OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 11 — Nov. 1, 2008
  • pp: 2879–2883

Multiple path analysis of reflectance from turbid media

Geoffrey L. Rogers  »View Author Affiliations

JOSA A, Vol. 25, Issue 11, pp. 2879-2883 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (112 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A novel method to calculate the reflectance of light from a turbid medium is presented. The method takes an approach similar to that of the Beer–Lambert law, where the intensity of light is attenuated by an exponential factor involving the path length and the absorption coefficient. Due to scatter, however, there are many path lengths; in the present method all possible path lengths are weighted by their probabilities and summed over. A path length probability density is derived by considering a photon random walk through the medium. The result is a simple expression for the reflectance based on the physical properties of the medium.

© 2008 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(290.1990) Scattering : Diffusion
(290.4210) Scattering : Multiple scattering
(290.7050) Scattering : Turbid media
(330.1690) Vision, color, and visual optics : Color

ToC Category:

Original Manuscript: February 21, 2008
Revised Manuscript: September 2, 2008
Manuscript Accepted: September 4, 2008
Published: October 31, 2008

Virtual Issues
Vol. 4, Iss. 1 Virtual Journal for Biomedical Optics

Geoffrey L. Rogers, "Multiple path analysis of reflectance from turbid media," J. Opt. Soc. Am. A 25, 2879-2883 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. Philips-Invernizzi, D. Dupont, and C. Caze, “Bibliographical review for reflectance of diffusing media,” Opt. Eng. (Bellingham) 40, 1082-1092 (2001). [CrossRef]
  2. R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).
  3. P. Kubelka and F. Munk, “Ein beitrag zur optik der farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931) (in German).
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 1.
  5. A. A. Kokhanovsky, “Physical interpretation and accuracy of the Kubelka--Munk theory,” J. Phys. D: Appl. Phys. 40, 2210-2216 (2007). [CrossRef]
  6. L. Yang and S. Miklavcic, “Revised Kubelka--Munk theory. III. A general theory of light propagation in scattering and absorptive media,” J. Opt. Soc. Am. A 22, 1866-1873 (2005). [CrossRef]
  7. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  8. H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas and Applications (Academic, 1980).
  9. K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, 1967).
  10. R. A. J. Groenhuis, H. A. Ferwerda, and J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory,” Appl. Opt. 22, 2456-2467 (1983). [CrossRef] [PubMed]
  11. G. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41, 643-656 (1997).
  12. R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, “Model for photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423-432 (1987). [CrossRef] [PubMed]
  13. A. Gandjbakhche, R. Nossal, and R. Bonner, “Scaling relationships for theories of anisotropic random walks applied to tissue optics,” Appl. Opt. 32, 504-516 (1993). [CrossRef] [PubMed]
  14. R. F. Lutomirski, A. P. Ciervo, and G. J. Hall, “Moments of multiple scattering,” Appl. Opt. 34, 7125-7136 (1995). [CrossRef] [PubMed]
  15. V. Kolinko, F. de Mul, J. Greve, and A. Priezzhev, “Probabilistic model of multiple light scattering based on rigorous computation of the first and the second moments of photon coordinates,” Appl. Opt. 35, 4541-4550 (1996). [CrossRef] [PubMed]
  16. G. H. Weiss, J. M. Porr, and J. Masoliver, “The continuoustime random walk description of photon motion in an isotropic medium,” Opt. Commun. 146, 268-276 (1998). [CrossRef]
  17. A. A. Kokhanovsky, “Statistical properties of a photon gas in random media,” Phys. Rev. E 66, 037601 (2002). [CrossRef]
  18. P. S. Mudgett and L. W. Richards, “Multiple scattering calculations for technology,” Appl. Opt. 10, 1485-1502 (1971). [CrossRef] [PubMed]
  19. L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995). [CrossRef] [PubMed]
  20. G. Wyszecki and W. S. Stiles, Color Science (Wiley, 1982).
  21. R. A. Bolt and J. J. ten Bosch, “On the determination of optical parameters for turbid materials,” Waves Random Media 4, 233-242 (1994). [CrossRef]
  22. S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1-89 (1943). [CrossRef]
  23. S. M. Ross, Stochastic Processes (Wiley, 1983).
  24. S. Redner, A Guide to First-Passage Processes (Cambridge U. Press, 2001).
  25. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North Holland, 1981).

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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited