Abstract

I propose a model for predicting the total reflectance of color halftones printed on paper incorporating fluorescent brighteners. The total reflectance is modeled as the additive superposition of the relative fluorescent emission and the pure reflectance of the color print. The fluorescent emission prediction model accounts for both the attenuation of light by the halftone within the excitation wavelength range and for the attenuation of the fluorescent emission by the same halftone within the emission wavelength range. The model’s calibration relies on reflectance measurements of the optically brightened paper and of the solid colorant patches with two illuminants, one including and one excluding the UV components. The part of the model predicting the pure reflectance relies on an ink-spreading extended Clapper–Yule model. On uniformly distributed surface coverages of cyan, magenta, and yellow halftone patches, the proposed model predicts the relative fluorescent emission with a high accuracy (mean ΔE94=0.42 under a D65 standard illuminant). For optically brightened paper exhibiting a moderate fluorescence, the total reflectance prediction improves the spectral reflectance prediction mainly for highlight color halftones, comprising a proportion of paper white above 12%. Applications include the creation of improved printer characterization tables for color management purposes and the prediction of color gamuts for new combinations of optically brightened papers and inks.

© 2008 Optical Society of America

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References

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  1. J. A.S Viggiano, “Modeling the color of multi-colored halftones,” Proc. TAGA 44-62 (1990).
  2. K. Iino and R. S. Berns, “Building color management modules using linear optimization I. Desktop,” J. Imaging Sci. Technol. 42, 79-94 (1998).
  3. R. Balasubramanian, “Optimization of the spectral Neugebauer model for printer characterization,” J. Electron. Imaging 8, 156-166 (1999).
    [CrossRef]
  4. G. Rogers, “A generalized Clapper-Yule model of halftone reflectance,” Color Res. Appl. 25, 402-407 (2000).
    [CrossRef]
  5. R. D. Hersch, P. Emmel, F. Crété, and F. Collaud, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 033001 (2005).
    [CrossRef]
  6. T. Bugnon, M. Brichon, and R. D. Hersch, “Model-based deduction of CMYK surface coverages from visible and infrared spectral measurements of halftone prints,” Proc. SPIE 6493, 649310 (2007).
    [CrossRef]
  7. A. J. Calabria and D. C. Rich, “Brigher is better? Investigating spectral color prediction of ink on optically brightened substrate,” Proceedings IS&T/SID 11th Color Imaging Conference (Society for Imaging Science and Technology, 2003), pp. 288-293.
  8. International Color Consortium, “The effects of fluorescence in the characterization of imaging media,” Summary of CIE Publication 163, www.icc.org.
  9. 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]
  10. K. Nassau, The Physics and Chemistry of Color (Wiley, 1983).
  11. P. Emmel, “Physical models for color prediction,” in Digital Color Imaging, G. Sharma, ed. (CRC, 2003), pp. 173-238.
  12. F. Grum, “Colorimetry of fluorescent materials,” in Optical Radiation Measurements, Volume 2, Color Measurements, F. Grum and C. J. Bartelson, eds. (Academic, 1980), pp. 235-288.
  13. R. Donaldson, “Spectrophotometry of fluorescent pigments,” Br. J. Appl. Phys. 5, 210-214 (1954).
    [CrossRef]
  14. E. Allen, “Separation of the spectral radiance factor curve of fluorescent substrates into reflected and fluoresced components,” Appl. Opt. 12, 289-293 (1973).
    [CrossRef] [PubMed]
  15. P. Emmel and R. D. Hersch, “Spectral prediction model for a transparent fluorescent ink on paper,” in Proceedings IS&T/SID 6th Color Imaging Conference (Society for Imaging Science and Technology, 1998), pp. 116-122.
  16. T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4-14(2003).
    [CrossRef]
  17. G. L. Rogers, “Spectral model of a fluorescent ink halftone,” J. Opt. Soc. Am. A 17, 1975-1981 (2000).
    [CrossRef]
  18. R. D. Hersch, P. Donzé, and S. Chosson, “Color images visible under UV light,” Proc. SIGGRAPH 2007, ACM Trans. Graph. 26 (3), Article 75, 1-9 (2007).
  19. L. Yang, “Spectral model of halftone on a fluorescent substrate,” J. Imaging Sci. Technol. 49, 179-184 (2005).
  20. D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19(2000).
    [CrossRef]
  21. M. E. Demichel, Procédé 26, 17-21 (1924).
  22. D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. (U.S.) 29, 329-332 (1942).
  23. J. L. Saunderson, “Calculation of the color pigmented plastics,” J. Opt. Soc. Am. 32, 727-736 (1942).
    [CrossRef]
  24. H. E. J. Neugebauer, “The theoretical basis of multicolor letterpress printing,” Color Res. Appl. 30, 322-331 (2005).
    [CrossRef]
  25. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), Table 1(1.2.1 ), pp. 4-6.
  26. In all equations, the attenuation of light exiting though the print-air interface is modeled by the Fresnel diffuse transmittance term (1−ri). When performing measurements, this would imply that an integrated sphere is used to capture all exiting irradiance components. If a measurement instrument is used that captures the exiting radiance perpendicularly (θ=0°) or at a small angle (θ=8°), the exit attenuation term (1−ri)=0.386 appearing in Eqs. should, according to radiometric considerations, be replaced by the attenuation of the radiance across the print-air interface due both to Fresnel transmittivity and to cone spreading (1−rs(θ))/(nprint)2 in the present case (1−0.0438)/(1.532)=0.408 (see ). However, since both terms are numerically close one to another and since the print-air interface is not perfectly flat, I do not recommend performing these changes. This is consistent with observations by C. Kortüm who did not observe, for diffusely reflecting media, significant reflectance factor differences between collimated 45°/0° and integrated sphere 45°/d or d/0° measurement geometries .
  27. R. Bala, R. Eschbach, and Y. Zhao, “Substrate fluorescence: bane or boon?,” in Proceedings IS&T/SID 15th Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 12-17.
  28. M. Hebert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).
  29. G. Kortüm, “Optical geometry of the measurement arrangement,” in Reflectance Spectroscopy (Springer, 1969), pp. 170-175.

