Abstract

This work deals with the efficient and accurate modeling of fluorescence in the context of stochastic Monte Carlo methods for which we propose a novel multiscale method. As in other approaches of this category, the transport theory is employed to describe the physics. The new framework was successfully applied for a quantitative assessment of halftone reflectance measurements with three different devices. It could be demonstrated that the described method is faster than classical Monte Carlo by multiple orders of magnitude, and that it is capable of correctly handling the geometrical device differences. It is also shown that optical dot gain is accurately predicted for the whole ink coverage range.

© 2009 Optical Society of America

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  1. P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).
  2. K. Simon and B. Trachsler, “A random walk approach for light scattering in material,” in Discrete Random Walks, DRW'03, Proceedings of Discrete Mathematics and Theoretical Computer Science 2003, C.Banderier and C.Krattenthaler, eds., Vol. AC (2003), pp. 289-300.
  3. L. Wang, J. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
    [CrossRef] [PubMed]
  4. P. Jenny, M. Vöge, S. Mourad, and T. Stamm, “Modeling light scattering in paper for halftone print,” in Proceedings of 2006 International Conference on Computer Graphics, Imaging and Visualisation (IEEE, 2006), pp. 443-447.
  5. P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A 24, 2206-2219 (2007).
    [CrossRef]
  6. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).
  7. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Monograph NBS MN-160, National Bureau of Standards (US) (1977).
  8. 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, 033001-12 (2005).
    [CrossRef]
  9. J. W. P. Bakker, G. Bryntse, and H. Arwin, “Determination of refractive index of printed and uprinted paper using spectroscopy ellipsometry,” Thin Solid Films 455-456, 361-365 (2004).
    [CrossRef]
  10. L. Yang, A. Fogden, N. Pauler, Ö. Sävborg, and B. Kruse, “A novel method for studying ink penetration of a print,” Nord. Pulp Pap. Res. J. 20, 423-429 (2005).
    [CrossRef]
  11. S. Mourad, “Improved calibration of optical characteristics of paper by an adapted paper-MTF model,” J. Imaging Sci. Technol. 51, 283-292 (2007).
    [CrossRef]

2007 (2)

2005 (2)

L. Yang, A. Fogden, N. Pauler, Ö. Sävborg, and B. Kruse, “A novel method for studying ink penetration of a print,” Nord. Pulp Pap. Res. J. 20, 423-429 (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, 033001-12 (2005).
[CrossRef]

2004 (1)

J. W. P. Bakker, G. Bryntse, and H. Arwin, “Determination of refractive index of printed and uprinted paper using spectroscopy ellipsometry,” Thin Solid Films 455-456, 361-365 (2004).
[CrossRef]

1995 (1)

L. Wang, J. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

1931 (1)

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Arwin, H.

J. W. P. Bakker, G. Bryntse, and H. Arwin, “Determination of refractive index of printed and uprinted paper using spectroscopy ellipsometry,” Thin Solid Films 455-456, 361-365 (2004).
[CrossRef]

Bakker, J. W. P.

J. W. P. Bakker, G. Bryntse, and H. Arwin, “Determination of refractive index of printed and uprinted paper using spectroscopy ellipsometry,” Thin Solid Films 455-456, 361-365 (2004).
[CrossRef]

Bryntse, G.

J. W. P. Bakker, G. Bryntse, and H. Arwin, “Determination of refractive index of printed and uprinted paper using spectroscopy ellipsometry,” Thin Solid Films 455-456, 361-365 (2004).
[CrossRef]

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, 033001-12 (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, 033001-12 (2005).
[CrossRef]

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, 033001-12 (2005).
[CrossRef]

Fogden, A.

L. Yang, A. Fogden, N. Pauler, Ö. Sävborg, and B. Kruse, “A novel method for studying ink penetration of a print,” Nord. Pulp Pap. Res. J. 20, 423-429 (2005).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Monograph NBS MN-160, National Bureau of Standards (US) (1977).

Hersch, R. D.

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, 033001-12 (2005).
[CrossRef]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Monograph NBS MN-160, National Bureau of Standards (US) (1977).

Jacques, J. L.

L. Wang, J. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Jenny, P.

P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A 24, 2206-2219 (2007).
[CrossRef]

P. Jenny, M. Vöge, S. Mourad, and T. Stamm, “Modeling light scattering in paper for halftone print,” in Proceedings of 2006 International Conference on Computer Graphics, Imaging and Visualisation (IEEE, 2006), pp. 443-447.

Kruse, B.

L. Yang, A. Fogden, N. Pauler, Ö. Sävborg, and B. Kruse, “A novel method for studying ink penetration of a print,” Nord. Pulp Pap. Res. J. 20, 423-429 (2005).
[CrossRef]

Kubelka, P.

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Monograph NBS MN-160, National Bureau of Standards (US) (1977).

Mourad, S.

P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A 24, 2206-2219 (2007).
[CrossRef]

S. Mourad, “Improved calibration of optical characteristics of paper by an adapted paper-MTF model,” J. Imaging Sci. Technol. 51, 283-292 (2007).
[CrossRef]

P. Jenny, M. Vöge, S. Mourad, and T. Stamm, “Modeling light scattering in paper for halftone print,” in Proceedings of 2006 International Conference on Computer Graphics, Imaging and Visualisation (IEEE, 2006), pp. 443-447.

Munk, F.

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Monograph NBS MN-160, National Bureau of Standards (US) (1977).

Pauler, N.

L. Yang, A. Fogden, N. Pauler, Ö. Sävborg, and B. Kruse, “A novel method for studying ink penetration of a print,” Nord. Pulp Pap. Res. J. 20, 423-429 (2005).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Monograph NBS MN-160, National Bureau of Standards (US) (1977).

Sävborg, Ö.

L. Yang, A. Fogden, N. Pauler, Ö. Sävborg, and B. Kruse, “A novel method for studying ink penetration of a print,” Nord. Pulp Pap. Res. J. 20, 423-429 (2005).
[CrossRef]

Simon, K.

P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A 24, 2206-2219 (2007).
[CrossRef]

K. Simon and B. Trachsler, “A random walk approach for light scattering in material,” in Discrete Random Walks, DRW'03, Proceedings of Discrete Mathematics and Theoretical Computer Science 2003, C.Banderier and C.Krattenthaler, eds., Vol. AC (2003), pp. 289-300.

Stamm, T.

P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A 24, 2206-2219 (2007).
[CrossRef]

P. Jenny, M. Vöge, S. Mourad, and T. Stamm, “Modeling light scattering in paper for halftone print,” in Proceedings of 2006 International Conference on Computer Graphics, Imaging and Visualisation (IEEE, 2006), pp. 443-447.

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).

Trachsler, B.

K. Simon and B. Trachsler, “A random walk approach for light scattering in material,” in Discrete Random Walks, DRW'03, Proceedings of Discrete Mathematics and Theoretical Computer Science 2003, C.Banderier and C.Krattenthaler, eds., Vol. AC (2003), pp. 289-300.

Vöge, M.

P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A 24, 2206-2219 (2007).
[CrossRef]

P. Jenny, M. Vöge, S. Mourad, and T. Stamm, “Modeling light scattering in paper for halftone print,” in Proceedings of 2006 International Conference on Computer Graphics, Imaging and Visualisation (IEEE, 2006), pp. 443-447.

Wang, L.

L. Wang, J. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).

Yang, L.

L. Yang, A. Fogden, N. Pauler, Ö. Sävborg, and B. Kruse, “A novel method for studying ink penetration of a print,” Nord. Pulp Pap. Res. J. 20, 423-429 (2005).
[CrossRef]

Zheng, L.

L. Wang, J. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Comput. Methods Programs Biomed. (1)

L. Wang, J. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

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, 033001-12 (2005).
[CrossRef]

J. Imaging Sci. Technol. (1)

S. Mourad, “Improved calibration of optical characteristics of paper by an adapted paper-MTF model,” J. Imaging Sci. Technol. 51, 283-292 (2007).
[CrossRef]

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

Nord. Pulp Pap. Res. J. (1)

L. Yang, A. Fogden, N. Pauler, Ö. Sävborg, and B. Kruse, “A novel method for studying ink penetration of a print,” Nord. Pulp Pap. Res. J. 20, 423-429 (2005).
[CrossRef]

Thin Solid Films (1)

J. W. P. Bakker, G. Bryntse, and H. Arwin, “Determination of refractive index of printed and uprinted paper using spectroscopy ellipsometry,” Thin Solid Films 455-456, 361-365 (2004).
[CrossRef]

Z. Tech. Phys. (Leipzig) (1)

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Other (4)

K. Simon and B. Trachsler, “A random walk approach for light scattering in material,” in Discrete Random Walks, DRW'03, Proceedings of Discrete Mathematics and Theoretical Computer Science 2003, C.Banderier and C.Krattenthaler, eds., Vol. AC (2003), pp. 289-300.

