121–4128MathSciNetCrossRefzbMATHADSGoogle Scholar
  71. Kokhanovsky AA (2003) Optical properties of irregularly shaped particles. J Phys D36:915–923ADSGoogle Scholar
  72. Kokhanovsky AA (2004) Optical properties of terrestrial clouds. Earth-Sci Rev 64:189–241CrossRefADSGoogle Scholar
  73. Kokhanovsky AA, Zege EP (2004) Scattering optics of snow. Appl Opt 43:1589–1602CrossRefADSGoogle Scholar
  74. Kokhanovsky AA (2005a) Reflection of light from particulate media with irregularly shaped particles. J Quant Spectr Rad Transfer 96:1–10CrossRefADSGoogle Scholar
  75. Kokhanovsky AA (2005b) Phase matrix of ice crystals in noctilucent clouds. Proc SPIE 5829:44–52CrossRefADSGoogle Scholar
  76. Kokhanovsky AA (2006) Cloud optics. Springer, Dordrecht, p 2006CrossRefGoogle Scholar
  77. Kokhanovsky AA, Deuzé JL, Diner DJ, Dubovik O, Ducos Emde C et al (2010) The intercomparison of major aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light. Atmos Meas Tech 3:909–932. doi:
  78. Kokhanovsky AA (2011) Solar radiation transport in clouds and snow cover and its application to the problems satellite Earth Remote sensing, Doct. Thesis, St. PetersburgGoogle Scholar
  79. Kokhanovsky AA (2015) The modern aerosol retrieval algorithms based on the simultaneous measurements of the intensity and polarization of reflected solar light: a review, Frontiers in Environmental Science, 3Google Scholar
  80. Kong JA (1974) Optics of bianisotropic media. J Opt Soc Am 64(10):1304–1308Google Scholar
  81. Kong JA (1990) Electromagnetic waves theory, 2nd edn. Wiley Interscience Publising. John Wiley and Sons Inc, New YorkGoogle Scholar
  82. Kravtsov YuA, Bieg B, Bliokh KYu (2007) Stokes-vector evolution in a weakly anisotropic inhomogeneous medium, Scholar
  83. Kravtsov YuA, Bieg B (2010) Propagation of electromagnetic waves in wearly anisotropic media: theory and applications. Optica Applicata XL(4)Google Scholar
  84. Kravtsov YuA, Orlov YuI (1990) Geometrical optics of inhomogeneous media. Springer Verlag, Berlin, HeidelbergCrossRefGoogle Scholar
  85. Kurt H, Turduev M, Giden IH (2012) Crescent shaped dielectric periodic structure for light manipulation. Opt Express 20:7184–7194CrossRefADSGoogle Scholar
  86. Kuzmina MG (1976) Polarized radiation transport equation in anisotropic media, Preprint KIAM-68, (in Russian)Google Scholar
  87. Kuzmina MG (1978) General functional properties of polarized radiation transport equation. Sov Docl 238:314–317 (in Russian)Google Scholar
  88. Kuzmina MG (1986a) To the formulation of polarized radiation transfer problems for slabs of optically active media, Preprint KIAM-110, (in Russian)Google Scholar
  89. Kuzmina MG (1986b). Polarized radiation transport in slabs of optically active media, Preprint KIAM-123, (in Russian)Google Scholar
  90. Kuzmina MG (1987) The perturbation method in transport problems for optically active media, Preprint KIAM-9, (in Russian)Google Scholar
  91. Kuzmina MG (1989) The perturbation method in radiation transfer problems for slabs of optically active media. Sov Dokl 308:335–341Google Scholar
  92. Kuzmina MG (1991) A perturbation method and Stokes parameters estimates in polarized radiation transfer problems in the slabs of optically active media. TTSP 20(1):69–81zbMATHADSGoogle Scholar
  93. Landau LD, Lifshitz EM (1960) Electrodynamics of continuous media. Addison–Wesley, Reading, MassGoogle Scholar
  94. Larin KV, Motamedi M, Eledrisi MS, Esenaliev RO (2002) Noninvasive blood glucose monitoring with optical coherence tomography. Diabetes Care 25:2263–2267CrossRefGoogle Scholar
  95. Lax M (1951) Multiple scattering of waves. Rev Mod Phys 23:287–310MathSciNetCrossRefzbMATHADSGoogle Scholar
  96. Linder T (2014) Light Scattering in Fiber-based Materials. A foundation for characterization of structural properties, Doct. Thesis, Dept. of Computer Science, Electrical and Space Engineering Lule˚a University of Technology Lule˚a, SwedenGoogle Scholar
  97. Liou KN, Takano Y, Yang P (2011) Light absorption and scattering by aggregates: application to black carbon and snow grains. JQSRT 112:1581–1594CrossRefADSGoogle Scholar