2007 (2)

T. Bugnon, M. Brichon, and R. D. Hersch, “Model-based deduction of CMYK surface coverages from visible and infrared spectral measurements of halftone prints,” Proc. SPIE 6493, 649310 (2007).
[CrossRef]

R. D. Hersch, P. Donzé, and S. Chosson, “Color images visible under UV light,” Proc. SIGGRAPH 2007, ACM Trans. Graph. 26 (3), Article 75, 1-9 (2007).

2005 (3)

L. Yang, “Spectral model of halftone on a fluorescent substrate,” J. Imaging Sci. Technol. 49, 179-184 (2005).

H. E. J. Neugebauer, “The theoretical basis of multicolor letterpress printing,” Color Res. Appl. 30, 322-331 (2005).
[CrossRef]

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

2004 (1)

M. Hebert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

2003 (1)

T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4-14(2003).
[CrossRef]

2000 (3)

G. Rogers, “A generalized Clapper-Yule model of halftone reflectance,” Color Res. Appl. 25, 402-407 (2000).
[CrossRef]

D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19(2000).
[CrossRef]

G. L. Rogers, “Spectral model of a fluorescent ink halftone,” J. Opt. Soc. Am. A 17, 1975-1981 (2000).
[CrossRef]

1999 (1)

R. Balasubramanian, “Optimization of the spectral Neugebauer model for printer characterization,” J. Electron. Imaging 8, 156-166 (1999).
[CrossRef]

1998 (1)

K. Iino and R. S. Berns, “Building color management modules using linear optimization I. Desktop,” J. Imaging Sci. Technol. 42, 79-94 (1998).

