OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 38, Iss. 7 — Mar. 1, 1999
  • pp: 1077–1085

Two-flux radiative transfer model under nonisotropic propagating diffuse radiation

William E. Vargas  »View Author Affiliations


Applied Optics, Vol. 38, Issue 7, pp. 1077-1085 (1999)
http://dx.doi.org/10.1364/AO.38.001077


View Full Text Article

Enhanced HTML    Acrobat PDF (153 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A two-flux model is considered as a particular case of a more-general four-flux approach to describing the properties of highly diffusing materials derived from the radiative transfer equation. Any degree of anisotropy is taken into account by means of average path-length parameters and forward-scattering ratios for diffuse radiation propagating in forward and backward directions. The conditions for applicability of the standard two-flux model of Kubelka and Munk are characterized in terms of particle size and refractive index as well as of optical thickness. Scattering and absorption coefficients are obtained in terms of the effective average path-length parameter and forward-scattering ratio of the propagating radiation as well as of the intrinsic scattering and absorption coefficients per unit length of the particulate medium.

© 1999 Optical Society of America

OCIS Codes
(160.4670) Materials : Optical materials
(260.2160) Physical optics : Energy transfer
(290.4020) Scattering : Mie theory
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles
(290.7050) Scattering : Turbid media

History
Original Manuscript: June 17, 1998
Revised Manuscript: November 30, 1998
Published: March 1, 1999

Citation
William E. Vargas, "Two-flux radiative transfer model under nonisotropic propagating diffuse radiation," Appl. Opt. 38, 1077-1085 (1999)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-7-1077


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  2. P. Kubelka, “New contributions to the optics of intensely scattering materials. I,” J. Opt. Soc. Am. 38, 448–457 (1948). [CrossRef] [PubMed]
  3. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  4. J. L. Saunderson, “Calculation of the color of pigmented plastics,” J. Opt. Soc. Am. 32, 727–736 (1942). [CrossRef]
  5. W. E. Vargas, G. A. Niklasson, “Applicability conditions of the Kubelka–Munk theory,” Appl. Opt. 36, 5580–5586 (1997). [CrossRef] [PubMed]
  6. M. K. Gunde, J. K. Logar, Z. C. Orel, B. Orel, “Optimum thickness determination to maximise the spectral selectivity of black pigmented coatings for solar collectors,” Thin Solid Films 277, 185–191 (1996). [CrossRef]
  7. B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-flux models to solve the scattering transfer equation in terms of Lorenz–Mie parameters,” Appl. Opt. 26, 3353–3362 (1984). [CrossRef]
  8. G. A. Niklasson, T. S. Eriksson, “Radiative cooling with pigmented polyethylene foils,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion VII, C. G. Granqvist, C. M. Lampert, eds., Proc. SPIE1016, 89–99 (1988). [CrossRef]
  9. T. M. J. Nilsson, G. A. Niklasson, “Optimization of optical properties of pigmented foils for radiative cooling applications: model calculations,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion X, C. M. Lampert, C. G. Granqvist, eds., Proc. SPIE1536, 169–182 (1991). [CrossRef]
  10. W. E. Vargas, G. A. Niklasson, “Pigment mass density and refractive index determination from optical measurements,” J. Phys. Condens. Matter. 9, 1661–1670 (1997). [CrossRef]
  11. T. Tesfamichael, W. E. Vargas, E. Wackelgard, G. A. Niklasson, “Optical properties of silicon pigmented alumina films,” J. Appl. Phys. 82, 3508–3513 (1997). [CrossRef]
  12. W. E. Vargas, G. A. Niklasson, “Forward scattering ratios and average pathlength parameter in radiative transfer models,” J. Phys. Condens. Matter. 9, 9083–9096 (1997). [CrossRef]
  13. W. E. Vargas, G. A. Niklasson, “Forward average path-length parameter in four-flux radiative transfer models,” Appl. Opt. 36, 3735–3738 (1997). [CrossRef] [PubMed]
  14. W. E. Vargas, “Generalized four-flux radiative transfer model,” Appl. Opt. 37, 2615–2623 (1998). [CrossRef]
  15. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991). [CrossRef]
  16. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996). [CrossRef] [PubMed]
  17. M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997). [CrossRef]
  18. W. E. Vargas, G. A. Niklasson, “Generalized method for evaluating scattering parameters used in radiative transfer models,” J. Opt. Soc. Am. A 14, 2243–2252 (1997). [CrossRef]
  19. W. E. Vargas, G. A. Niklasson, “Intensity of diffuse radiation in particulate media,” J. Opt. Soc. Am. A 14, 2253–2262 (1997). [CrossRef]
  20. W. Hartel, “Zur Theorie der Lichtstreuung durch trübe Schichten besonders Trübgläser,” Licht 10, 141–143, 165, 190, 191, 214, 215, 232–234 (1940).
  21. D. C. Rich, “Computer-aided design and manufacturing of the color of decorative and protective coatings,” J. Coatings Technol. 67, 53–60 (1995).
  22. B. J. Brinkworth, “Interpretation of the Kubelka–Munk coefficients in reflection theory,” Appl. Opt. 11, 1434 (1972). [CrossRef] [PubMed]
  23. K. Klier, “Absorption and scattering in plane parallel turbid media,” J. Opt. Soc. Am. 62, 882–885 (1972). [CrossRef]
  24. D. G. Phillips, F. W. Billmeyer, “Predicting reflectance and color of paint films by Kubelka–Munk analysis. IV. Kubelka–Munk scattering coefficient,” J. Coatings Technol. 48, 30–36 (1972).
  25. P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology. II,” J. Colloid Interface Sci. 39, 551–567 (1972). [CrossRef]
  26. B. L. Drolen, C. L. Tien, “Independent and dependent scattering in packed-sphere systems,” J. Thermophys. 1, 63–68 (1987). [CrossRef]
  27. S. A. El-Wakil, A. R. Degheidy, N. K. Radwan, “Light transfer problem in turbid media with surface reflectivity,” Waves Random Media 6, 101–118 (1996). [CrossRef]
  28. L. W. Richards, “The calculation of the optical performance of paint films,” J. Coatings Technol. 42, 276–286 (1970).
  29. W. L. Butler, “Absorption of light by turbid materials,” J. Opt. Soc. Am. 52, 292–299 (1962). [CrossRef]
  30. Y. Ma, V. K. Varadan, V. V. Varadan, “Enhanced absorption due to dependent scattering,” J. Heat Transfer 112, 402–407 (1990). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited