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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 7 — Jul. 1, 2008
  • pp: 1480–1485

Relationship between the Kubelka–Munk scattering and radiative transfer coefficients

Suresh N. Thennadil  »View Author Affiliations

JOSA A, Vol. 25, Issue 7, pp. 1480-1485 (2008)

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The relationship between the Kubelka–Munk (K–M) and the transport scattering coefficient is obtained through a semi-empirical approach. This approach gives the same result as that given by Gate [Appl. Opt. 13, 236 (1974)] when the incident beam is diffuse. This result and those given by Star et al. [Phys. Med. Biol. 33, 437 (1988)] and Brinkworth [Appl. Opt. 11, 1434 (1972)] are compared with the exact solution of the radiative transfer equation over a large range of optical properties. It is found that the latter expressions, which include an absorption component, do not give accurate results over the range considered. Using the semi-empirical approach, the relationship between the K–M and the transport scattering coefficient is derived for the case where the incident light is collimated. It is shown that although the K–M equation is derived based on diffuse incident light, it can also represent very well the reflectance from a slab of infinite thickness when the incident light is collimated. However, in this case the relationship between the coefficients has to include a function that is dependent on the anisotropy factor. Analysis indicates that the K–M transform achieves the objective of obtaining a measure that gives the ratio of absorption to scattering effects for both diffuse and collimated incident beams over a large range of optical properties.

© 2008 Optical Society of America

OCIS Codes
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles
(290.7050) Scattering : Turbid media
(010.5620) Atmospheric and oceanic optics : Radiative transfer

ToC Category:

Original Manuscript: January 22, 2008
Revised Manuscript: March 27, 2008
Manuscript Accepted: April 24, 2008
Published: June 3, 2008

Virtual Issues
Vol. 3, Iss. 8 Virtual Journal for Biomedical Optics

Suresh N. Thennadil, "Relationship between the Kubelka-Munk scattering and radiative transfer coefficients," J. Opt. Soc. Am. A 25, 1480-1485 (2008)

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  1. G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, 1969).
  2. M. K. Gunde, J. K. Logar, Z. C. Orel, and B. Orel, “Application of the Kubelka-Munk theory to thickness-dependent diffuse reflectance of black paint in the mid-IR,” Appl. Spectrosc. 49, 623-629 (1995). [CrossRef]
  3. L. E. McNeil and R. H. French, “Light scattering from red pigment particles: multiple scattering in a strongly absorbing system,” J. Appl. Phys. 89, 283-293 (2001). [CrossRef]
  4. G. Dupuis and M. Menu, “Quantitative characterisation of pigment mixtures used in art by fibre-optics diffuse-reflectance spectroscopy,” Appl. Phys. A 83, 469-474 (2006). [CrossRef]
  5. J. Sirita, S. Phanichphant, and F. C. Meunier, “Quantitative analysis of adsorbate concentrations by diffuse reflectance FT-IR,” Anal. Chem. 79, 3912-3918 (2007). [CrossRef] [PubMed]
  6. P. Jeevanandam, R. S. Mulukutla, M. Phillips, S. Chaudhuri, L. E. Erickson, and K. J. Klabunde, “Near infrared reflectance properties of metal oxide particles,” J. Phys. Chem. 111, 1912-1918 (2007).
  7. B. J. Brinkworth, “Interpretation of the Kubelka-Munk coefficients in reflection theory,” Appl. Opt. 11, 1434-1435 (1972). [CrossRef] [PubMed]
  8. L. F. Gate, “Comparison of the photon diffusion model and Kubelka-Munk equation with the exact solution of the radiative transport equation,” Appl. Opt. 13, 236-238 (1974). [CrossRef] [PubMed]
  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] [PubMed]
  10. S. L. Jacques, “Reflectance spectroscopy with optical fiber devices, and transcutaneous bilirubinometers,” in Biomedical Optical Instrumentation and Laser-Assisted Biotechnology, Proceedings of the NATO Advanced Science Institute, A.M.Verga Scheggi, S.Martelluci, A.N.Chester, and R.Pratesi (Kluwer Academic, 1995).
  11. S. A. Prahl, “The adding-doubling method,” in Optical Thermal Response of Laser Irradiated Tissue, A.J.Welch and M.J. C.van Gemert, eds. (Plenum, 1995), pp. 101-129.
  12. M. A. Velazco-Roa and S. N. Thennadil, “Estimation of complex refractive index of polydisperse particulate systems from multiple-scattered ultraviolet-visible-near-infrared measurements,” Appl. Opt. 46, 3730-3735 (2007). [CrossRef] [PubMed]

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