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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 13 — May. 1, 1998
  • pp: 2615–2623

Generalized Four-Flux Radiative Transfer Model

William E. Vargas  »View Author Affiliations


Applied Optics, Vol. 37, Issue 13, pp. 2615-2623 (1998)
http://dx.doi.org/10.1364/AO.37.002615


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Abstract

General solutions for a four-flux radiative transfer model, derivedfrom the radiative transfer equation and based on Lorenz–Miescattering and absorption parameters, have been obtained. Forwardand backward average path-length parameters have been considered aswell as forward-scattering ratios for diffuse anisotropic radiationgoing into the forward and the backward hemispheres. The reportedsolutions are generalizations of those obtained by Maheu <i>et al</i>. [Appl. Opt. <b>23,</b> 3353–3362(1984)]. Compared with the generalized solutions, numericalcalculations indicate that the δ-Eddington approximation and thestandard four-flux model of Maheu <i>et al</i>. overestimate thecollimated–diffuse reflectance of particulate coatings, whereas thesemodels give similar results in the case of collimated–diffusetransmittance.

© 1998 Optical Society of America

Citation
William E. Vargas, "Generalized Four-Flux Radiative Transfer Model," Appl. Opt. 37, 2615-2623 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-13-2615


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References

  1. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).
  2. J. I. Frankel, “Computational attributes of the integral form of the equation of transfer,” J. Quant. Spectrosc. Radiat. Transfer 46, 329–342 (1991).
  3. W. Hartel, “Zur Theorie der Lichtstreuung durch trübe Schichten besonders Trübgläser,” Licht 10, 141–143, 165, 190, 191, 214, 215, 232–234 (1940).
  4. A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. 21, 1–22 (1905).
  5. P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  6. J. Reichman, “Determination of absorption and scattering coefficients for nonhomogeneous media. 1: Theory,” Appl. Opt. 12, 1811–1815 (1973).
  7. P. S. Mudgett and L. W. Richards, “Multiple scattering calculations for technology,” Appl. Opt. 10, 1485–1502 (1971).
  8. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  9. C. M. Chu and S. W. Churchill, “Numerical solution of problems in multiple scattering of electromagnetic radiation,” Multiple Scatt. Electromag. Radiation 59, 855–863 (1955).
  10. B. Maheu, J. N. Lotoulouzan, and G. Gouesbet, “Four-flux models to solve the scattering transfer equation in terms of Lorenz–Mie parameters,” Appl. Opt. 23, 3353–3362 (1984).
  11. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  12. J. K. Beasley, J. T. Atkins, and F. W. Billmeyer, “Scattering and absorption of light in turbid media,” in Electromagnetic Scattering, R. L. Rowell and R. S. Stein, eds. (Gordon & Breach, New York, 1967), pp. 765–785.
  13. W. E. Vargas and G. A. Niklasson, “Forward scattering ratios and average path-length parameters in radiative transfer models,” J. Phys. Condens. Matter 9, 9083–9096 (1997).
  14. W. E. Vargas and G. A. Niklasson, “Average path-length parameter in radiative transfer models,” Appl. Opt. 36, 3735–3738 (1997).
  15. W. E. Vargas and G. A. Niklasson, “Generalized method for evaluating scattering parameters used in radiative transfer models,” J. Opt. Soc. Am. A 14, 2243–2252 (1997).
  16. W. E. Vargas and G. A. Niklasson, “Intensity of diffuse radiation in particulate media,” J. Opt. Soc. Am. A 14, 2253–2262 (1997).
  17. K. Klier, “Absorption and scattering in plane parallel turbid media,” J. Opt. Soc. Am. 62, 882–885 (1972).
  18. G. V. Efimov, W. von Waldenfels, and R. Wehrse, “Analytical solution of the nondiscretized radiative transfer equation for a slab of finite optical depth,” J. Quant. Spectrosc. Radiat. Transfer 53, 59–74 (1995).
  19. T. Kunitomo, Y. Tsuboi, S. Iwashita, and H. M. Shafey, “Theoretical study on spectrally selective paint coatings,” in Proceedings of the Eighth Biennial Congress International Solar Energy Society, Vol. 3, S. V. Szokolay, ed. (Pergamon, Oxford, UK, 1983), pp. 1943–1947.
  20. S. Ito, “Optical wave propagation in discrete random media with large particles: a treatment of the phase function,” Appl. Opt. 32, 1652–1656 (1993).
  21. F. B. Yurevich and L. A. Konyukh, “Radiation attenuation by disperse media,” Int. J. Heat Mass Transfer 18, 819–829 (1975).
  22. E. P. Shettle and J. A. Weinman, “The transfer of solar irradiance through inhomogeneous turbid atmospheres evaluated by Eddington’s approximation,” J. Atmos. Sci. 27, 1048–1055 (1970).
  23. J. H. Joseph and W. J. Wiscombe, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
  24. F. Liu, J. Swithenbank, and E. S. Garbett, “The boundary condition of the PN-approximation used to solve the radiative transfer equation,” Int. J. Heat Mass Transfer 35, 2043–2052 (1992).
  25. S. Karanjai and M. Talukder, “Solution of the equation of transfer with general phase function by a modified spherical-harmonic method,” Astrophys. Space Sci. 197, 309–336 (1992).
  26. W. E. Meador and W. R. Weaver, “Two-stream approximations to radiative transfer in planetary atmospheres: a unified description of existing methods and a new improvement,” J. Atmos. Sci. 37, 630–643 (1980).
  27. Harshvardhan and M. D. King, “Comparative accuracy of diffuse radiative properties computed using selected multiple scattering approximations,” J. Atmos. Sci. 50, 247–259 (1993).
  28. G. A. Niklasson and T. S. Eriksson, “Radiative cooling with pigmented polyethylene foils,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion VII, C. Grandqvist and C. M. Lampert, eds., Proc. SPIE 1016, 89–99 (1988).
  29. W. E. Vargas and G. A. Niklasson, “Pigment mass density and refractive index determination from optical measurements,” J. Phys. Condens. Matter 9, 1661–1670 (1997).
  30. L. Fukshansky, N. Fukshansky-Kazarinova, and A. M. Remisowsky, “Estimation of optical parameters in a living tissue by solving the inverse problem of the multiflux radiative transfer,” Appl. Opt. 30, 3145–3153 (1991).
  31. H. R. Wilson and W. Eck, “Transmission variation using scattering/transparent switching films,” Sol. Energy Mat. Sol. Cells 31, 197–214 (1993).
  32. W. E. Vargas and G. A. Niklasson, “Applicability conditions of the Kubelka–Munk theory,” Appl. Opt. 36, 5580–5586 (1997).
  33. B. Maheu and G. Gouesbet, “Four-flux models to solve the scattering transfer equation: special cases,” Appl. Opt. 25, 1122–1128 (1986).

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