OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 36, Iss. 22 — Aug. 1, 1997
  • pp: 5580–5586

Applicability conditions of the Kubelka–Munk theory

William E. Vargas and Gunnar A. Niklasson  »View Author Affiliations


Applied Optics, Vol. 36, Issue 22, pp. 5580-5586 (1997)
http://dx.doi.org/10.1364/AO.36.005580


View Full Text Article

Enhanced HTML    Acrobat PDF (274 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The description of optical properties of light-scattering materials has made extensive use of radiative transfer models. One of the most successful and simplest models is that of Kubelka and Munk (KM). With this model, optical properties of particulate films under diffuse illumination can be predicted from effective absorption and scattering coefficients of the material. We consider the applicability conditions of this kind of model. An extended KM model for the case of perpendicular collimated illumination is compared with results from a more general four-flux approach, and the differences between them are characterized in terms of a correction factor that depends on particle scattering and absorption, concentration of the scatterers, and film thickness. It is proved formally that the extended KM model under perpendicular illumination is a good approximation for the cases of optically thick films that contain weakly or nonabsorbing particles.

© 1997 Optical Society of America

History
Original Manuscript: November 13, 1996
Revised Manuscript: February 24, 1997
Published: August 1, 1997

Citation
William E. Vargas and Gunnar A. Niklasson, "Applicability conditions of the Kubelka–Munk theory," Appl. Opt. 36, 5580-5586 (1997)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-36-22-5580


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  2. P. Kubelka, “New contributions to the optics of intensely scattering materials. Part I,” J. Opt. Soc. Am. 38, 448–457 (1948). [CrossRef] [PubMed]
  3. D. C. Rich, “Computer-aided design and manufacturing of the color of decorative and protective coatings,” J. Coating Technol. 67, 53–60 (1995).
  4. A. B. Krewinghaus, “Infrared reflectance of paints,” Appl. Opt. 8, 807–812 (1969). [CrossRef] [PubMed]
  5. C. Rennel, M. Rigdahl, “Enhancement of the light-scattering ability of coatings by using hollow pigments,” Colloid Polym. Sci. 272, 1111–1117 (1994). [CrossRef]
  6. M. M. Beppu, E. C. de Oliveira Lima, F. Galembeck, “Aluminum phosphate particles containing closed pores: preparation, characterization, and use as a white pigment,” J. Colloid Interface Sci. 178, 93–103 (1996). [CrossRef]
  7. F. Thiébaud, F. K. Kneubuühl, “Infrared properties of quartz fibers and wool,” Infrared Phys. 23, 131–148 (1983). [CrossRef]
  8. J. Kuhn, S. Korder, M. C. Arduini-Schuster, R. Caps, J. Fricke, “Infrared-optical transmission and reflection measurements on loose powders,” Rev. Sci. Instrum. 64, 2523–2530 (1993). [CrossRef]
  9. N. Yamada, S. Fujimura, “Nondestructive measurement of chlorophyll pigment content in plant leaves from three-color reflectance and transmittance,” Appl. Opt. 30, 3964–3973 (1991). [CrossRef] [PubMed]
  10. L. Fukshansky, N. Fukshansky-Kazarinova, A. M. Remi-sowsky, “Estimation of optical parameters in a living tissue by solving the inverse problem of the multiflux radiative transfer,” Appl. Opt. 30, 3145–3153 (1991). [CrossRef] [PubMed]
  11. R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13–19 (1981). [CrossRef] [PubMed]
  12. J. D. Lindberg, R. E. Douglass, D. M. Garvey, “Absorption-coefficient-determination method for particulate materials,” Appl. Opt. 33, 4314–4319 (1994). [CrossRef] [PubMed]
  13. P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology II,” J. Colloid Interface Sci. 39, 551–567 (1972). [CrossRef]
  14. D. G. Phillips, F. W. Billmeyer, “Predicting reflectance and color of paint films by Kubelka-Munk analysis,” J. Coating Technol. 48, 30–36 (1976).
  15. L. F. Gate, “The determination of light absorption in diffusing materials by a photon diffusion model,” J. Phys. D 4, 1049–1056 (1971). [CrossRef]
  16. W. R. Blevin, W. J. Brown, “Total reflectance of opaque diffusers,” J. Opt. Soc. Am. 52, 1250–1255 (1962). [CrossRef]
  17. M. K. Gunde, J. K. Logar, Z. C. Orel, B. Orel, “Application of the Kubelka-Munk theory to thickness-dependent diffuse reflectance of black paints in the mid-IR,” Appl. Spectrosc. 49, 623–629 (1995). [CrossRef]
  18. B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-flux models to solve the scattering transfer equation in terms of Lorenz-Mie parameters,” Appl. Opt. 23, 3353–3362 (1984). [CrossRef] [PubMed]
  19. G. A. Niklasson, “Comparison between four-flux theory and multiple scattering theory,” Appl. Opt. 26, 4034–4036 (1987). [CrossRef] [PubMed]
  20. B. Maheu, J. P. Briton, G. Gouesbet, “Four-flux model and a Monte Carlo code: comparisons between two simple, complementary tools for multiple scattering calculations,” Appl. Opt. 28, 22–24 (1989). [CrossRef] [PubMed]
  21. J. P. Briton, B. Maheu, G. Gréhan, G. Gouesbet, “Monte Carlo simulations of multiple scattering in arbitrary 3-D geometry,” Part. Part. Syst. Charact. 9, 52–58 (1992). [CrossRef]
  22. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), pp. 191–196. [CrossRef]
  23. J. L. Saunderson, “Calculation of the color of pigmented plastics,” J. Opt. Soc. Am. 32, 727–736 (1942). [CrossRef]
  24. W. Theiss “wind: A radiation transfer program for simulating optical spectra of light scattering materials,” in Electromagnetic and Light Scattering: Theory and Applications, T. Wriedt, M. Quinten, K. Bauckhage, eds. (Universität Bremen, Bremen, Germany, 1996), pp. 79–82.
  25. P. Chylek, “Mie scattering into the backward hemisphere,” J. Opt. Soc. Am. 63, 1467–1471 (1973). [CrossRef]
  26. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 82–129.
  27. Y. P. Wang, Z. S. Wu, K. F. Ren, “Four-flux model with adjusted average crossing parameter to solve the scattering transfer equation,” Appl. Opt. 28, 24–26 (1989). [CrossRef] [PubMed]
  28. A. Ben-David, “Multiple-scattering transmission and an effective average photon path length of a plane–parallel beam in a homogeneous medium,” Appl. Opt. 34, 2802–2810 (1995). [CrossRef] [PubMed]
  29. W. E. Vargas, G. A. Niklasson “Forward average path-length parameter in four-flux radiative transfer models,” Appl. Opt. 36, 3735–3738 (1997). [CrossRef] [PubMed]
  30. W. E. Vargas, G. A. Niklasson, “Generalized method for evaluating scattering parameters used in radiative transfer models,” J. Opt. Soc. Am. A 14 (September1997). [CrossRef]
  31. B. Maheu, G. Gouesbet, “Four-flux models to solve the scattering transfer equation: special cases,” Appl. Opt. 25, 1122–1128 (1986). [CrossRef] [PubMed]
  32. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 281.
  33. D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. 29, 329–332 (1942). [CrossRef]
  34. C. F. Bohren, “Applicability of effective-medium theories to problems of scattering and absorption by nonhomogeneous atmospheric particles,” J. Atmos. Sci. 43, 468–475 (1986). [CrossRef]
  35. J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904). [CrossRef]
  36. G. A. Niklasson, T. S. Eriksson, “Radiative cooling with pigmented polyethylene foils,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion VII, C. Granqvist, C. M. Lampert, eds., Proc. SPIE1016, 89–99 (1988). [CrossRef]
  37. T. M. J. Nilsson, G. A. Niklasson, “Optimization of optical properties of pigmented foils for radiative cooling applications: model calculations,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion X, C. G. Granqvist, C. M. Lampert, eds., Proc. SPIE1536, 169–182 (1991). [CrossRef]
  38. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 151.
  39. M. K. Gunde, J. K. Logar, Z. C. Orel, B. Orel, “Optimum thickness determination to maximize the spectral selectivity of black pigmented coatings for solar collectors,” Thin Solid Films 277, 185–191 (1996). [CrossRef]
  40. N. P. Ryde, E. Matijevic, “Color effects of uniform colloidal particles of different morphologies packed into films,” Appl. Opt. 33, 7275–7281 (1994). [CrossRef] [PubMed]

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited