OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 43, Iss. 12 — Apr. 20, 2004
  • pp: 2580–2587

Special visual effect of art glazes explained by the radiative transfer equation

Lionel Simonot, Mady Elias, and Eric Charron  »View Author Affiliations

Applied Optics, Vol. 43, Issue 12, pp. 2580-2587 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (309 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present the first modeling of the light scattered by a paint layer in a bidirectional configuration. The studied medium is composed of small concentrated pigments embedded in an oil binder. The color is modulated by changing the number of paint layers, called glazes. The radiative transfer equation is established for incoherent light scattered by the pigments with use of a collimated illumination. The equation is solved by use of the auxiliary function method. This new method, applied here for the first time to a practical case, allows for exact computations of the scattered flux for any incident and collected directions. Spectroscopic and goniometric measurements are implemented in bidirectional and backscattered configurations. The excellent agreement between the measurement and the simulation validates the assumptions used for the glaze model and proves the effectiveness of the auxiliary function method.

© 2004 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(290.4210) Scattering : Multiple scattering
(290.5820) Scattering : Scattering measurements
(300.6550) Spectroscopy : Spectroscopy, visible

Original Manuscript: August 5, 2003
Revised Manuscript: January 2, 2004
Published: April 20, 2004

Lionel Simonot, Mady Elias, and Eric Charron, "Special visual effect of art glazes explained by the radiative transfer equation," Appl. Opt. 43, 2580-2587 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. Panofski, Les Primitifs Flamands (Hazan, Paris, 1992).
  2. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  3. B. Maheu, N. Letouzan, 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]
  4. W. E. Vargas, “Generalized four-flux radiative transfer model,” Appl. Opt. 37, 2615–2623 (1998). [CrossRef]
  5. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  6. P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology,” Appl. Opt. 10, 1485–1502 (1971). [CrossRef] [PubMed]
  7. K. Stamnes, S.-C. Tsay, W. Wiscombe, K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layer media,” Appl. Opt. 27, 2502–2510 (1988). [CrossRef] [PubMed]
  8. M. Elias, G. Elias, “New and fast calculation for incoherent multiple scattering,” J. Opt. Soc. Am. A 19, 894–905 (2002). [CrossRef]
  9. A. da Silva, M. Elias, C. Andraud, J. Lafait, “Comparison between the auxiliary function method and the discrete-ordinate-method for solving the radiative transfer equation for light scattering,” J. Opt. Soc. Am. A 20, 2321–2329 (2003). [CrossRef]
  10. M. Elias, G. Elias, “Radiative transfer in inhomogeneous stratified media using the auxiliary function method,” J. Opt. Soc. Am. A 21, 580–589 (2004). [CrossRef]
  11. L. Simonot, A. Zobelli, M. Elias, J. Salomon, J. C. Dran, “Pigment distribution in art glazes,” J. Trace Microprobe Tech. 21, 35–48 (2003). [CrossRef]
  12. A. da Silva, C. Andraud, E. Charron, B. Stout, J. Lafait, “Multiple light scattering in multilayered media: theory, experiments,” J. Mod. Phys. 51, 313–332 (2004).
  13. M. Elias, M. Menu, “Characterisation of surface states on patrimonial works of art,” Surf. Eng. 17, 225–229 (2001). [CrossRef]
  14. E. R. De La Rie, “The influence of varnishes on the appearance of paintings,” Stud. Conserv. 32, 1–13 (1987). [CrossRef]
  15. R. Molenaar, J. J. ten Bosch, J. R. Zijp, “Determination of Kubelka-Munk scattering and absorption coefficients by diffuse illumination,” Appl. Opt. 38, 2068–2077 (1999). [CrossRef]
  16. M. Elias, L. Simonot, “Bi-directional reflectance of a varnished painting. Part 1: influence of the refractive indices without using the approximations of Saunderson correction—exact computation,” Opt. Commun. 231, 17–24 (2004). [CrossRef]
  17. M. Elias, M. Menu, “Experimental characterization of a random metallic rough surface by spectrophometric measurements in the visible range,” Opt. Commun. 180, 191–198 (2000). [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