OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 28 — Oct. 1, 2002
  • pp: 5969–5978

Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra

Fernando Curiel, William E. Vargas, and Rubén G. Barrera  »View Author Affiliations


Applied Optics, Vol. 41, Issue 28, pp. 5969-5978 (2002)
http://dx.doi.org/10.1364/AO.41.005969


View Full Text Article

Enhanced HTML    Acrobat PDF (178 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A spectral-projected gradient method and an extension of the Kubelka-Munk theory are applied to obtain the relevant parameters of the theory from measured diffuse reflectance spectra of pigmented samples illuminated with visible diffuse radiation. The initial estimate of the spectral dependence of the parameters, required by a recursive spectral-projected gradient method, was obtained by use of direct measurements and up-to-date theoretical estimates. We then tested the consistency of the Kubelka-Munk theory by repeating the procedure with samples of different thicknesses.

© 2002 Optical Society of America

OCIS Codes
(290.3200) Scattering : Inverse scattering
(290.4020) Scattering : Mie theory
(290.4210) Scattering : Multiple scattering
(290.5820) Scattering : Scattering measurements
(290.7050) Scattering : Turbid media

History
Original Manuscript: February 20, 2002
Published: October 1, 2002

Citation
Fernando Curiel, William E. Vargas, and Rubén G. Barrera, "Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra," Appl. Opt. 41, 5969-5978 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-28-5969


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. Fitzwater, J. W. Hook, “Dependent scattering theory: a new approach to predicting scattering in paints,” J. Coatings Technol. 57, 39–47 (1985).
  2. 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]
  3. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998). [CrossRef]
  4. The reflection coefficients of diffuse radiation at the interfaces are defined as the ratio of the reflected diffuse flux over the (diffuse) incident flux.
  5. C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979). [CrossRef]
  6. P. Chylek, “Light scattering by small particles in an absorbing medium,” J. Opt. Soc. Am. 67, 561–563 (1977). [CrossRef]
  7. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593–601 (1931).
  8. P. Kubelka, “New contributions to the optics of intensely light-scattering materials. Part I,” J. Opt. Soc. Am. 38, 448–457 (1948). [CrossRef] [PubMed]
  9. P. Kubelka, “New contributions to the optics of intensely light-scattering materials. Part II: Nonhomogeneous layers,” J. Opt. Soc. Am. 44, 330–335 (1954). [CrossRef]
  10. G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex-sphere suspensions and scattering powders,” Waves Random Media 5, 413–426 (1995). [CrossRef]
  11. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  12. D. G. Phillips, F. W. Billmeyer, “Predicting reflectance and color of paint films by Kubelka-Munk analysis,” J. Coatings Technol. 48, 30–36 (1976).
  13. 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]
  14. W. E. Vargas, G. A. Niklasson, “Applicability conditions of the Kubelka-Munk theory,” Appl. Opt. 36, 5580–5586 (1997). [CrossRef] [PubMed]
  15. M. W. Ribarsky, “Titanium dioxide (TiO2) (rutile),” in Handbook of Optical Constants, E. D. Palik, ed. (Academic, New York, 1985), pp. 795–804. [CrossRef]
  16. W. E. Vargas, “Light scattering and absorption in pigmented coatings,” Ph.D. dissertation (Department of Materials Science, Uppsala University, Uppsala, Sweden, 1997).
  17. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, Ontario, Canada, 1985).
  18. Another possible source of absorption is the coating of the rutile crystallites added by the manufacturers of TiO2 to help in the dispersion of the pigment as well as to prevent the pigment to react with the resin.
  19. C. F. Bohren, “Applicability of effective-medium theories to problems of scattering and absorption by inhomogeneous atmospheric particles,” J. Atmos. Sci. 43, 468–475 (1986). [CrossRef]
  20. M. Athans, M. L. Dertouzos, R. N. Spann, S. J. Mason, Systems, Networks, and Computations: Multivariable Methods (McGraw-Hill, New York, 1974), pp. 132–143.
  21. R. Fletcher, C. M. Reeves, “Function minimization by conjugate gradients,” Comput. J. 7, 149–154 (1964). [CrossRef]
  22. D. F. Shanno, “Conjugate gradient methods with inexact searches,” Math. Op. Res. 3, 244–256 (1978). [CrossRef]
  23. M. Raydan, “The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem,” SIAM J. Optim. 7, 26–33 (1997). [CrossRef]
  24. J. Barzilai, J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Anal. 8, 141–148 (1988). [CrossRef]
  25. L. Grippo, F. Lampariello, S. Lucidi, “A nonmonotone line search technique for Newton’s method,” SIAM J. Numer. Anal. 23, 707–716 (1986). [CrossRef]
  26. E. G. Birgin, J. M. Martinez, M. Raydan, “Nonmonotone spectral projected gradient methods on convex sets,” SIAM J. Optim. 10, 1196–1211 (2000). [CrossRef]
  27. E. G. Birgin, I. Chambouleyron, J. M. Martinez, “Estimation of the optical constants and the thickness of thin films using unconstrained optimization,” J. Comput. Phys. 151, 862–880 (1999). [CrossRef]
  28. W. E. Vargas, D. E. Azofeifa, N. Clark, “Retrieved optical properties of thin films on absorbing substrates from transmittance measurements” (submitted to Thin Solid Films).
  29. M. Quinten, J. Rostalski, “Lorenz-Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996). [CrossRef]
  30. W. E. Vargas, “Two-flux radiative transfer model under nonisotropic propagating diffuse radiation,” Appl. Opt. 38, 1077–1085 (1999). [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