Abstract

The transmittance spectrum of halftone prints on paper is predicted thanks to a model inspired by the Yule–Nielsen modified spectral Neugebauer model used for reflectance predictions. This model is well adapted for strongly scattering printing supports and applicable to recto–verso prints. Model parameters are obtained by a few transmittance measurements of calibration patches printed on one side of the paper. The model was verified with recto–verso specimens printed by inkjet with classical and custom inks, at different halftone frequencies and on various types of paper. Predictions are as accurate as those obtained with a previously developed reflectance and transmittance prediction model relying on the multiple reflections of light between the paper and the print–air interfaces. Optimal n values are smaller in transmission mode compared with the reflection model. This indicates a smaller amount of lateral light propagation in the transmission mode.

© 2011 Optical Society of America

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References

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  1. R. D. Hersch and M. Hébert, “Interaction between light, paper and color halftones: challenges and modelization approaches,” in Proceedings of the Third European Conference on Color in Graphics, Imaging and Vision (CGIV) (Society for Imaging Science and Technology, 2006), pp. 1–7.
  2. J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proc. TAGA 3, 65–76 (1951).
  3. J. A. S. Viggiano, “The color of halftone tints,” Proc. TAGA 37, 647–661 (1985).
  4. 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]
  5. R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 033001 (2005).
    [CrossRef]
  6. 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]
  7. 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]
  8. F. C. Williams and F. R. Clapper, “Multiple internal reflections in photographic color prints,” J. Opt. Soc. Am. 43, 595–597(1953).
    [CrossRef] [PubMed]
  9. 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, 434–445 (2005).
    [CrossRef]
  10. M. Hébert and R. D. Hersch, “Yule–Nielsen approach for predicting the spectral transmittance of halftone prints,” in Proceedings of the IS&T/SID 17th Conference on Color Imaging (Society for Imaging Science and Technology, 2009), pp. 155–158.
  11. P. Kubelka, “New contributions to the optics of intensely light-scattering materials. Part II: Nonhomogeneous layers,” J. Opt. Soc. Am. 44, 330–334 (1954).
    [CrossRef]
  12. 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]
  13. M. E. Demichel, Procédés 26, 17–21 (1924).
  14. H. E. J. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbendrucks,” Zeitschrift fuer wissenschaftliche Photographie 36, 36–73 (1937) [“The theoretical basis of multicolour letterpress printing,” Color Res. Appl. 30, 322–331 (2005) (in English)].
    [CrossRef]
  15. F. R. Ruckdeschel and O. G. Hauser, “Yule–Nielsen effect in printing: a physical analysis,” Appl. Opt. 17, 3376–3383(1978).
    [CrossRef] [PubMed]
  16. G. Sharma, Digital Color Imaging Handbook (CRC Press, 2003), pp. 30–36.

2009 (1)

2007 (1)

2006 (1)

2005 (2)

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 033001 (2005).
[CrossRef]

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, 434–445 (2005).
[CrossRef]

1985 (1)

J. A. S. Viggiano, “The color of halftone tints,” Proc. TAGA 37, 647–661 (1985).

1978 (1)

1954 (1)

1953 (2)

1951 (1)

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proc. TAGA 3, 65–76 (1951).

1937 (1)

H. E. J. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbendrucks,” Zeitschrift fuer wissenschaftliche Photographie 36, 36–73 (1937) [“The theoretical basis of multicolour letterpress printing,” Color Res. Appl. 30, 322–331 (2005) (in English)].
[CrossRef]

1924 (1)

M. E. Demichel, Procédés 26, 17–21 (1924).

Becker, J. -M.

Clapper, F. R.

Collaud, F.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 033001 (2005).
[CrossRef]

Crété, F.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 033001 (2005).
[CrossRef]

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, 434–445 (2005).
[CrossRef]

Demichel, M. E.

M. E. Demichel, Procédés 26, 17–21 (1924).

Emmel, P.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 033001 (2005).
[CrossRef]

Hauser, O. G.

Hébert, M.

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]

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]

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]

M. Hébert and R. D. Hersch, “Yule–Nielsen approach for predicting the spectral transmittance of halftone prints,” in Proceedings of the IS&T/SID 17th Conference on Color Imaging (Society for Imaging Science and Technology, 2009), pp. 155–158.

R. D. Hersch and M. Hébert, “Interaction between light, paper and color halftones: challenges and modelization approaches,” in Proceedings of the Third European Conference on Color in Graphics, Imaging and Vision (CGIV) (Society for Imaging Science and Technology, 2006), pp. 1–7.

Hersch, R.

Hersch, R. D.

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]

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]

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, 434–445 (2005).
[CrossRef]

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 033001 (2005).
[CrossRef]

M. Hébert and R. D. Hersch, “Yule–Nielsen approach for predicting the spectral transmittance of halftone prints,” in Proceedings of the IS&T/SID 17th Conference on Color Imaging (Society for Imaging Science and Technology, 2009), pp. 155–158.

R. D. Hersch and M. Hébert, “Interaction between light, paper and color halftones: challenges and modelization approaches,” in Proceedings of the Third European Conference on Color in Graphics, Imaging and Vision (CGIV) (Society for Imaging Science and Technology, 2006), pp. 1–7.

Kubelka, P.

Neugebauer, H. E. J.

H. E. J. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbendrucks,” Zeitschrift fuer wissenschaftliche Photographie 36, 36–73 (1937) [“The theoretical basis of multicolour letterpress printing,” Color Res. Appl. 30, 322–331 (2005) (in English)].
[CrossRef]

Nielsen, W. J.

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proc. TAGA 3, 65–76 (1951).

Ruckdeschel, F. R.

Sharma, G.

G. Sharma, Digital Color Imaging Handbook (CRC Press, 2003), pp. 30–36.

Viggiano, J. A. S.

J. A. S. Viggiano, “The color of halftone tints,” Proc. TAGA 37, 647–661 (1985).

Williams, F. C.

Yule, J. A. C.

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]

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proc. TAGA 3, 65–76 (1951).

Appl. Opt. (1)

J. Electron. Imaging (1)

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 033001 (2005).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (3)

Proc. SPIE (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, 434–445 (2005).
[CrossRef]

Proc. TAGA (2)

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proc. TAGA 3, 65–76 (1951).

J. A. S. Viggiano, “The color of halftone tints,” Proc. TAGA 37, 647–661 (1985).

Procédés (1)

M. E. Demichel, Procédés 26, 17–21 (1924).

Zeitschrift fuer wissenschaftliche Photographie (1)

H. E. J. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbendrucks,” Zeitschrift fuer wissenschaftliche Photographie 36, 36–73 (1937) [“The theoretical basis of multicolour letterpress printing,” Color Res. Appl. 30, 322–331 (2005) (in English)].
[CrossRef]

Other (3)

G. Sharma, Digital Color Imaging Handbook (CRC Press, 2003), pp. 30–36.

M. Hébert and R. D. Hersch, “Yule–Nielsen approach for predicting the spectral transmittance of halftone prints,” in Proceedings of the IS&T/SID 17th Conference on Color Imaging (Society for Imaging Science and Technology, 2009), pp. 155–158.

R. D. Hersch and M. Hébert, “Interaction between light, paper and color halftones: challenges and modelization approaches,” in Proceedings of the Third European Conference on Color in Graphics, Imaging and Vision (CGIV) (Society for Imaging Science and Technology, 2006), pp. 1–7.

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Figures (4)

Fig. 1
Fig. 1

Physical model of the interaction of light with a recto– verso print on paper accounting for the multiple reflections between the paper bulk and the print–air interfaces.

Fig. 2
Fig. 2

Example of ink spreading curve, giving the effective surface coverage of ink i when superposed on colorant j as a function of the nominal surface coverage q 0 .

Fig. 3
Fig. 3

Set B of patches printed with cyan, magenta, yellow inks on the recto side, and red and green inks on the verso side.

Fig. 4
Fig. 4

Dot gain curves (difference between effective and nominal ink coverages as a function of the nominal ink coverage for a single halftoned ink) calibrated in reflectance mode (dashed lines) and transmittance mode (continuous lines). The 12 graphs correspond to cyan, magenta, or yellow halftones printed either alone on paper or superposed with a solid ink layer composed of the second ink, the third ink, or the second and third inks.

Tables (2)

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Table 1 Average Color Difference Between Measured and Predicted Transmission Spectra

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Table 2 Prediction Results in Reflection and Transmission Modes

Equations (11)

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a w = ( 1 c ) ( 1 m ) ( 1 y ) , a c = c ( 1 m ) ( 1 y ) , a m = ( 1 c ) m ( 1 y ) , a y = ( 1 c ) ( 1 m ) y , a m + y = ( 1 c ) m y , a c + y = c ( 1 m ) y , a c + m = c m ( 1 y ) , a c + m + y = c m y .
T ( λ ) = j = 1 8 a j T j ( λ ) .
T ( λ ) = [ j = 1 8 a j T j 1 / n ( λ ) ] n .
P ( λ ) = [ ( 1 x ) T j 1 / n ( λ ) + x T i & j 1 / n ( λ ) ] n
q i / j = argmin 0 x 1 λ = 380 nm 730 nm [ M ( λ ) P ( λ ) ] 2 ,
c = ( 1 m ) ( 1 y ) f c ( c 0 ) + m ( 1 y ) f c / m ( c 0 ) + ( 1 m ) y f c / y ( c 0 ) + m y f c / m + y ( c 0 ) , m = ( 1 c ) ( 1 y ) f m ( m 0 ) + c ( 1 y ) f m / c ( m 0 ) + ( 1 c ) y f m / y ( m 0 ) + c y f m / c + y ( m 0 ) , y = ( 1 c ) ( 1 m ) f y ( y 0 ) + c ( 1 m ) f y / c ( y 0 ) + ( 1 c ) m f y / m ( y 0 ) + c m f y / c + m ( y 0 ) .
T ( λ ) = [ u = 1 8 v = 1 8 a u a v T u v 1 / n ( λ ) ] n .
t j ( λ ) = T j ( λ ) / T p ( λ ) .
T u v ( λ ) = T p ( λ ) t u ( λ ) t v ( λ )
T ( λ ) = T p ( λ ) [ u a u t u 1 / n ( λ ) ] n [ v a v t v 1 / n ( λ ) ] n .
T ( λ ) = T p ( λ ) [ u a u t u 1 / n u ( λ ) ] n u [ v a v t v 1 / n v ( λ ) ] n v .

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