OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 9 — Jul. 6, 2010

Anisotropic reflectance from turbid media. II. Measurements

Magnus Neuman and Per Edström  »View Author Affiliations

JOSA A, Vol. 27, Issue 5, pp. 1040-1045 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (243 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The anisotropic reflectance from turbid media predicted using the radiative transfer based DORT2002 model is experimentally verified through goniophotometric measurements. A set of paper samples with varying amounts of dye and thickness is prepared, and their angle resolved reflectance is measured. An alleged perfect diffusor is also included. The corresponding simulations are performed. A complete agreement between the measurements and model predictions is seen regarding the characteristics of the anisotropy. They show that relatively more light is reflected at large polar angles when the absorption or illumination angle is increased or when the medium thickness is decreased. This is due to the relative amount of near-surface bulk scattering increasing in these cases. This affects the application of the Kubelka–Munk model as well as standards for reflectance measurements and calibration routines.

© 2010 Optical Society of America

OCIS Codes
(290.4210) Scattering : Multiple scattering
(290.5820) Scattering : Scattering measurements
(290.7050) Scattering : Turbid media
(290.1483) Scattering : BSDF, BRDF, and BTDF

ToC Category:

Original Manuscript: October 19, 2009
Revised Manuscript: February 16, 2010
Manuscript Accepted: February 22, 2010
Published: April 13, 2010

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

Magnus Neuman and Per Edström, "Anisotropic reflectance from turbid media. II. Measurements," J. Opt. Soc. Am. A 27, 1040-1045 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J.  21, 1–22 (1905). [CrossRef]
  2. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  3. P. Kubelka and F. Munk, “Ein beitrag zur optik der farbanstriche,” Z. Tech. Phys.  11a, 593–601 (1931).
  4. P. Kubelka, “New contributions to the optics of intensely light scattering materials. Part I,” J. Opt. Soc. Am.  38, 330–335 (1948).
  5. P. Kubelka, “New contributions to the optics of intensely light scattering materials. Part II,” J. Opt. Soc. Am.  44, 448–457 (1954). [CrossRef]
  6. K. Stamnes, S.-C. Tsay, and I. Laszlo, “DISORT, a general-purpose fortran program for discrete-ordinate-method radiative transfer in scattering and emitting layered media,” (Goddard Space Flight Center, NASA, 2000).
  7. P. Edström, “A fast and stable solution method for the radiative transfer problem,” SIAM Rev.  47, 447–468 (2005). [CrossRef]
  8. J. H. Nobbs, “Kubelka-Munk theory and the prediction of reflectance,” Rev. Prog. Coloration  15, 66–75 (1985). [CrossRef]
  9. M. J. Leskelä, “Optical calculations for multilayer papers,” TAPPI  78, 167–172 (1995).
  10. P. Latimer and S. J. Noh, “Light propagation in moderately dense particle systems: a reexamination of the Kubelka-Munk theory,” Appl. Opt.  26, 514–523 (1987). [CrossRef] [PubMed]
  11. P. Edström, “Comparison of the DORT2002 radiative transfer solution method and the Kubelka-Munk model,” Nord. Pulp Pap. Res. J.  19, 397–403 (2004). [CrossRef]
  12. M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. I. Theory,” J. Opt. Soc. Am. A  27, 1032–1039 (2010). [CrossRef]
  13. J. A. van den Akker, “Scattering and absorption of light in paper and other diffusing media,” TAPPI  32, 498–501 (1949).
  14. ISO 11664-1:2008(E)/CIE S 014-1/E:2006: Colorimetry—Part 1: CIE Standard Colorimetric Observers (Commission Internationale de l’Eclairage, 2008).
  15. H. Granberg and P. Edström, “Quantification of the intrinsic error of the Kubelka-Munk model caused by strong light absorption,” J. Pulp Pap. Sci.  29, 386–390 (2003).
  16. P. Edström, “A two-phase parameter estimation method for radiative transfer problems in paper industry applications,” J. Comput. Appl. Math.  16, 927–951 (2008).
  17. P. Edström, “Examination of the revised Kubelka-Munk theory: considerations of modeling strategies,” J. Opt. Soc. Am. A  24, 548–556 (2007). [CrossRef]
  18. P. Edström, “Numerical performance of stability enhancing and speed increasing steps in radiative transfer solution methods,” J. Comput. Appl. Math.  228, 104–114 (2009). [CrossRef]
  19. ISO 2469: Paper, Board and Pulps—Measurement of Diffuse Reflectance Factor (International Organization for Standardization, 1994).
  20. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J.  93, 70–83 (1941). [CrossRef]
  21. H. Granberg and M.-C. Béland, “Modelling the angle-dependent light scattering from sheets of pulp fibre fragments,” Nord. Pulp Pap. Res. J.  19, 54–359 (2004). [CrossRef]
  22. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Lamperis, “Geometrical considerations and nomenclature for reflectance” (National Bureau of Standards, 1977).
  23. ISO 9416: Paper—Determination of Light Scattering and Absorption Coefficients (Using Kubelka-Munk Theory) (International Organization for Standardization, 1998). [PubMed]
  24. DIN 5033-4: Colorimetry; Spectrophotometric Method (Deutsches Institut Für Normung E. V., 1992). [PubMed]
  25. P. Edström, M. Neuman, S. Avramidis, and M. Andersson, “Geometry related inter-instrument differences in spectrophotometric measurements,” Nord. Pulp Pap. Res. J. (to be published).

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 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited