OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 5 — Apr. 29, 2014

Deriving Kubelka–Munk theory from radiative transport

Christopher Sandoval and Arnold D. Kim  »View Author Affiliations


JOSA A, Vol. 31, Issue 3, pp. 628-636 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000628


View Full Text Article

Enhanced HTML    Acrobat PDF (381 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We derive Kubelka–Munk (KM) theory systematically from the radiative transport equation (RTE) by analyzing the system of equations resulting from applying the double spherical harmonics method of order one and transforming that system into one governing the positive- and negative-going fluxes. Through this derivation, we establish the theoretical basis of KM theory, identify all parameters, and determine its range of validity. Moreover, we are able to generalize KM theory to take into account general boundary sources and nonhomogeneous terms, for example. The generalized Kubelka–Munk (gKM) equations are also much more accurate at approximating the solution of the RTE. We validate this theory through comparison with numerical solutions of the RTE.

© 2014 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(030.5620) Coherence and statistical optics : Radiative transfer
(290.4210) Scattering : Multiple scattering
(290.7050) Scattering : Turbid media

ToC Category:
Scattering

History
Original Manuscript: November 12, 2013
Manuscript Accepted: January 6, 2014
Published: February 21, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Christopher Sandoval and Arnold D. Kim, "Deriving Kubelka–Munk theory from radiative transport," J. Opt. Soc. Am. A 31, 628-636 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-31-3-628


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1996).
  3. P. Kubelka and F. Munk, “Ein beitrag zur optik der farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  4. P. Kubelka, “New contributions to the optics of intensely light-scattering materials. Part I,” J. Opt. Soc. Am. 38, 448–457 (1948). [CrossRef]
  5. B. Philips-Invernizzi, D. Dupont, and C. Cazé, “Bibliographical review for reflectance of diffusing media,” Opt. Eng. 40, 1082–1092 (2001). [CrossRef]
  6. B. J. Brinkworth, “Interpretations of the Kubelka-Munk coefficients in reflection theory,” Appl. Opt. 11, 1434–1435 (1972). [CrossRef]
  7. L. F. Gate, “Comparison of the photon diffusion model and Kubelka-Munk equation with exact solution of the radiative transport equation,” Appl. Opt. 13, 236–238 (1974). [CrossRef]
  8. J. Nobbs, “Kubelka-Munk theory and the prediction of reflectance,” Rev. Prog. Coloration 15, 66–75 (1985). [CrossRef]
  9. W. M. Star, J. P. A. Marijnissen, and M. J. C. Van Gemert, “Light dosimetry in optical phantoms and in tissues: I. Multiple flux and transport theory,” Phys. Med. Biol. 33, 437–454 (1988). [CrossRef]
  10. W. E. Vargas and G. A. Niklasson, “Applicability conditions of the Kubelka-Munk theory,” Appl. Opt. 36, 5580–5586 (1997). [CrossRef]
  11. R. Molenaar, J. ten Bosch, and J. Zijp, “Determination of Kubelka-Munk scattering and absorption coefficients by diffuse illumination,” Appl. Opt. 38, 2068–2077 (1999). [CrossRef]
  12. L. Yang and B. Kruse, “Revised Kubelka-Munk theory. I. Theory and application,” J. Opt. Soc. Am. A 21, 1933–1941 (2004). [CrossRef]
  13. L. Yang, B. Kruse, and S. J. Miklavcic, “Revised Kubelka-Munk theory. II. Unified framework for homogeneous and inhomogeneous optical media,” J. Opt. Soc. Am. A 21, 1942–1952 (2004). [CrossRef]
  14. L. Yang and S. J. 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]
  15. P. Edström, “Examination of the revised Kubelka-Munk theory: considerations of modeling strategies,” J. Opt. Soc. Am. A 24, 548–556 (2007). [CrossRef]
  16. S. N. Thennadil, “Relationships between the Kubelka-Munk scattering and radiative transfer coefficients,” J. Opt. Soc. Am. A 25, 1480–1485 (2008). [CrossRef]
  17. M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. I. Theory,” J. Opt. Soc. Am. A 27, 1032–1039 (2010). [CrossRef]
  18. M. L. Myrick, M. N. Simcock, M. Baranowski, H. Brooke, S. L. Morgan, and J. N. McCutcheon, “The Kubelka-Munk diffuse reflectance formula revisited,” Appl. Spectrosc. Rev. 46, 140–165 (2011).
  19. B. Davison, Neutron Transport Theory (Oxford University, 1958).
  20. K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, 1967).
  21. E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport (American Nuclear Society, 1993).
  22. R. Aronson, “PN vs. double-PN approximations for highly anisotropic scattering,” Transp. Theory Stat. Phys. 15, 829–840 (1986). [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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited