OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 8 — Aug. 1, 2008
  • pp: 2066–2077

Spectral prediction model for piles of nonscattering sheets

Mathieu Hébert, Roger D. Hersch, and Lionel Simonot  »View Author Affiliations

JOSA A, Vol. 25, Issue 8, pp. 2066-2077 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (1051 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The present paper investigates the reflection and transmission properties of piles of nonscattering sheets. Using a spectral prediction model, we perform a detailed analysis of the spectral and color variations induced by variations of the number of superposed sheets, the absorbance of the sheet material, the refractive index of the medium between the sheets, and the reflectance of the background. The spectral prediction model accounts for the multiple reflections and transmissions of light between the interfaces bounding the layers. We describe in detail the procedure for deducing model parameters from measured data. Tests performed with nonscattering plastic sheets demonstrate the excellent accuracy of the predictions. A large set of predicted spectra illustrate the different evolutions of reflected and transmitted spectra as well as the corresponding colors for various types of piles.

© 2008 Optical Society of America

OCIS Codes
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.7000) Instrumentation, measurement, and metrology : Transmission
(230.4170) Optical devices : Multilayers
(300.6170) Spectroscopy : Spectra
(300.6550) Spectroscopy : Spectroscopy, visible

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: March 21, 2008
Revised Manuscript: June 13, 2008
Manuscript Accepted: June 16, 2008
Published: July 22, 2008

Mathieu Hébert, Roger D. Hersch, and Lionel Simonot, "Spectral prediction model for piles of nonscattering sheets," J. Opt. Soc. Am. A 25, 2066-2077 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. L. Saunderson, “Calculation of the color pigmented plastics,” J. Opt. Soc. Am. 32, 727-736 (1942). [CrossRef]
  2. P. Kubelka, “New contributions to the optics of intensely light-scattering material, part I,” J. Opt. Soc. Am. 38, 448-457 (1948). [CrossRef] [PubMed]
  3. F. C. Williams and F. R. Clapper, “Multiple internal reflections in photographic color prints,” J. Opt. Soc. Am. 29, 595-599 (1953). [CrossRef]
  4. J. D. Shore and J. P. Spoonhower, “Reflection density in photographic color prints: Generalizations of the Williams-Clapper transform,” J. Imaging Sci. Technol. 45, 484-488 (2001).
  5. F. R. Clapper and J. A. C. Yule, “The effect of multiple internal reflections on the densities of halftone prints on paper,” J. Opt. Soc. Am. 43, 600-603 (1953). [CrossRef]
  6. M. Hébert and R. D. Hersch, “Deducing ink-transmittance spectra from reflectance and transmittance measurements of prints,” Proc. SPIE 6493, 649314-1-13 (2007).
  7. L. Simonot, M. Hébert, and R. D. Hersch, “Extension of the Williams-Clapper model to stacked nondiffusing colored coatings with different refractive indices,” J. Opt. Soc. Am. A 23, 1432-1441 (2006). [CrossRef]
  8. H.-H. Perkampus, Encyclopedia of Spectroscopy (VCH, 1995).
  9. M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).
  10. W. R. McCluney, Introduction to Radiometry and Photometry (Artech House, 1994).
  11. M. Hébert and R. D. Hersch, “Classical print reflection models: A radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).
  12. G. Sharma, “Color fundamentals for digital imaging,” in Digital Color Imaging Handbook, G. Sharma, ed. (CRC Press, 2003), pp. 30-36.
  13. M. Hébert and J.-M. Becker, “Correspondence between continuous and discrete 2 flux models for reflectance and transmittance of diffusing layers,” J. Opt. A, Pure Appl. Opt. 10, 035006 (2008). [CrossRef]
  14. 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]
  15. M. Hébert, R. Hersch, and J.-M. Becker, “Compositional reflectance and transmittance model for multilayer specimens,” J. Opt. Soc. Am. A 24, 2628-2644 (2007). [CrossRef]
  16. D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).
  17. M. Elias and L. Simonot, “Separation between the different fluxes scattered by art glazes: Explanation of the special color saturation,” Appl. Opt. 45, 3163-3172 (2006). [CrossRef] [PubMed]
  18. L. Simonot, M. Elias, and E. Charron, “Special visual effect of art-glazes explained by the radiative transfer equation,” Appl. Opt. 43, 2580-2587 (2004). [CrossRef] [PubMed]
  19. M. Hébert and R. D. Hersch, “A reflectance and transmittance model for recto-verso halftone prints,” J. Opt. Soc. Am. A 22, 1952-1967 (2006). [CrossRef]
  20. M. Hébert, “Compositional model for predicting multilayer reflectances and transmittances in color reproduction,” Ph.D. dissertation (Ecole Polytchnique Fédérale de Lausanne, 2006), p. 139.

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