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Applied Optics

Applied Optics


  • Vol. 38, Iss. 9 — Mar. 20, 1999
  • pp: 1877–1883

Average path-length parameter of diffuse light in scattering media

Camilo A. Arancibia-Bulnes and Jesús C. Ruiz-Suárez  »View Author Affiliations

Applied Optics, Vol. 38, Issue 9, pp. 1877-1883 (1999)

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We use Monte Carlo simulations to study in detail the propagation of light in a plane-parallel medium containing scattering particles. In particular, we compute the forward and backward average path-length parameters (FAPP and BAPP, respectively) of four-flux radiative transfer models as functions of the optical depth. Strong dependence on the single scattering albedo and phase function asymmetry is found for both quantities. In general the values of the FAPP decrease with increasing absorption, whereas the opposite occurs for the BAPP. A similar effect is produced when changing from isotropic phase functions to phase functions with a large asymmetry in the forward direction. We present analytical results for the asymptotic values of the FAPP and BAPP as functions of albedo for the particular case of isotropic scattering. Our results differ markedly from the predictions obtained recently with two multiple-scattering models by Vargas and Niklasson [J. Opt. Soc. Am. A 14, 2243 (1997); Appl. Opt. 36, 3735 (1997)]. The differences found point out the intrinsic limitations of these models.

© 1999 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(290.4020) Scattering : Mie theory
(290.4210) Scattering : Multiple scattering

Original Manuscript: April 10, 1998
Revised Manuscript: November 30, 1998
Published: March 20, 1999

Camilo A. Arancibia-Bulnes and Jesús C. Ruiz-Suárez, "Average path-length parameter of diffuse light in scattering media," Appl. Opt. 38, 1877-1883 (1999)

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  1. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), Chap. 1.
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, New York, 1997), Chaps. 7–13.
  3. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  4. 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]
  5. B. Maheu, G. Gouesbet, “Four-flux models to solve the scattering transfer equation: special cases,” Appl. Opt. 25, 1122–1128 (1986). [CrossRef] [PubMed]
  6. C. A. Arancibia-Bulnes, J. C. Ruiz-Suárez, “Spectral selectivity of Cermets with large metallic inclusions,” J. Appl. Phys. 83, 5421–5426 (1998). [CrossRef]
  7. T. Tesfamichael, W. E. Vargas, E. Wäcklegård, G. A. Niklasson, “Optical properties of silicon pigmented alumina films,” J. Appl. Phys. 82, 3508–3513 (1997). [CrossRef]
  8. 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]
  9. A. P. Prishivalko, A. F. Sinyuk, “Studies of spectral characteristics of layers of ultradisperse silver particles taking into account the size dependence of optical constants and multiple light scattering,” Opt. Spectros. 79, 128–133 (1995).
  10. W. E. Vargas, “Generalized four-flux radiative transfer model,” Appl. Opt. 37, 2615–2623 (1998). [CrossRef]
  11. 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]
  12. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chap. 3.
  13. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chaps. 3 and 4.
  14. 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]
  15. W. E. Vargas, G. A. Niklasson, “Forward-scattering ratios and average path length parameter in radiative transfer models,” J. Phys. Condens. Matter 9, 9083–9096 (1997). [CrossRef]
  16. K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967), Chap. 4.
  17. M. N. Özisik, Radiative Transfer and Interactions with Conduction and Convection (Wiley, New York, 1973), Chap. 10.
  18. W. E. Hartel, “Zur Theorie der Lichtstreuung durch trübe Schichten besonders Trübgläser,” Licht 10, 141–143, 165, 190, 191, 214, 215, 232–234 (1940).
  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. G. N. Plass, G. W. Kattawar, F. E. Catchings, “Matrix operator theory of radiative transfer. 1. Rayleigh scattering,” Appl. Opt. 12, 314–329 (1973). [CrossRef] [PubMed]
  21. H.-W. Chang, T.-L. Wu, “Numerical solutions of matrix Riccati equations for radiative transfer in a plane-parallel geometry,” Waves Random Media 7, 147–168 (1997). [CrossRef]

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