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Applied Optics

Applied Optics


  • Vol. 36, Iss. 16 — Jun. 1, 1997
  • pp: 3735–3738

Forward average path-length parameter in four-flux radiative transfer models

William E. Vargas and Gunnar A. Niklasson  »View Author Affiliations

Applied Optics, Vol. 36, Issue 16, pp. 3735-3738 (1997)

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The optical properties of films containing spherical particles in a nonabsorbing matrix have been modeled by using a four-flux radiative transfer theory. The forward average path-length parameter takes into account the different path lengths for collimated and diffuse components of the radiation field. This parameter, whose value was known only in special cases, has been used previously as a fitting quantity. We establish a method for evaluating the forward average path-length parameter in a rigorous way. Single-scattering parameters are evaluated from the Lorenz–Mie theory, and multiple-scattering effects are taken into account by means of an extended Hartel’s theory.

© 1997 Optical Society of America

Original Manuscript: June 26, 1996
Revised Manuscript: October 28, 1996
Published: June 1, 1997

William E. Vargas and Gunnar A. Niklasson, "Forward average path-length parameter in four-flux radiative transfer models," Appl. Opt. 36, 3735-3738 (1997)

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  1. B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-flux models to solve the scattering transfer equation in terms of Lorenz–Mie parameters,” Appl. Opt. 23, 3353–3362 (1984). [CrossRef]
  2. Y. P. Wang, S. W. Zheng, K. F. Ren, “Four-flux model with adjusted average crossing parameter to solve the scattering transfer equation,” Appl. Opt. 28, 24–26 (1989). [CrossRef] [PubMed]
  3. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 10.
  4. G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, Berlin, 1969). [CrossRef]
  5. C. Sagan, J. B. Pollack, “Anisotropic nonconservative scattering and the clouds of venus,” J. Geophys. Res. 72, 469–477 (1967). [CrossRef]
  6. P. Kubelka, “New contributions to the optics of intensely light scattering materials. Part I,” J. Opt. Soc. Am. 38, 448–457 (1948). [CrossRef] [PubMed]
  7. P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology II,” J. Colloid Interface Sci. 39, 551–567 (1972). [CrossRef]
  8. W. Hartel, “Zur Theorie der Lichtstreuung durch trübe Schichten besonders Trübgläser,” Licht 10, 141–143, 165, 190, 191, 214, 215, 232–234 (1940).
  9. S. E. Orchard, “Multiple scattering by spherical dielectric particles,” J. Opt. Soc. Am. 55, 737 (1965). [CrossRef]
  10. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.
  11. C. M. Chu, S. W. Churchill, “Representation of the angular distribution of radiation scattered by a spherical particle,” J. Opt. Soc. Am. 45, 958–962 (1955). [CrossRef]
  12. G. C. Clark, C. M. Chu, S. W. Churchil, “Angular distribution coefficients for radiation scattered by a spherical particle,” J. Opt. Soc. Am. 47, 81–84 (1957). [CrossRef]

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