  98. Liou KN (2002) An introduction to atmospheric radiation, 2nd ed. Academic Press, San Diego, USAGoogle Scholar
  99. Liou KN (1992) Radiation and cloud processes in the atmosphere: theory, observation, and modeling. Oxford University Press, New YorkGoogle Scholar
  100. Liu J, Kattawar GW (2013) Detection of dinoflagellates by the light scattering properties of the chiral structure of their chromosomes. J Quant Spectrosc Radiat Transfer 131:24–33CrossRefADSGoogle Scholar
  101. Maslennikov MV (1968, 1969). The Milne problem with anisotropic scattering, Proc. Steklov Inst. of Math., 97, 1968 (in Russian); Amer. Math. Soc., Providence, Rhode Island, 1969Google Scholar
  102. Menyuk CR (1988) Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes, J of the Opt Soc of Am B 5(2):392–402Google Scholar
  103. Marinyuk VV, Dlugach JM, Yanovitskij EG (1992) Multiple light scattering by polydispersions of randomly distributed, perfectly aligned Mie cylinders illuminated perpendicularly to their axes. J Quant Spectrosc Radiat Transfer 47:401–410CrossRefADSGoogle Scholar
  104. Marshak A, Davis AB (eds) (2005) 3D radiative transfer in cloudy atmospheres. Springer, BerlinGoogle Scholar
  105. Maruo K, Tsurugi M, Chin J, Ota T, Arimoto H, Yamada Y, Tamura M, Ishii M, Ozaki Y (2003) Noninvasive blood glucose assay using a newly developed near-infrared system. IEEE J Sel Top Quantum Electron 9:322–330CrossRefGoogle Scholar
  106. Mishchenko MI (1994a) Transfer of polarized infrared radiation in optically anisotropic media: application to horizontally oriented ice crystals: comment. J Opt Soc Am A 11:4Google Scholar
  107. Mishchenko MI (1994b) Asymmetry parameters of the phase function for densely packed scattering grains. JQSRT 52:95–110CrossRefADSGoogle Scholar
  108. Mishchenko MI, Hovenier JW, Travis LD (Eds), (2000). Light Scattering by Nonspherical Particles. Theory, Measurements, and Applications, Academic PressGoogle Scholar
  109. Mishchenko MI (2002) Vector radiative transfer equation for arbitrarily shaped and arbitrarily oriented particles: a microphysical derivation from statistical electromagnetics. Appl Opt 41:7114–7134CrossRefADSGoogle Scholar
  110. Mishchenko MI (2003) Microphysical approach to polarized radiative transfer: extension to the case of an external observation point. Appl Opt 42:4963–4967CrossRefADSGoogle Scholar
  111. Mishchenko MI (2014a) Electromagnetic scattering by particles and particle groups: an introduction. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  112. Mishchenko MI (2014b) Light propagation in a two-dimensional medium with large inhomogeneities. J Opt Soc Am A 32:1330–1336Google Scholar
  113. Mishchenko MI, Travis LD, Lacis AA (2002) Scattering, Absorption and Emission of Light by Small Particles. Cambridge University Press, CambridgeGoogle Scholar
  114. Mishchenko MI, Travis LD, Lacis AA (2006) Multiple scattering of light by particles: radiative transfer and coherent backscattering. Cambridge University Press, Cambridge, UKGoogle Scholar
  115. Mishchenko MI (2011) Directional radiometry and radiative transfer: a new paradigm. J Quant Spectrosc Radiat Transf 112:2079–2094CrossRefADSGoogle Scholar
  116. Mishchenko MI, Tishkovets VP, Travis LD et al (2011) Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions. J Quant Spectrosc Radiat Transf 112:671–692CrossRefADSGoogle Scholar
  117. Mishchenko MI (2008a) Multiple scattering by particles embedded in an absorbing medium. 1. Foldy-Lax equations, order-of-scattering expansion, and coherent field. Opt Express 16:2288–2301CrossRefADSGoogle Scholar
  118. Mishchenko MI (2008b) b). Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation. J Quant Spectrosc Radiat Transf 109:2386–2390CrossRefADSGoogle Scholar
  119. Mishchenko MI, Liu L, Mackowski DV, Cairns B, Videen G (2007) Multiple scattering by random particulate media: exact 3D results. Opt Express 15:2822–2836CrossRefADSGoogle Scholar
  120. Mishchenko MI, Dlugach JM, Yanovitskij EG (1992) Multiple light scattering by polydispersions of randomly distributed, perfectly aligned Mie cylinders illuminated perpendicularly to their axes. J Quant Spectrosc Radiat Transfer 47:401–410CrossRefADSGoogle Scholar