1990 (1)

J. A.S Viggiano, “Modeling the color of multi-colored halftones,” Proc. TAGA 44-62 (1990).

1973 (1)

1954 (1)

R. Donaldson, “Spectrophotometry of fluorescent pigments,” Br. J. Appl. Phys. 5, 210-214 (1954).
[CrossRef]

1953 (1)

1942 (2)

D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. (U.S.) 29, 329-332 (1942).

J. L. Saunderson, “Calculation of the color pigmented plastics,” J. Opt. Soc. Am. 32, 727-736 (1942).
[CrossRef]

1924 (1)

M. E. Demichel, Procédé 26, 17-21 (1924).

Allen, E.

Bala, R.

R. Bala, R. Eschbach, and Y. Zhao, “Substrate fluorescence: bane or boon?,” in Proceedings IS&T/SID 15th Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 12-17.

Balasubramanian, R.

R. Balasubramanian, “Optimization of the spectral Neugebauer model for printer characterization,” J. Electron. Imaging 8, 156-166 (1999).
[CrossRef]

Berns, R. S.

D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19(2000).
[CrossRef]

K. Iino and R. S. Berns, “Building color management modules using linear optimization I. Desktop,” J. Imaging Sci. Technol. 42, 79-94 (1998).

Brichon, M.

T. Bugnon, M. Brichon, and R. D. Hersch, “Model-based deduction of CMYK surface coverages from visible and infrared spectral measurements of halftone prints,” Proc. SPIE 6493, 649310 (2007).
[CrossRef]

Bugnon, T.

T. Bugnon, M. Brichon, and R. D. Hersch, “Model-based deduction of CMYK surface coverages from visible and infrared spectral measurements of halftone prints,” Proc. SPIE 6493, 649310 (2007).
[CrossRef]

Calabria, A. J.

A. J. Calabria and D. C. Rich, “Brigher is better? Investigating spectral color prediction of ink on optically brightened substrate,” Proceedings IS&T/SID 11th Color Imaging Conference (Society for Imaging Science and Technology, 2003), pp. 288-293.

Chosson, S.

R. D. Hersch, P. Donzé, and S. Chosson, “Color images visible under UV light,” Proc. SIGGRAPH 2007, ACM Trans. Graph. 26 (3), Article 75, 1-9 (2007).

Clapper, F. R.

Collaud, F.

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

Demichel, M. E.

M. E. Demichel, Procédé 26, 17-21 (1924).

Donaldson, R.

R. Donaldson, “Spectrophotometry of fluorescent pigments,” Br. J. Appl. Phys. 5, 210-214 (1954).
[CrossRef]

Donzé, P.

R. D. Hersch, P. Donzé, and S. Chosson, “Color images visible under UV light,” Proc. SIGGRAPH 2007, ACM Trans. Graph. 26 (3), Article 75, 1-9 (2007).

Emmel, P.

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

P. Emmel, “Physical models for color prediction,” in Digital Color Imaging, G. Sharma, ed. (CRC, 2003), pp. 173-238.

P. Emmel and R. D. Hersch, “Spectral prediction model for a transparent fluorescent ink on paper,” in Proceedings IS&T/SID 6th Color Imaging Conference (Society for Imaging Science and Technology, 1998), pp. 116-122.

Eschbach, R.

R. Bala, R. Eschbach, and Y. Zhao, “Substrate fluorescence: bane or boon?,” in Proceedings IS&T/SID 15th Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 12-17.

Grum, F.

F. Grum, “Colorimetry of fluorescent materials,” in Optical Radiation Measurements, Volume 2, Color Measurements, F. Grum and C. J. Bartelson, eds. (Academic, 1980), pp. 235-288.

Hebert, M.

M. Hebert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

Hersch, R. D.

