سابِق|تال

Radiative transfer： From phenomenology to first principles

  • role： First author第一作者
  • Affiliation：

    Institute of Remote Sensing and Geographic Information System, School of Space and Earth Sciences, Peking University, Beijing 100871, China

  • Email：wuzihua@pku.edu.cn
  • Introduction：吴自华，研究方向为定量遥感理论。E-mail： wuzihua@pku.edu.cn
WU Zihua,  
  • role： Corresponding author通信作者
  • Affiliation：

    Institute of Remote Sensing and Geographic Information System, School of Space and Earth Sciences, Peking University, Beijing 100871, China

  • Email：qmqin@pku.edu.cn
  • Introduction：秦其明，研究方向为定量遥感与地理信息系统。E-mail： qmqin@pku.edu.cn
QIN Qiming*

ملخص

Radiative Transfer Theory (RTT) is one of the essential foundations in astrophysics, engineering thermophysics, computer graphics, biomedical imaging, and remote sensing. RTT is particularly widely used in the field of quantitative remote sensing. However, classical RTT is a phenomenological theory based on heuristic summarizations of experiments instead of being directly derived from the first principles. Given the ignorance of the wave property, RTT cannot explain interference and diffraction phenomena, e.g., the well-known coherent backscattering.The root of RTT dates back to the photometry study by Bouguer, Lambert, and Beer. Von Lommel and Chwolson are believed to propose the integral form of the Radiative Transfer Equation (RTE) for the first time in the 1880s. Afterward, many other scientists, including Schuster, Schwarzschild, Eddington, Milne, Gans, Sobolev, Chandrasekhar, Rozenberg, and Tsang, contributed to the establishment of RTT as a strict theory. However, classical RTT implicitly depends on the assumption of independent scattering, which fails when applied to dense matter. It requires the first-principle approach to bridge the gap between classical RTT and classical electromagnetics and extend the application of RTT. Three ways can be applied: (1) direct derivation, (2) numerical simulations, and (3) controlled experiments.Direct derivation of the RTE from first principles (i.e., Maxwell equations) is the most fundamental approach. Mishchenko and his colleagues’ derivation is currently considered the most rigorous. This derivation is primarily based on previous research on multiple scattering of electromagnetic waves, to which Foldy, Lax, Twersky, and many others have made significant contributions. Mishchenko et al. managed to derive the RTE from Maxwell equations for both coherent and incoherent intensities under the condition of plane wave and discrete random media. The derivation proves that RTT is not a disconnected “island” from the “mainland” of classical electromagnetics.Besides derivations, numerical simulations and controlled experiments help reveal the connection between RTT and numerically exacted computational electromagnetics. In these simulations and experiments, the RTT and electromagnetic computation results are compared under different conditions. Results show that RTT can yield satisfactory results when the volume percentage of scatterers is low. Some corrections, e.g., the Percus-Yevick model, can be introduced to compensate for the errors of RTT when the density of scatterers further increases. Based on these studies, some efforts have been made to extend RTT to the case of dense matter. Notable achievements include the DMRT and the R2T2 theories.Although these studies are still limited to some ideal situations, they have provided some guidance for the mechanistic revision of RTT, thereby expanding the scope of its application. On the contrary, the combination of radiative transfer methods with computational electromagnetics becomes a research direction of interest, along with the development of computer performance and the improvement of relevant algorithms. At present, different methods are used in quantitative remote sensing for different wavebands and different research objects: for example, optical remote sensing and microwave remote sensing for vegetation or vegetation remote sensing and atmospheric remote sensing. Although the names of the methods used are “radiative transfer,” they are based on different assumptions and approximations. The combination of RTT and computational electromagnetics is a promising approach to unifying the remote sensing modeling and inversion studies of different wavelengths and objects.

مفهوم

radiative transfer;phenomenology;first principles;classical electromagnetics;Maxwell equations

References

  1. 1.
    Arons A B and Peppard M B. 1965. Einstein’s proposal of the photon concept—a translation of the Annalen der Physik Paper of 1905. American Journal of Physics, 33(5): 367-374
  2. 2.
    Bablet A, Vu P V H, Jacquemoud S, Viallefont-Robinet F, Fabre S, Briottet X, Sadeghi M, Whiting M L, Baret F and Tian J. 2018. MARMIT: a multilayer radiative transfer model of soil reflectance to estimate surface soil moisture content in the solar domain (400-2500 nm). Remote Sensing of Environment, 217: 1-17
  3. 3.
    Balsara D. 2001. Fast and accurate discrete ordinates methods for multidimensional radiative transfer. Part I, basic methods. Journal of Quantitative Spectroscopy and Radiative Transfer, 69(6): 671-707
  4. 4.
    Barabanenkov Y N. 1969. On the spectral theory of radiation transport equations. Soviet Physics Journal of Experimental and Theoretical Physics, 29(4): 679-684
  5. 5.
    Barabanenkov Y N, Kravtsov Y A, Rytov S M and Tamarskiĭ V I. 1971. Status of the theory of propagation of waves in a randomly inhomogeneous medium. Soviet Physics Uspekhi, 13(5): 551-575
  6. 6.
    Beer A. 1854. Grundriss des photometrischen Calcüles. Braunschweig: Friedrich Vieweg und Sohn
  7. 7.
    Benassi M, Garcia R D M, Karp A H and Siewert C E. 1984. A high-order spherical harmonics solution to the standard problem in radiative transfer. The Astrophysical Journal, 280: 853-864
  8. 8.
    Bernes C. 1979. A Monte Carlo approach to non-LTE radiative transfer problems. Astronomy and Astrophysics, 73: 67-73
  9. 9.
    Borovoi A G. 1966. The iteration method in multiple scattering: the transfer equation. Soviet Physics Journal, 9(6): 27-29
  10. 10.
    Bouguer P. 1729. Essai d’optique sur la gradation de la lumière. Paris: Claude Jombert
  11. 11.
    Bouguer P. 1760. Traité d’optique sur la gradation de la lumière. Paris: H. L. Guerin & L. F. Delatour
  12. 12.
    Bremmer H. 1964. Random volume scattering. Radio Science, 68(9): 967-981
  13. 13.
    Chandrasekhar S. 1950. Radiative Transfer. Oxford: Oxford University Press
  14. 14.
    Chang W M, Tan S R, Lemmetyinen J, Tsang L, Xu X L and Yueh S H. 2014. Dense media radiative transfer applied to SnowScat and SnowSAR. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 7(9): 3811-3825
  15. 15.
    Chwolson O D. 1889. Grundzüge einer mathematischen Theorie der inneren Diffusion des Lichtes. Bulletin de l’Académie Impériale des sciences de St.-Pétersbourg, 33: 221-256
  16. 16.
    Doicu A and Mishchenko M I. 2018. Overview of methods for deriving the radiative transfer theory from the Maxwell equations. I: approach based on the far-field Foldy equations. Journal of Quantitative Spectroscopy and Radiative Transfer, 220: 123-139
  17. 17.
    Doicu A and Mishchenko M I. 2019a. An overview of methods for deriving the radiative transfer theory from the Maxwell equations. II: approach based on the Dyson and Bethe–Salpeter equations. Journal of Quantitative Spectroscopy and Radiative Transfer, 224: 25-36
  18. 18.
    Doicu A and Mishchenko M I. 2019b. An overview of methods for deriving the radiative transfer theory from the Maxwell equations. III: Effects of random rough boundaries and packing density. Journal of Quantitative Spectroscopy and Radiative Transfer, 224: 154-170
  19. 19.
    Doicu A, Mishchenko M I and Trautmann T. 2020a. Electromagnetic scattering by discrete random media illuminated by a Gaussian beam II: Solution of the radiative transfer equation. Journal of Quantitative Spectroscopy and Radiative Transfer, 256: 107297 [DOI:
  20. 20.
    Doicu A, Mishchenko M I and Trautmann T. 2020b. Electromagnetic scattering by discrete random media illuminated by a Gaussian beam I: derivation of the radiative transfer equation. Journal of Quantitative Spectroscopy and Radiative Transfer, 256: 107301 [DOI:
  21. 21.
    Dyson F J. 1949. The S matrix in quantum electrodynamics. Physical Review, 75(11): 1736
  22. 22.
    Eddington A S. 1916. On the radiative equilibrium of the stars. Monthly Notices of the Royal Astronomical Society, 77(1): 16-35
  23. 23.
    Efremenko D and Kokhanovsky A. 2021. Light scattering, absorption, extinction, and propagation in the terrestrial atmosphere//Foundations of Atmospheric Remote Sensing. Switzerland: Springer: 77-147
  24. 24.
    Egel A, Pattelli L, Mazzamuto G, Wiersma D S and Lemmer U. 2017. CELES: CUDA-accelerated simulation of electromagnetic scattering by large ensembles of spheres. Journal of Quantitative Spectroscopy and Radiative Transfer, 199: 103-110
  25. 25.
    Ergül Ö and Gürel L. 2014. The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetics Problems. Piscataway: John Wiley and Sons
  26. 26.
    Foldy L L. 1945. The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers. Physical Review, 67(3/4): 107-119
  27. 27.
    Furutsu K. 1975. Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation. Radio Science, 10(1): 29-44
  28. 28.
    Gans R. 1924. Die Farbe des Meeres. Annalen der Physik, 380(17): 1-22
  29. 29.
    Garcia R D M and Siewert C E. 1986. A generalized spherical harmonics solution for radiative transfer models that include polarization effects. Journal of Quantitative Spectroscopy and Radiative Transfer, 36(5): 401-423
  30. 30.
    Gastellu-Etchegorry J P, Martin E and Gascon F. 2004. DART: a 3D model for simulating satellite images and studying surface radiation budget. International Journal of Remote Sensing, 25(1): 73-96
  31. 31.
    Glassner A S. 1989. An Introduction to Ray Tracing. London: Academic Press
  32. 32.
    Guo J, Tsang L, Asher W, Ding K H and Chen C T. 2001. Applications of dense media radiative transfer theory for passive microwave remote sensing of foam covered ocean. IEEE Transactions on Geoscience and Remote Sensing, 39(5): 1019-1027
  33. 33.
    Howell J R, Mengüc M P and Siegel R. 2010. Thermal Radiation Heat Transfer. Boca Raton: CRC Press
  34. 34.
    Ishimaru A. 1978. Wave Propagation and Scattering in Random Media. New York: Academic Press
  35. 35.
    Ishimaru A and Kuga Y. 1982. Attenuation constant of a coherent field in a dense distribution of particles. Journal of the Optical Society of America, 72(10): 1317-1320
  36. 36.
    Ito G, Arnold J A and Glotch T D. 2017. T-matrix and radiative transfer hybrid models for densely packed particulates at mid-infrared wavelengths. Journal of Geophysical Research: Planets, 122(5): 822-838
  37. 37.
    Ito G, Mishchenko M I and Glotch T D. 2018. Radiative-transfer modeling of spectra of planetary regoliths using cluster-based dense packing modifications. Journal of Geophysical Research: Planets, 123(5): 1203-1220
  38. 38.
    Jin Y. 1992. Radiative Transfer of multi-layer random media with multi-component dense random scattering particles. Science China A, (12): 1311-1317
  39. 39.
    Jin Y. 1997. Radiative transfer of snowpack/vegetation canopy at the SSM/I channels and satellite data analysis. Remote Sensing of Environment, 61(1): 55-63
  40. 40.
    Kaasalainen S, Kaasalainen M, Mielonen T, Suomalainen J, Peltoniemi J I and Näränen J. 2006. Optical properties of snow in backscatter. Journal of Glaciology, 52(179): 574-584
  41. 41.
    Kravtsov Y A and Apresyan L A. 1996. Radiative transfer: new aspects of the old theory//Progress in Optics. Amsterdam: Elsevier, 36: 179-244
  42. 42.
    Kuusk A. 2018. Canopy radiative transfer modeling//Comprehensive Remote Sensing. Oxford: Elsevier: 9-22
  43. 43.
    Kuzmina M G, Bass L P and Nikolaeva O V. 2018. Polarized radiative transfer in optically active light scattering media//Kokhanovsky A, ed. Springer Series in Light Scattering Volume 2: Light Scattering, Radiative Transfer and Remote Sensing. [s.l.]: Springer: 1-53
  44. 44.
    Lambert J H. 1760. Photometria sive de mensura et gradibus luminis, colorum et umbrae. Augsburg: Detlefsen
  45. 45.
    Lax M. 1951. Multiple scattering of waves. Reviews of Modern Physics, 23(4): 287-310
  46. 46.
    Lax M. 1952. Multiple scattering of waves. II. The effective field in dense systems. Physical Review, 85: 621
  47. 47.
    Liang S L and Mishchenko M I. 1997. Calculations of the soil hot-spot effect using the coherent backscattering theory. Remote Sensing of Environment, 60(2): 163-173
  48. 48.
    Lommel E. 1887. Die Photometrie der diffusen Zurückwerfung. Sitzber Acad Wissensch München, 17: 95-124
  49. 49.
    Ma L X, Tan J Y, Zhao J M, Wang F Q and Wang C A. 2017. Multiple and dependent scattering by densely packed discrete spheres: comparison of radiative transfer and Maxwell theory. Journal of Quantitative Spectroscopy and Radiative Transfer, 187: 255-266
  50. 50.
    Mackowski D W and Mishchenko M I. 2011. A multiple sphere T-matrix Fortran code for use on parallel computer clusters. Journal of Quantitative Spectroscopy and Radiative Transfer, 112(13): 2182-2192
  51. 51.
    Milne E A. 1921. Radiative equilibrium in the outer layers of a star: the temperature distribution and the law of darkening. Monthly Notices of the Royal Astronomical Society, 81(5): 361-375
  52. 52.
    Mishchenko M I. 2002. Vector radiative transfer equation for arbitrarily shaped and arbitrarily oriented particles: a microphysical derivation from statistical electromagnetics. Applied Optics, 41(33): 7114
  53. 53.
    Mishchenko M I. 2010. Poynting–Stokes tensor and radiative transfer in discrete random media: the microphysical paradigm. Optics Express, 18(19): 19770
  54. 54.
    Mishchenko M I. 2014a. Directional radiometry and radiative transfer: the convoluted path from centuries-old phenomenology to physical optics. Journal of Quantitative Spectroscopy and Radiative Transfer, 146: 4-33
  55. 55.
    Mishchenko M I. 2014b. Electromagnetic Scattering by Particles and Particle Groups: An Introduction. Cambridge: Cambridge University Press
  56. 56.
    Mishchenko M I, Dlugach J M, Yanovitskij E G and Zakharova N T. 1999. Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces. Journal of Quantitative Spectroscopy and Radiative Transfer, 63(2/6): 409-432
  57. 57.
    Mishchenko M I, Dlugach J M, Yurkin M A, Bi L, Cairns B, Liu L, Panetta R L, Travis L D, Yang P and Zakharova N T. 2016. First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media. Physics Reports, 632: 1-75
  58. 58.
    Mishchenko M I, Goldstein D H, Chowdhary J and Lompado A. 2013. Radiative transfer theory verified by controlled laboratory experiments. Optics Letters, 38(18): 3522
  59. 59.
    Mishchenko M I, Hovenier J W and Mackowski D W. 2004. Single scattering by a small volume element. Journal of the Optical Society of America A, 21(1): 71-87
  60. 60.
    Mishchenko M I and Liu L. 2007. Weak localization of electromagnetic waves by densely packed many-particle groups: exact 3D results. Journal of Quantitative Spectroscopy and Radiative Transfer, 106(1/3): 616-621
  61. 61.
    Mishchenko M I, Liu L, Mackowski D W, Cairns B and Videen G. 2007. Multiple scattering by random particulate media: exact 3D results. Optics Express, 15(6): 2822
  62. 62.
    Mishchenko M I, Travis L D and Lacis A A. 2002. Scattering, Absorption, and Emission of Light by Small Particles. Cambridge: Cambridge University Press
  63. 63.
    Mishchenko M I, Travis L D and Lacis A A. 2006. Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering. Cambridge: Cambridge University Press
  64. 64.
    Mobley C D. 2001. Radiative transfer in the ocean//Encyclopedia of Ocean Sciences. San Diego: Academic Press: 2321-2330
  65. 65.
    Muinonen K. 2004. Coherent backscattering of light by complex random media of spherical scatterers: numerical solution. Waves in Random Media, 14(3): 365-388
  66. 66.
    Muinonen K, Markkanen J, Väisänen T, Peltoniemi J and Penttilä A. 2018. Multiple scattering of light in discrete random media using incoherent interactions. Optics Letters, 43(4): 683-686
  67. 67.
    Muinonen K, Mishchenko M I, Dlugach J M, Zubko E, Penttilä A and Videen G. 2012. Coherent backscattering verified numerically for a finite volume of spherical particles. The Astrophysical Journal, 760(2): 118
  68. 68.
    Panetta R L, Liu C and Yang P. 2013. A pseudo-spectral time domain method for light scattering computation//Kokhanovsky A A, ed. Light Scattering Reviews 8. Berlin: Springer: 139-188
  69. 69.
    Peraiah A. 2002. An Introduction to Radiative Transfer: Methods and Applications in Astrophysics. Cambridge: Cambridge University Press
  70. 70.
    Prahl S A. 1995. The adding-doubling method//Optical-Thermal Response of Laser-Irradiated Tissue. New York: Springer: 101-129
  71. 71.
    Preisendorfer R W. 1965. Radiative Transfer on Discrete Spaces. Oxford: Pergamon Press
  72. 72.
    Prishivalko A P, Babenko V A and Kuzmin V N. 1984. Scattering and absorption of light by inhomogeneous and anisotropic spherical particles. Minsk: Hauka i Tehnika
  73. 73.
    Qin Q M, Chen J, Zhang Y G, Ren H Z, Wu Z H, Zhang C S, Wu L S and Liu J L. 2020. A discussion on some frontier directions of quantitative remote sensing. Remote Sensing for Land and Resources, 32(4): 8-15
  74. 74.
    Qin Q M, Fan W J and Ren H Z. 2018. Theories, Methods and Applications of Quantitative Remote Sensing for Croplands. Beijing: Science Press
  75. 75.
    Royer A, Roy A, Montpetit B, Saint-Jean-Rondeau O, Picard G, Brucker L and Langlois A. 2017. Comparison of commonly-used microwave radiative transfer models for snow remote sensing. Remote Sensing of Environment, 190: 247-259
  76. 76.
    Rozenberg G V. 1955. Vector-parameter Stokes. UAN 56(1): 79-110
  77. 77.
    Sadeghi M, Babaeian E, Tuller M and Jones S B. 2018. Particle size effects on soil reflectance explained by an analytical radiative transfer model. Remote Sensing of Environment, 210: 375-386
  78. 78.
    Salpeter E E and Bethe H A. 1951. A relativistic equation for bound-state problems. Physical Review, 84(6): 1232-1242
  79. 79.
    Schäfer J and Kienle A. 2008. Scattering of light by multiple dielectric cylinders: comparison of radiative transfer and Maxwell theory. Optics Letters, 33(20): 2413
  80. 80.
    Schmugge T J. and Choudhury B J. 1981. A comparison of radiative transfer models for predicting the microwave emission from soils. Radio Science, 16(5), 927-938
  81. 81.
    Schuster A. 1905. Radiation through a foggy atmosphere. The Astrophysical Journal, 21: 1
  82. 82.
    Schwarzschild K. 1906. Über das gleichgewicht der sonnenatmosphäre. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1906: 41-53
  83. 83.
    Siewert C E. 2000. A discrete-ordinates solution for radiative-transfer models that include polarization effects. Journal of Quantitative Spectroscopy and Radiative Transfer, 64(3): 227-254
  84. 84.
    Sobolev V V. 1949. On polarization of scattered light. Trudy Astron. Obs. Leningr. Univ, 13: 3-16
  85. 85.
    Sun B Q, Bi L, Yang P, Kahnert M and Kattawar G. 2019. Invariant Imbedding T-Matrix Method for Light Scattering by Nonspherical and Inhomogeneous Particles. Amsterdam: Elsevier
  86. 86.
    Titov G A. 1990. Statistical description of radiation transfer in clouds. Journal of the Atmospheric Sciences, 47(1): 24-38
  87. 87.
    Tsang L. 1984. Thermal emission of nonspherical particles. Radio Science, 19(4): 966-974
  88. 88.
    Tsang L, Chen C T, Chang A T C, Guo J J and Ding K H. 2000a. Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow. Radio Science, 35(3): 731-749
  89. 89.
    Tsang L and Ishimaru A. 1987. Radiative wave equations for vector electromagnetic propagation in dense nontenuous media. Journal of Electromagnetic Waves and Applications, 1(1): 59-72
  90. 90.
    Tsang L and Kong J A. 2001. Scattering of Electromagnetic Waves: Advanced Topics. New York: John Wiley and Sons
  91. 91.
    Tsang L and Kong J A. 1980. Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism. Journal of Applied Physics, 51(7): 3465-3485
  92. 92.
    Tsang L, Kong J A and Ding K H. 2000b. Scattering of Electromagnetic Waves: Theories and Applications. New York: John Wiley and Sons
  93. 93.
    Tsang L, Kong J A and Habashy T. 1982. Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with the quasicrystalline and Percus–Yevick approximation. The Journal of the Acoustical Society of America, 71(3): 552-558
  94. 94.
    Tsang L, Pan J, Liang D, Li Z X, Cline D W and Tan Y H. 2007. Modeling active microwave remote sensing of snow using dense media radiative transfer (DMRT) theory with multiple-scattering effects. IEEE Transactions on Geoscience and Remote Sensing, 45(4): 990-1004
  95. 95.
    Tseng S H and Huang B. 2007. Comparing Monte Carlo simulation and pseudospectral time-domain numerical solutions of Maxwell’s equations of light scattering by a macroscopic random medium. Applied Physics Letters, 91(5): 051114