  121. Mishchenko MI (2010) The Poynting-Stokes tensor and radiative transfer in discrete random media: the microphysical paradigm. Opt Express 18:19770–19791CrossRefADSGoogle Scholar
  122. Mishchenko MI, Dlugach JM, Yurkin MA, Bi L, Cairns B, Liu L, Panetta RL, Travis LD, Yang P, Zakharova NT (2016a) First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media. Phys Rep 632:1–75MathSciNetCrossRefADSGoogle Scholar
  123. Mishchenko MI, Dlugach JM, Zakharova NT (2016b) Demonstration of numerical equivalence of ensemble and spectral averaging in electromagnetic scattering by random particulate media. J Opt Soc Am A 33:618–624CrossRefADSGoogle Scholar
  124. Munneke PK (2009). Snow, ice and solar radiation, Institute of Marine and Atm. Research Utrecht (IMAU); Dept. of Physics and Astronomy, Faculty of Sci., Utrecht UniversityGoogle Scholar
  125. Newton RG (1982) Scattering theory of waves and particles, 2nd edn. Springer-Verlag, New YorkGoogle Scholar
  126. Nikolaeva OV, Bass LP, Germogenova TA, Kuznetsov VS (2007) Algorithms to calculation of radiative fields from localized sources via the Code Raduga-5.1(P). Transport Theory Stat Phy 36(4–6):439–474Google Scholar
  127. Okada Y, Kokhanovsky AA (2009) Light scattering and absorption by densely packed groups of spherical particles. JQSRT 110:902–917CrossRefADSGoogle Scholar
  128. Prigarin SM, Boovoi AG, Buscaglioni P, Cohen A, Grishin IA, Oppel UG, Zhuravleva TB (2005) Monte Carlo simulation of radiation transfer in optically anisotropic clouds. Proc SPIE 5829:88–94CrossRefADSGoogle Scholar
  129. Prigarin SM, Oppel UG (2005) A hypothesis of ’fractal’ optical anisotropy in clouds and Monte Carlo simulation of relative radiation effects. Proc SPIE 5829:102–108CrossRefADSGoogle Scholar
  130. Prigarin SM, Borovoi AG, Grishin IA, Oppel UG (2007) Monte Carlo simulation of radiation transfer in optically anisotropic crystal clouds, Atmos Oceanic Opt. 20(3):183–188Google Scholar
  131. Prigarin SM, Borovoi AG, Grishin IA, Oppel UG (2008) Monte Carlo simulation of halos in crystal clouds, XV International Symposium “Atmospheric and Ocean Optics. Atmospheric Physics”, June 22–28, 2008, Krasnoyarsk. Abstracts. p 109Google Scholar
  132. Randrianalisoa J, Baillis D (2010) Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach. JQSRT 111(10):1372–1388Google Scholar
  133. Rogovtsov NN, Borovik FN (2009) The characteristic equation of radiative transfer theory. In: Kokhanovsky AA (Eds) Light Scattering Reviews, vol 4. Springer-Praxis Publishing, Chichester, UK, pp 47–429Google Scholar
  134. Rogovtsov NN (2015a) Constructive theory of scalar characteristic equations of the theory of radiation transport: I Basic assertions of theory and conditions for the applicability of truncation method. Differen Equat 51:268–281MathSciNetCrossRefzbMATHGoogle Scholar
  135. Rogovtsov NN (2015b) Constructive theory of scalar characteristic equations of the theory of radiation transport: II Algorithms for finding solutions and their analytic representations. Differen Equat 51:661–273Google Scholar
  136. Rogovtsov NN, Borovik FN (2016) Application of general invariance relations reduction method to solution of radiation transfer problems. J Quant Spectrosc Radiat Transfer 183:128–153CrossRefzbMATHADSGoogle Scholar
  137. Roux L, Mareschal P, Vukadinovic N, Thibaud J-B, Greffet JJ (2001) Scattering by a slab containing randomly located cylinders: comparison between radiative transfer and electromagnetic simulation. J Opt Soc Am A 18:374–384MathSciNetCrossRefADSGoogle Scholar
  138. Rosenberg GV (1955) Usp Fiz Nauk 61:77CrossRefGoogle Scholar
  139. Rudin W (1976) Principles of mathematical analysis, 3rd ed. McGraw HillGoogle Scholar
  140. Rytov SM, Kravtsov YuA, Tatarsky VI (1978) Introduction to statistical radiophysics: random fields. Fizmat, Moscow (in Russian)Google Scholar
  141. Shefer O (2013) Numerical study of extinction of visible and infrared radiation transformed by preferentially oriented plate crystals. J Quant Spectrosc Radiat Transfer 117:104–113CrossRefADSGoogle Scholar