R. D. Hersch, P. Donzé, and S. Chosson, “Color images visible under UV light,” Proc. SIGGRAPH 2007, ACM Trans. Graph. 26 (3), Article 75, 1-9 (2007).

T. Bugnon, M. Brichon, and R. D. Hersch, “Model-based deduction of CMYK surface coverages from visible and infrared spectral measurements of halftone prints,” Proc. SPIE 6493, 649310 (2007).
[CrossRef]

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

M. Hebert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

P. Emmel and R. D. Hersch, “Spectral prediction model for a transparent fluorescent ink on paper,” in Proceedings IS&T/SID 6th Color Imaging Conference (Society for Imaging Science and Technology, 1998), pp. 116-122.

Iino, K.

K. Iino and R. S. Berns, “Building color management modules using linear optimization I. Desktop,” J. Imaging Sci. Technol. 42, 79-94 (1998).

Judd, D. B.

D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. (U.S.) 29, 329-332 (1942).

Kortüm, G.

G. Kortüm, “Optical geometry of the measurement arrangement,” in Reflectance Spectroscopy (Springer, 1969), pp. 170-175.

Nassau, K.

K. Nassau, The Physics and Chemistry of Color (Wiley, 1983).

Neugebauer, H. E. J.

H. E. J. Neugebauer, “The theoretical basis of multicolor letterpress printing,” Color Res. Appl. 30, 322-331 (2005).
[CrossRef]

Rich, D. C.

A. J. Calabria and D. C. Rich, “Brigher is better? Investigating spectral color prediction of ink on optically brightened substrate,” Proceedings IS&T/SID 11th Color Imaging Conference (Society for Imaging Science and Technology, 2003), pp. 288-293.

Rogers, G.

G. Rogers, “A generalized Clapper-Yule model of halftone reflectance,” Color Res. Appl. 25, 402-407 (2000).
[CrossRef]

Rogers, G. L.

Saunderson, J. L.

Shakespeare, J.

T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4-14(2003).
[CrossRef]

Shakespeare, T.

T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4-14(2003).
[CrossRef]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), Table 1(1.2.1 ), pp. 4-6.

Viggiano, J. A.S

J. A.S Viggiano, “Modeling the color of multi-colored halftones,” Proc. TAGA 44-62 (1990).

Wyble, D. R.

D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19(2000).
[CrossRef]

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), Table 1(1.2.1 ), pp. 4-6.

Yang, L.

L. Yang, “Spectral model of halftone on a fluorescent substrate,” J. Imaging Sci. Technol. 49, 179-184 (2005).

Yule, J. A. C.

Zhao, Y.

R. Bala, R. Eschbach, and Y. Zhao, “Substrate fluorescence: bane or boon?,” in Proceedings IS&T/SID 15th Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 12-17.

Appl. Opt. (1)

Br. J. Appl. Phys. (1)

R. Donaldson, “Spectrophotometry of fluorescent pigments,” Br. J. Appl. Phys. 5, 210-214 (1954).
[CrossRef]

Color Res. Appl. (4)

D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19(2000).
[CrossRef]

G. Rogers, “A generalized Clapper-Yule model of halftone reflectance,” Color Res. Appl. 25, 402-407 (2000).
[CrossRef]

H. E. J. Neugebauer, “The theoretical basis of multicolor letterpress printing,” Color Res. Appl. 30, 322-331 (2005).
[CrossRef]

T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4-14(2003).
[CrossRef]

J. Electron. Imaging (2)

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

R. Balasubramanian, “Optimization of the spectral Neugebauer model for printer characterization,” J. Electron. Imaging 8, 156-166 (1999).
[CrossRef]

J. Imaging Sci. Technol. (3)

L. Yang, “Spectral model of halftone on a fluorescent substrate,” J. Imaging Sci. Technol. 49, 179-184 (2005).

K. Iino and R. S. Berns, “Building color management modules using linear optimization I. Desktop,” J. Imaging Sci. Technol. 42, 79-94 (1998).