  96. 96.
    Twersky V. 1964. On propagation in random media of discrete scatterers//Bellman R, ed. Proceedings of Symposia in Applied Mathematics. Providence: American Mathematical Society: 84-116
  97. 97.
    Twersky V. 1983. Propagation in correlated distributions of large-spaced scatterers. Journal of the Optical Society of America, 73(3): 313-320
  98. 98.
    Väisänen T. 2020. Light Scattering in Dense Particulate Media. Helsinki: University of Helsinki
  99. 99.
    Väisänen T, Markkanen J, Hadamcik E, Renard J B, Lasue J, Levasseur-Regourd A C, Blum J and Muinonen K. 2020a. Scattering of light by a large, densely packed agglomerate of small silica spheres. Optics Letters, 45(7): 1679
  100. 100.
    Väisänen T, Martikainen J and Muinonen K. 2020b. Scattering of light by dense particulate media in the geometric optics regime. Journal of Quantitative Spectroscopy and Radiative Transfer, 241: 106719
  101. 101.
    Väisänen T, Markkanen J, Penttilä A and Muinonen K. 2019. Radiative transfer with reciprocal transactions: numerical method and its implementation. PLoS ONE, 14(1): e0210155
  102. 102.
    Verhoef W. 1998. Theory of Radiative Transfer Models Applied in Optical Remote Sensing of Vegetation Canopies. Wageningen: Wageningen Agricultural University
  103. 103.
    Voit F, Hohmann A, Schäfer J and Kienle A. 2012. Multiple scattering of polarized light: comparison of Maxwell theory and radiative transfer theory. Journal of Biomedical Optics, 17(4): 045003
  104. 104.
    Voit F, Schäfer J and Kienle A. 2009. Light scattering by multiple spheres: comparison between Maxwell theory and radiative-transfer-theory calculations. Optics Letters, 34(17): 2593
  105. 105.
    Wang L V and Wu H. 2007. Biomedical Optics: Principles and Imaging. Hoboken: John Wiley and Sons
  106. 106.
    Watson K M. 1953. Multiple scattering and the many-body problem—applications to photomeson production in complex nuclei. Physical Review, 89(3): 575-587
  107. 107.
    Wen B, Tsang L, Winebrenner D P and Ishimaru A. 1990. Dense medium radiative transfer theory: comparison with experiment and application to microwave remote sensing and polarimetry. IEEE Transactions on Geoscience and Remote Sensing, 28(1): 46-59
  108. 108.
    Wendisch M and Yang P. 2012. Theory of Atmospheric Radiative Transfer: A Comprehensive Introduction. Singapore: John Wiley and Sons
  109. 109.
    Whitney B A. 2011. Monte Carlo radiative transfer//Fluid Flows to Black Holes: A Tribute to S Chandrasekhar on His Birth Centenary. Singapore: World Scientific: 151-176
  110. 110.
    Wolf E. 1976. New theory of radiative energy transfer in free electromagnetic fields. Physical Review D, 13(4): 869-886
  111. 111.
    Wolf P E and Maret G. 1985. Weak localization and coherent backscattering of photons in disordered media. Physical Review Letters, 55(24): 2696-2699
  112. 112.
    Yang W, Jin X and Gao X Q. 2021. Vector radiative transfer equation for arbitrary shape particles derived from Maxwell’s electromagnetic theory. Journal of Quantitative Spectroscopy and Radiative Transfer, 265: 107307
  113. 113.
    Yu J H, Bi L, Han W and Zhang X Y. 2022. Application of a neural network to store and compute the optical properties of non-spherical particles. Advances in Atmospheric Sciences, 39(12): 2024-2039
  114. 114.
    Yurkin M A and Hoekstra A G. 2011. The discrete-dipole-approximation code ADDA: capabilities and known limitations. Journal of Quantitative Spectroscopy and Radiative Transfer, 112(13): 2234-2247
  115. 115.
    Zhai P W, Hu Y X, Trepte C R and Lucker P L. 2009. A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method. Optics Express, 17(4): 2057-2079
  116. 116.
    Zhou L, Tsang L and Chen D. 2003. Polarimetric passive microwave remote sensing of wind vectors with foam-covered rough ocean surfaces. Radio Science, 38(4): 1073

قراءة النص الكامل

The above content is generated by Large Model Translation. The translated content is for reference only. We do not assume any commercial or legal responsibilty for any consequences arising from the use of our website