  142. Shefer O (2016) Extinction of radiant energy by large atmospheric crystals with different shapes. J Quant Spectrosc Radiat Transfer 178:350–360CrossRefADSGoogle Scholar
  143. Stamnes J, Sithambaranathan GS (2001) Reflection and refraction of an arbitrary electromagnetic wave at a plane interface separating anisotropic and a biaxial medium. J Opt Soc Am A 22:3119–3129CrossRefADSGoogle Scholar
  144. Takano Y, Liou KN (1989) Solar radiative transfer in cirrus clouds. Part II: theory and computations of multiple scattering in a anisotropic medium. J of Atm Sci 46(3)Google Scholar
  145. Takano Y, Liou KL (1993) Transfer of polarized infrared radiation in optically anisotropic media: application to horizontally oriented ice crystals. J Opt Soc Am A 10:1243–1256CrossRefADSGoogle Scholar
  146. Tishkovets V, Mishchenko MI (2004) Coherent backscattering of light by a layer of discrete random media. JQSRT 86:161CrossRefADSGoogle Scholar
  147. Tsang L, Ding K-H (1991) Polametric signatures of a layer of random nonspherical discrete scatterers overlying a homogeneous half-space based on first- and second-order vector radiative transfer theory. IEEE Trans Geosci Remote Sens 29:242–253CrossRefADSGoogle Scholar
  148. Tsang L, Kong JA (2001) Scattering of electromagnetic waves. John Wiley and Sons, IncGoogle Scholar
  149. Tsang L, Pan J, Liang D, Li Z (2011) Modeling Active Microwave Remote Sensing of Snow Using Dense Media Radiative Transfer (DMRT) Theory with Muftiple Scattering Effects. IEEE Trans Geoscience Remote Sensing 45(4)Google Scholar
  150. Tsang L, Pan J, Liang D, Li Z, Cline DW, Tan Y (2007) Modeling active microwave remote sensing of snow using dense media radiative transfer (DMRT) theory With Multiple-Scattering Effects. IEEE Trans Geosci 45(4)Google Scholar
  151. Tse KK, Tsang L, Chan CH, Ding KH, Leung KW (2007) Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow. Radio Sci. 42:RS5001Google Scholar
  152. Tseng S (2008) Optical characteristics of a cluster of closely-packed dielectric spheres. Opt Commun 281:1986–1990CrossRefADSGoogle Scholar
  153. Volkovitski OA, Pavlova LN, Petrushin AG (1984) Optical properties of crystal clouds. Gidrometeoizdat, Leningrad (in Russian)Google Scholar
  154. Watson KM (1953) Multiple scattering and the many-body problem—applications to photomeson production in complex nuclei. Phys Rev 89:575–587MathSciNetCrossRefzbMATHADSGoogle Scholar
  155. Watson KM (1969) Multiple scattering of electromagnetic waves in an underdense plasma. J Math Phys 10:688–702CrossRefADSGoogle Scholar
  156. Wiscombe WJ, Warren SG (1980) A model for the spectral albedo of snow. I: Pure snow. J Atmos Sci 37:2712–2733CrossRefADSGoogle Scholar
  157. Wood MFG, Guo X, Vitkin IA (2007) Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology. J Biomed Opt 121Google Scholar
  158. Xie Y, Yang P, Kattawar GW, Baum BA, Hu Y (2011) Simulation of the optical properties of plate aggregates for application to the remote sensing of cirrus clouds. Appl Opt 50:1065–1081CrossRefADSGoogle Scholar
  159. Yariv A, Yeh P (1984) Optical waves in crystals. Wiley, New YorkGoogle Scholar
  160. Yeh P (1979) Electromagnetic propagation in birefringent layered media. J Opt Soc Am 69:742–755MathSciNetCrossRefADSGoogle Scholar
  161. Yeh P (1980) Optics of anisotropic layered media: A New 4 × 4 matrix algebra. Surf Sci 96:41–53CrossRefADSGoogle Scholar
  162. Zege EP, Chaikovskaya LI (1984) Optics and Spectroskopy 5:1060Google Scholar
  163. Zege EP, Ivanov AP, Katsev IL (1991) Image transfer through a scattering medium. Springer, BerlinCrossRefGoogle Scholar
  164. Zheleznyakov VV (1996) Radiation in Astrophysical Plasma. KluwerGoogle Scholar
  165. Zheleznyakov VV (1977) Electromagnetic waves in cosmic plasma. Nauka, MoscowGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Margarita G. Kuzmina
    • 1
    Email author
  • Leonid P. Bass
    • 1
  • Olga V. Nikolaeva
    • 1
  1. 1.Keldysh Institute of Applied Mathematics RASMoscowRussia

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