M. Hebert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Res. Natl. Bur. Stand. (U.S.) (1)

D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. (U.S.) 29, 329-332 (1942).

Proc. SIGGRAPH 2007, ACM Trans. Graph. (1)

R. D. Hersch, P. Donzé, and S. Chosson, “Color images visible under UV light,” Proc. SIGGRAPH 2007, ACM Trans. Graph. 26 (3), Article 75, 1-9 (2007).

Proc. SPIE (1)

T. Bugnon, M. Brichon, and R. D. Hersch, “Model-based deduction of CMYK surface coverages from visible and infrared spectral measurements of halftone prints,” Proc. SPIE 6493, 649310 (2007).
[CrossRef]

Proc. TAGA (1)

J. A.S Viggiano, “Modeling the color of multi-colored halftones,” Proc. TAGA 44-62 (1990).

Procédé (1)

M. E. Demichel, Procédé 26, 17-21 (1924).

Other (10)

A. J. Calabria and D. C. Rich, “Brigher is better? Investigating spectral color prediction of ink on optically brightened substrate,” Proceedings IS&T/SID 11th Color Imaging Conference (Society for Imaging Science and Technology, 2003), pp. 288-293.

International Color Consortium, “The effects of fluorescence in the characterization of imaging media,” Summary of CIE Publication 163, www.icc.org.

K. Nassau, The Physics and Chemistry of Color (Wiley, 1983).

P. Emmel, “Physical models for color prediction,” in Digital Color Imaging, G. Sharma, ed. (CRC, 2003), pp. 173-238.

F. Grum, “Colorimetry of fluorescent materials,” in Optical Radiation Measurements, Volume 2, Color Measurements, F. Grum and C. J. Bartelson, eds. (Academic, 1980), pp. 235-288.

G. Kortüm, “Optical geometry of the measurement arrangement,” in Reflectance Spectroscopy (Springer, 1969), pp. 170-175.

P. Emmel and R. D. Hersch, “Spectral prediction model for a transparent fluorescent ink on paper,” in Proceedings IS&T/SID 6th Color Imaging Conference (Society for Imaging Science and Technology, 1998), pp. 116-122.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), Table 1(1.2.1 ), pp. 4-6.

In all equations, the attenuation of light exiting though the print-air interface is modeled by the Fresnel diffuse transmittance term (1−ri). When performing measurements, this would imply that an integrated sphere is used to capture all exiting irradiance components. If a measurement instrument is used that captures the exiting radiance perpendicularly (θ=0°) or at a small angle (θ=8°), the exit attenuation term (1−ri)=0.386 appearing in Eqs. should, according to radiometric considerations, be replaced by the attenuation of the radiance across the print-air interface due both to Fresnel transmittivity and to cone spreading (1−rs(θ))/(nprint)2 in the present case (1−0.0438)/(1.532)=0.408 (see ). However, since both terms are numerically close one to another and since the print-air interface is not perfectly flat, I do not recommend performing these changes. This is consistent with observations by C. Kortüm who did not observe, for diffusely reflecting media, significant reflectance factor differences between collimated 45°/0° and integrated sphere 45°/d or d/0° measurement geometries .

R. Bala, R. Eschbach, and Y. Zhao, “Substrate fluorescence: bane or boon?,” in Proceedings IS&T/SID 15th Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 12-17.

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Figures (8)

Fig. 1
Fig. 1

Attenuation of light by multiple reflections within a halftone print.

Fig. 2
Fig. 2

Dot gain curves representing effective minus nominal surface coverages, with effective surface coverages fitted on patches printed at 25, 50, and 75% nominal surface coverages on Canon MP-101 paper with a Canon IP4000 ink jet printer at a screen frequency of 100 lpi .

Fig. 3
Fig. 3

Spectral prediction model with ink spreading in all superposition conditions.

Fig. 4
Fig. 4

Incoming light within the excitation wavelength range, attenuated by the halftone ink layer, partially reflected by the paper bulk and then partially reflected at the print–air interface.

Fig. 5
Fig. 5

Fluorescent irradiance illuminating the halftone layer and the print–air interface from below.

Fig. 6
Fig. 6

Emission spectra of the two illuminants, UV included and UV excluded, present in the Gretag-Macbeth i7 spectrophotometer.

Fig. 7
Fig. 7

Measured reflectances of paper white and of solid cyan, magenta, and yellow patches under illuminants with and without UV component as a function of wavelength (nm).

Fig. 8
Fig. 8

Measured total reflectance (measTotalRefl), predicted fluorescent emission (predFluoEm), predicted total reflectance with the fluorescence model (predTotalReflFluo), and reflectance predicted with the Clapper–Yule model only (predReflCY) for a halftone printed on the MP-101 brightened paper at nominal surface coverages c = 0 , m = 0.25 , and y = 0.5 .

Tables (4)

Tables Icon

Table 1 Prediction Accuracy Improvement Due to the Ink-Spreading Model with 125 Cyan, Magenta, and Yellow Halftone Patches (CMY) Comprising All Combinations of Nominal Surface Coverages 0, 0.25, 0.5, 0.75, and 1 with UV Illumination Excluded (Canon IP4000 Printer, Screen Frequency 100 lpi , Resolution 600 dpi )

Tables Icon

Table 2 Prediction Accuracy of the Fluorescent Emission Component of a Spectral Reflectance with an Illuminant including UV Components (Gretag-Macbeth i7 Table Spectrophotometer with a d / 6 ° Geometry)

Tables Icon

Table 3 Comparison of Prediction Accuracies

Tables Icon

Table 4 Comparison of Prediction Accuracies for 27 Halftones Samples Comprising All Combinations of 0, 0.25, and 0.5 CMY Surface Coverages

