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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 8 — Aug. 1, 2012
  • pp: 1537–1548

Spectral reflectance and transmittance prediction model for stacked transparency and paper both printed with halftone colors

Jacques Machizaud and Mathieu Hébert  »View Author Affiliations

JOSA A, Vol. 29, Issue 8, pp. 1537-1548 (2012)

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When a transparency printed with a first halftone color is deposited on top of a paper printed with a second halftone color, we obtain a third color that we are able to predict in both reflectance and transmittance modes, thanks to a spectral prediction model. The model accounts for the multiple reflections of light between the printed paper and the printed transparency, which are themselves described by specific reflectance and transmittance models, each one being calibrated using a small number of printed colors. The model can account for light scattering by the inks. The measuring geometry and the orientations of light in the transparency are taken into account on the basis of radiometric rules and geometrical optical laws. Experimental testing carried out from several inkjet-printed CMY halftones shows fairly good agreement between predictions and measurements.

© 2012 Optical Society of America

OCIS Codes
(100.2810) Image processing : Halftone image reproduction
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.7000) Instrumentation, measurement, and metrology : Transmission

ToC Category:
Image Processing

Original Manuscript: November 22, 2011
Revised Manuscript: May 24, 2012
Manuscript Accepted: May 25, 2012
Published: July 12, 2012

Jacques Machizaud and Mathieu Hébert, "Spectral reflectance and transmittance prediction model for stacked transparency and paper both printed with halftone colors," J. Opt. Soc. Am. A 29, 1537-1548 (2012)

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  1. R. D. Hersch and F. Crété, “Improving the Yule–Nielsen modified spectral Neugebauer model by dot surface coverages depending on the ink superposition conditions,” Proc. SPIE 5667, 434–447 (2005). [CrossRef]
  2. J. A. S. Viggiano, “Modeling the color of multi-colored halftones,” in Proceedings of the Technical Association of the Graphic Arts (TAGA, 1990), pp. 44–62.
  3. F. Clapper and J. Yule, “The effect of multiple internal reflections on the densities of halftones prints on paper,” J. Opt. Soc. Am. 43, 600–603 (1953). [CrossRef]
  4. F. C. Williams and F. R. Clapper, “Multiple internal reflections in photographic color prints,” J. Opt. Soc. Am. 43, 595–597 (1953). [CrossRef]
  5. M. Hébert and R. D. Hersch, “Reflectance and transmittance model for recto-verso halftone prints,” J. Opt. Soc. Am. A 23, 2415–2432 (2006). [CrossRef]
  6. M. Hébert and R. D. Hersch, “Reflectance and transmittance model for recto-verso halftone prints: spectral predictions with multi-ink halftones,” J. Opt. Soc. Am. A 26, 356–364 (2009). [CrossRef]
  7. M. Hébert and R. D. Hersch, “Yule–Nielsen based recto-verso color halftone transmittance prediction model,” Appl. Opt. 50, 519–525 (2011). [CrossRef]
  8. M. Hébert and R. D. Hersch, “Deducing ink-transmittance spectra from reflectance and transmittance measurements of prints,” Proc. SPIE 6493, 649314 (2007). [CrossRef]
  9. M. Hébert, R. D. Hersch, and J. Becker, “Compositional reflectance and transmittance model for multilayer specimens,” J. Opt. Soc. Am. A 24, 2628–2644 (2007). [CrossRef]
  10. M. Hébert, R. D. Hersch, and L. Simonot, “Spectral prediction model for piles of nonscattering sheets,” J. Opt. Soc. Am. A 25, 2066–2077 (2008). [CrossRef]
  11. F. R. Ruckdeschel and O. G. Hauser, “Yule–Nielsen effect in printing: a physical analysis,” Appl. Opt. 17, 3376–3383 (1978). [CrossRef]
  12. P. Emmel, I. Amidror, V. Ostromoukhov, and R. D. Hersch, “Predicting the spectral behaviour of colour printers for transparent inks on transparent support,” in Proceedings of IS&T/SID 96, Color Imaging Conference (Society for Imaging Science, 1996), pp. 86–91.
  13. J. McElvain, J. Miller, and E. Jin, “Spectral printer modeling for transparency media: toward high dynamic range scene reproduction,” Proc. SPIE 7241, 72410U (2009). [CrossRef]
  14. I. Amidror, The Theory of the Moiré Phenomenon: Periodic Layers, 2nd ed. (Springer, 2009).
  15. V. Ostromoukhov and R. D. Hersch, “Stochastic clustered-dot dithering,” J. Electron. Imag. 8, 439–445 (1999).
  16. M. Qi, C. Yang, C. Tu, X. Meng, and Y. Sun, “A GPU-based algorithm for building stochastic clustered-dot screens,” Adv. Vis. Comput. 4841, 98–105 (2007). [CrossRef]
  17. J. Stover, Optical Scattering: Measurement and Analysis (SPIE Press, 1995).
  18. F. Nicodemus, J. Richmond, J. Hsia, I. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (U.S. Dept. of Commerce, 1977).
  19. M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
  20. CIE, Colorimetry CIE Technical Report, 3rd ed. (CIE, 1998).
  21. H.-H. Perkampus, Encyclopedia of Spectroscopy (VCH, 1995).
  22. 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]
  23. I. Amidror and R. D. Hersch, “Neugebauer and Demichel: dependence and independence in n-screen superpositions for colour printing,” Color Res. Appl. 25, 267–277 (2000). [CrossRef]
  24. J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of the Technical Association of the Graphic Arts, Vol. 3 (TAGA, 1951), pp. 65–76.
  25. T. Bugnon and R. D. Hersch, “Constrained acquisition of ink spreading curves from printed color images,” IEEE Trans. Image Process. 20, 513–522 (2011). [CrossRef]
  26. A. Glassner, Principles of Digital Image Synthesis, Vol. 2 (Kaufmann, 1995).
  27. G. Sharma, Digital Color Imaging Handbook (CRC Press, 2003), pp. 30–36.

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