P. Jenny, M. Vöge, S. Mourad, and T. Stamm, “Modeling light scattering in paper for halftone print,” in Proceedings of 2006 International Conference on Computer Graphics, Imaging and Visualisation (IEEE, 2006), pp. 443-447.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Monograph NBS MN-160, National Bureau of Standards (US) (1977).

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Figures (15)

Fig. 1
Fig. 1

Domain with diffuse light source and representative dot pattern on paper substrate.

Fig. 2
Fig. 2

Sketch of particle interfering with substrate surface.

Fig. 3
Fig. 3

Sketch of measuring device geometry with illumination, sensor, and substrate.

Fig. 4
Fig. 4

Reflectance spectra measured with the Spectrolino device.

Fig. 5
Fig. 5

Model of paper with coating and ink dots.

Fig. 6
Fig. 6

Calculated and measured reflectance spectra with UV filter.

Fig. 7
Fig. 7

Calculated and measured reflectance spectra without UV filter.

Fig. 8
Fig. 8

Computed and measured reflectance as a function of ink coverage for different wavelengths.

Fig. 9
Fig. 9

Computed and measured reflectance as a function of ink coverage for wavelength of 500 nm .

Fig. 10
Fig. 10

Discrepancy between measurement and computation with and without multiscale approach for 30% and 60% of ink coverage. Reflectance difference represents increase of computed/measured reflectance due to fluorescence.

Fig. 11
Fig. 11

Illustrative test case: diffuse light source illuminates a sphere whose surface consists of a substrate with a halftone print (30% ink coverage) on black backing.

Fig. 12
Fig. 12

Comparisons between measurements performed with Spectrolino and i 1 devices.

Fig. 13
Fig. 13

Calculated and measured reflectance spectra without UV filter using the i 1 setup.

Fig. 14
Fig. 14

Comparisons between measurements performed with Spectrolino and microscope.

Fig. 15
Fig. 15

Calculated and measured reflectance spectra without UV filter using the microscope setup.

Tables (7)

Tables Icon

Table 1 Device Geometry Parameters According to Fig. 3 (in Millimeters)

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Table 2 Absorption Coefficients of Paper and Ink for Nine Wavelengths (in Centimeters)

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Table 3 Absolute Difference between Computed and Measured Reflectance with UV Filter

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Table 4 Absolute Difference between Computed and Measured Reflectance without UV Filter

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Table 5 Comparison of Accuracy between Simulations Performed with the Stencil Algorithm (SA) and the Multiscale Method (MS)

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Table 6 Absolute Difference between Computed and Measured Reflectance without UV Filter Using the i 1 Setup

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Table 7 Absolute Difference between Computed and Measured Reflectance without UV Filter Using the Microscope Setup

Equations (4)

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

d I ( x , s , λ , t ) d s = [ γ a ( x , λ ) + γ s ( x , λ ) ] I ( x , s , λ , t ) + γ s ( x , λ ) 4 π 4 π p ( x , s , s , λ ) I ( x , s , λ , t ) d ω + q ( x , s , λ , t ) ,
4 π p ( x , s , s , λ ) d ω 1 .
ψ ( x , t ) = 4 π λ I ( x , s , λ , t ) d λ d ω
e ̂ ̂ k = e ̂ i n e c [ γ a , i ( λ ̂ ) Δ t ̂ ̂ i , k 1 p + γ a , u ( λ ̂ ) Δ t ̂ ̂ u , k 1 p ] × e c [ γ a , i ( λ ̂ ) f i ( λ ̂ , λ ̂ ̂ ) ( Δ t ̂ ̂ i , k p Δ t ̂ ̂ i , k 1 p ) + γ a , u ( λ ̂ ) f u ( λ ̂ , λ ̂ ̂ ) ( Δ t ̂ ̂ u , k p Δ t ̂ ̂ u , k 1 p ) ] × e c [ γ a , i ( λ ̂ ̂ ) Δ t ̂ ̂ i , k + γ a , u ( ( λ ̂ ̂ ) Δ t ̂ ̂ u , k ) ] ,

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