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

R total ( λ ) = F ( λ ) + I 0 ( λ ) · R pure ( λ ) I 0 ( λ ) = F ( λ ) I 0 ( λ ) + R pure ( λ ) .
R ( λ ) = K · r s + ( 1 r s ) · r g ( λ ) · ( 1 r i ) · ( 1 a + a · t ( λ ) ) 2 · [ 1 + r i · r g ( λ ) · ( 1 a + a · t ( λ ) 2 ) + ( r i · r g ( λ ) · ( 1 a + a · t ( λ ) 2 ) ) 2 + ... + ( r i · r g ( λ ) · ( 1 a + a · t ( λ ) 2 ) ) n 1 ] .
R ( λ ) = K · r s + ( 1 r s ) · r g ( λ ) · ( 1 r i ) · ( 1 a + a · t ( λ ) ) 2 1 r g ( λ ) · r i · ( 1 a + a · t ( λ ) 2 ) .
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 r = ( 1 c ) · m · y , a g = c · ( 1 m ) · y , a b = c · m · ( 1 y ) , a k = c · m · y ,
R ( λ ) = K · r s + ( 1 r s ) · r g ( λ ) · ( 1 r i ) · ( j = 1 8 a j · t j ( λ ) ) 2 1 r g ( λ ) · r i · j = 1 8 a j · t j ( λ ) 2 .
r g ( λ ) = R w ( λ ) K · r s R w ( λ ) · r i K · r s · r i + ( 1 r s ) · ( 1 r i ) .
t j ( λ ) = R j ( λ ) K · r s r g ( λ ) · r i · ( R j ( λ ) K · r s ) + r g ( λ ) · ( 1 r i ) · ( 1 r s ) .
R ( λ ) = K · r s + ( 1 r s ) · r g ( λ ) · ( 1 r i ) · [ b · [ j = 1 8 a j · t j ( λ ) 2 1 r i · r g ( λ ) · t j ( λ ) 2 ] + ( 1 b ) · ( j = 1 8 a j · t j ( λ ) ) 2 1 r i · r g ( λ ) · j = 1 8 a j · t j ( λ ) 2 ] .
c = f c ( c ) ( 1 m ) ( 1 y ) + f c / m ( c ) m ( 1 y ) + f c / y ( c ) ( 1 m ) y + f c / m y ( c ) m y , m = f m ( m ) ( 1 c ) ( 1 y ) + f m / c ( m ) c ( 1 y ) + f m / y ( m ) ( 1 c ) y + f m / c y ( m ) c y , y = f y ( y ) ( 1 c ) ( 1 m ) + f y / c ( y ) c ( 1 m ) + f y / m ( y ) ( 1 c ) m + f y / c m ( y ) c m .
I u 1 ( λ ) = I u ( λ ) · ( 1 r s ) ( 1 a + a · t u ( λ ) ) ( 1 r g u ( λ ) ) .
I u 2 ( λ ) = I u ( 1 r s ) · ( 1 a + a · t u ( λ ) ) · ( 1 r g u ( λ ) ) · r g u ( λ ) · r i · ( 1 a + a · t u ( λ ) 2 ) .
I u 3 ( λ ) = I u ( λ ) · ( 1 r s ) · ( 1 a + a · t u ( λ ) ) · ( 1 r g u ( λ ) ) · r g u ( λ ) 2 · r i 2 · ( 1 a + a · t u ( λ ) 2 ) 2 .
I u n ( λ ) = I u ( λ ) · ( 1 r s ) · ( 1 a + a · t u ( λ ) ) · ( 1 r g u ( λ ) ) · r g u ( λ ) n 1 · r i n 1 ( 1 a + a · t u ( λ ) 2 ) n 1 .
I abs ( λ ) = k = 1 I u k ( λ ) = I u ( λ ) · ( 1 r s ) · ( 1 a + a · t u ( λ ) ) · ( 1 r g u ( λ ) ) 1 1 r g u ( λ ) · r i · ( 1 a + a t u ( λ ) 2 ) .
I abs ( λ ) = k = 1 I u k ( λ ) = I u ( λ ) · ( 1 r s ) · ( a j · t u j ( λ ) ) · ( 1 r g u ( λ ) ) · 1 1 r g u ( λ ) · r i · ( a j · t u j ( λ ) 2 ) .
E abs = λ e Inf λ e Sup I abs ( λ ) · d λ = λ e Inf λ e Sup I u ( λ ) · ( 1 r s ) · ( a j · t u j ( λ ) ) · ( 1 r g u ( λ ) ) 1 1 r g u ( λ ) · r i · ( a j · t u j 2 ( λ ) ) · d λ .
E abs P = λ e Inf λ e Sup I u ( λ ) ( 1 r s ) · ( 1 r g u ( λ ) ) 1 1 r g u ( λ ) · r i d λ = ( 1 r s ) · ( 1 r g u ' ) 1 1 r g u ' · r i λ e Inf λ e Sup I u ( λ ) d λ .
E abs J = λ e Inf λ e Sup I u ( λ ) ( 1 r s ) · t u j ( λ ) · ( 1 r g u ) 1 1 r g u · r i · t u j 2 ( λ ) d λ = ( 1 r s ) · t u j · ( 1 r g u ) 1 1 r g u · r i · ( t u j ) 2 λ e Inf λ e Sup I u ( λ ) · d λ .
E abs = ( 1 r s ) · ( a j · t u j ' ) · ( 1 r g u ) 1 1 r g u · r i · ( a j · t u j 2 ) · λ e Inf λ e Sup I u ( λ ) · d λ .
λ v Inf λ v Sup f e m ( λ ) · d λ 1.
F ( λ ) = E abs Q f e m ( λ ) .
F ( a j , t u j , λ ) = Q · f e m ( λ ) · ( 1 r s ) ( a j · t u j ) ( 1 r g u ) 1 1 r g u r i · ( a j · ( t u j ) 2 ) · λ v Inf λ v Sup I u ( λ ) d λ .
I e 1 ( λ ) = F ( a , t u j , λ ) · ( 1 r i ) · ( 1 a + a · t j ( λ ) ) ,
I e 2 ( λ ) = F ( a , t u i , λ ) · ( 1 r i ) · ( 1 a + a · t j ( λ ) ) · r g ( λ ) · r i · ( 1 a + a · t j ( λ ) 2 ) .
I e 3 ( λ ) = F ( a , t u i , λ ) · ( 1 r i ) · ( 1 a + a · t j ( λ ) ) · r g ( λ ) 2 · r i 2 · ( 1 a + a · t j ( λ ) 2 ) 2 .
I e n ( λ ) = F ( a , t u j , λ ) · ( 1 r i ) · ( 1 a + a · t j ( λ ) ) · r g ( λ ) n 1 · r i n 1 · ( 1 a + a · t j ( λ ) 2 ) n 1 .
I e ( λ ) = k = 1 I e k ( λ ) = F ( a , t u j ' , λ ) · ( 1 r i ) · ( 1 a + a · t j ( λ ) ) · 1 1 r g ( λ ) · r i · ( 1 a + a · t j ( λ ) 2 ) .
I e m ( λ ) = k = 1 I e k ( λ ) = F ( a j , t u j , λ ) · ( 1 r i ) · ( a j · t j ( λ ) ) · 1 1 r g ( λ ) · r i · ( a j · t j ( λ ) 2 ) .
E n ( λ ) = Q · f e m ( λ ) · λ U V inf λ U V sup I u ( λ ) d λ .
R U V + V ( λ ) = I e m ( λ ) I 0 ( λ ) + I r ( λ ) I 0 ( λ ) = I e m ( λ ) I 0 ( λ ) + R V ( λ ) ,
I e m ( λ ) I 0 ( λ ) = E n ( λ ) I 0 ( λ ) · ( 1 r s ) ( 1 r g u ) ( a j · t u j ) 1 r g u r i · ( a j · ( t u j ) 2 ) · ( 1 r i ) · ( a j · t j ( λ ) ) 1 r g ( λ ) · r i · ( a j · t j ( λ ) 2 ) .
I e m ( λ ) I 0 ( λ ) = R U V + V ( λ ) I r ( λ ) I 0 ( λ ) = R U V + V ( λ ) R V ( λ ) ,
E n ( λ ) I 0 ( λ ) = ( R U V + V ( λ ) R V ( λ ) ) · 1 r g u r i · ( a j · ( t u j ) 2 ) ( 1 r s ) ( 1 r g u ) ( a j · t u j ) · 1 r g ( λ ) · r i · ( a j · t j ( λ ) 2 ) ( 1 r i ) · ( a j · t j ( λ ) ) .
E n ( λ ) I 0 ( λ ) = ( R p U V + V ( λ ) R p V ( λ ) ) · 1 r g u r i ( 1 r s ) ( 1 r g u ) · 1 r g ( λ ) · r i ( 1 r i ) .
I e m ( λ ) I 0 ( λ ) = ( R p U V + V ( λ ) R p V ( λ ) ) · ( 1 r g u ' ) r i · t u j 1 r g u · r i · ( t u j ) 2 · ( 1 r g ( λ ) · r i ) · t j ( λ ) 1 r g ( λ ) · r i · t j ( λ ) 2 .
R U V + V ( λ ) = ( R p U V + V ( λ ) R p V ( λ ) ) · ( 1 r g u ) · r i · a i · t u i 1 r g u · r i · ( a i · ( t u i ) 2 ) · ( 1 r g ( λ ) r i ) · ( a i · t i ( λ ) ) 1 r g ( λ ) · r i · ( a i · t i ( λ ) 2 ) + R V ( λ ) ,

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