Abstract

The fundamental assumptions made in the revised Kubelka–Munk (KM) model of light propagation in scattering and absorptive media, recently proposed [J. Opt. Soc. Am. A 21, 1942 (2004); 22, 866 (2005) ], are critically reviewed and analyzed. The authors argue that the model, now questioned by Edström [J. Opt. Soc. Am. A 24, 548 (2007) ] is well founded on physical grounds and consistent with the original KM model, which has been the cornerstone of light propagation studies and utilized for more than half a century.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Yang and B. Kruse, "Revised Kubelka-Munk theory. I. Theory and applications," J. Opt. Soc. Am. A 21, 1933-1941 (2004).
    [CrossRef]
  2. 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]
  3. L. Yang and S. J. Miklavcic, "Theory of light propagation incorporating scattering and absorption in turbid media," Opt. Lett. 30, 792-794 (2005).
    [CrossRef] [PubMed]
  4. 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]
  5. P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).
  6. P. Kubelka, "New contributions to the optics of intensely light-scattering materials. Part I," J. Opt. Soc. Am. 38, 448-457 (1948).
    [CrossRef] [PubMed]
  7. P. Edström, "Examination of the revised Kubelka-Munk theory: considerations of modeling strategies," J. Opt. Soc. Am. A 24, 548-556 (2007).
    [CrossRef]
  8. W. Wendlandt and H. Hecht, Reflectance Spectroscopy (Wiley Interscience, 1966), Chap. 3.
  9. G. K. Bachelor, Introduction to Fluid Mechanics (Cambridge U. Press, 1967), Chap. 1.
  10. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  11. W. J. Foote, "An investigation of the fundamental scattering and absorption coefficients of dyes handsheets," Pap. Trade J. 109, 333-340 (1939).
  12. J. A. Van der Akker, "Scattering and absorption of light in paper and other diffusing media," Tappi J. 32, 498-501 (1949).
  13. T. Shakespeare and J. Shakespeare, "A fluorescent extension to the Kubelka-Munk model," Color Res. Appl. 28, 4-14 (2003).
    [CrossRef]

2007 (1)

2005 (2)

2004 (2)

2003 (1)

T. Shakespeare and J. Shakespeare, "A fluorescent extension to the Kubelka-Munk model," Color Res. Appl. 28, 4-14 (2003).
[CrossRef]

1949 (1)

J. A. Van der Akker, "Scattering and absorption of light in paper and other diffusing media," Tappi J. 32, 498-501 (1949).

1948 (1)

1939 (1)

W. J. Foote, "An investigation of the fundamental scattering and absorption coefficients of dyes handsheets," Pap. Trade J. 109, 333-340 (1939).

1931 (1)

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Bachelor, G. K.

G. K. Bachelor, Introduction to Fluid Mechanics (Cambridge U. Press, 1967), Chap. 1.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Edström, P.

Foote, W. J.

W. J. Foote, "An investigation of the fundamental scattering and absorption coefficients of dyes handsheets," Pap. Trade J. 109, 333-340 (1939).

Hecht, H.

W. Wendlandt and H. Hecht, Reflectance Spectroscopy (Wiley Interscience, 1966), Chap. 3.

Kruse, B.

Kubelka, P.

P. Kubelka, "New contributions to the optics of intensely light-scattering materials. Part I," J. Opt. Soc. Am. 38, 448-457 (1948).
[CrossRef] [PubMed]

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Miklavcic, S. J.

Munk, F.

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Shakespeare, J.

T. Shakespeare and J. Shakespeare, "A fluorescent extension to the Kubelka-Munk model," Color Res. Appl. 28, 4-14 (2003).
[CrossRef]

Shakespeare, T.

T. Shakespeare and J. Shakespeare, "A fluorescent extension to the Kubelka-Munk model," Color Res. Appl. 28, 4-14 (2003).
[CrossRef]

Van der Akker, J. A.

J. A. Van der Akker, "Scattering and absorption of light in paper and other diffusing media," Tappi J. 32, 498-501 (1949).

Wendlandt, W.

W. Wendlandt and H. Hecht, Reflectance Spectroscopy (Wiley Interscience, 1966), Chap. 3.

Yang, L.

Color Res. Appl. (1)

T. Shakespeare and J. Shakespeare, "A fluorescent extension to the Kubelka-Munk model," Color Res. Appl. 28, 4-14 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Lett. (1)

Pap. Trade J. (1)

W. J. Foote, "An investigation of the fundamental scattering and absorption coefficients of dyes handsheets," Pap. Trade J. 109, 333-340 (1939).

Tappi J. (1)

J. A. Van der Akker, "Scattering and absorption of light in paper and other diffusing media," Tappi J. 32, 498-501 (1949).

Z. Tech. Phys. (Leipzig) (1)

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Other (3)

W. Wendlandt and H. Hecht, Reflectance Spectroscopy (Wiley Interscience, 1966), Chap. 3.

G. K. Bachelor, Introduction to Fluid Mechanics (Cambridge U. Press, 1967), Chap. 1.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Schematic illustration of the dependence of the KM absorption coefficient K on light scattering. (a) Scattering medium, (b) nonscattering medium.

Fig. 2
Fig. 2

Illustration of the effect of light scattering on path length.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

d I = ( K + S ) I d z + S J d z ,
d J = ( K + S ) J d z S I d z .
K = 2 a , S = s .
K = α μ a , S = α μ s 2 .
μ = α s D ,
D = 1 A 1 2 A w p exp ( A w p ) exp ( 2 A w p ) 1 2 exp ( A w p ) + exp ( 2 A w p ) ,
A = ( K 2 + 2 K S ) 1 2 ,
μ = Δ l Δ r .
μ = lim Δ z 0 μ = d l d r ,

Metrics