Abstract

The modulation transfer function (MTF) of 22 paper samples is computed using Monte Carlo simulations with isotropic or strongly forward single scattering. The inverse frequency at half maximum of the MTF (kp) is found inappropriate as a single metric for the MTF since it is insensitive to the shape of the modeled and simulated MTF. The single scattering phase function has a significant impact on the shape of the MTF, leading to more lateral scattering. However, anisotropic single scattering cannot explain the larger lateral scattering observed in paper. It is argued that the directional inhomogeneity of paper requires a light scattering model with both the phase function and scattering distances being dependent on the absolute direction.

© 2011 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011

2010

2009

2008

P. Edström, “A two-phase parameter estimation method for radiative transfer problems in paper industry applications,” Inverse Probl. Sci. En. 16, 927–951 (2008).
[CrossRef]

R. D. Hersch, “Spectral prediction model for color prints on paper with fluorescent additives,” Appl. Opt. 47, 6710–6722 (2008).
[CrossRef] [PubMed]

2007

S. Mourad, “Improved Calibration of Optical Characteristics of Paper by an Adapted Paper-MTF Model,” J. Imaging Sci. Techn. 51, 283–292 (2007).
[CrossRef]

2005

P. Edström, “A fast and stable solution method for the radiative transfer problem,” SIAM Rev. 47, 447–468 (2005).
[CrossRef]

2004

H. Granberg and M.-C. Béland, “Modelling the angle-dependent light scattering from sheets of pulp fiber fragments,” Nord. Pulp Pap. Res. J. 19, 354–359 (2004).
[CrossRef]

2001

S. Mourad, P. Emmel, K. Simon, and R. D. Hersch, “Extending Kubelka-Munk’s theory with lateral light scattering,” in IS&T’s NIP17: International Conference on Digital Printing Technologies, Lauderdale, Florida, USA, (2001), pp. 469–473.

1999

J. M. Schmitt, “Optical coherence tomography (OCT): A review,” IEEE J. Sel. Top. Quant. 5, 1205–1215 (1999).
[CrossRef]

1995

A. S. Glassner, Principles of Digital Image Synthesis, Volume Two, (Morgan Kauffman, 1995).

1953

1951

J. Yule and W. Neilsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of TAGA ,vol.  3 (1951), pp. 65–67.

1948

1941

L. G. Henyey and J. L. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Anderson, P.G.

J.S. Arney, J. Chauvin, J. Nauman, and P.G. Anderson, “Kubelka-Munk theory and the MTF of paper,” J. Imaging Sci. Techn.47, 339–345 (2003).

Arney, J.S.

J.S. Arney, J. Chauvin, J. Nauman, and P.G. Anderson, “Kubelka-Munk theory and the MTF of paper,” J. Imaging Sci. Techn.47, 339–345 (2003).

Béland, M.-C.

H. Granberg and M.-C. Béland, “Modelling the angle-dependent light scattering from sheets of pulp fiber fragments,” Nord. Pulp Pap. Res. J. 19, 354–359 (2004).
[CrossRef]

Chauvin, J.

J.S. Arney, J. Chauvin, J. Nauman, and P.G. Anderson, “Kubelka-Munk theory and the MTF of paper,” J. Imaging Sci. Techn.47, 339–345 (2003).

Clapper, F. R.

Coppel, L. G.

M. Neuman, L. G. Coppel, and P. Edström, “Point spreading in turbid media with anisotropic single scattering,” Opt. Express 19, 1915–1920 (2011).
[CrossRef] [PubMed]

L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H. Niskanen, and J. Hämäläinen, eds. (Kuopio, 2009).

Edström, P.

M. Neuman, L. G. Coppel, and P. Edström, “Point spreading in turbid media with anisotropic single scattering,” Opt. Express 19, 1915–1920 (2011).
[CrossRef] [PubMed]

M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. II. Measurements,” J. Opt. Soc. Am. A 27, 1040–1045 (2010).
[CrossRef]

P. Edström, “A two-phase parameter estimation method for radiative transfer problems in paper industry applications,” Inverse Probl. Sci. En. 16, 927–951 (2008).
[CrossRef]

P. Edström, “A fast and stable solution method for the radiative transfer problem,” SIAM Rev. 47, 447–468 (2005).
[CrossRef]

L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H. Niskanen, and J. Hämäläinen, eds. (Kuopio, 2009).

Emmel, P.

S. Mourad, P. Emmel, K. Simon, and R. D. Hersch, “Extending Kubelka-Munk’s theory with lateral light scattering,” in IS&T’s NIP17: International Conference on Digital Printing Technologies, Lauderdale, Florida, USA, (2001), pp. 469–473.

Glassner, A. S.

A. S. Glassner, Principles of Digital Image Synthesis, Volume Two, (Morgan Kauffman, 1995).

Granberg, H.

H. Granberg and M.-C. Béland, “Modelling the angle-dependent light scattering from sheets of pulp fiber fragments,” Nord. Pulp Pap. Res. J. 19, 354–359 (2004).
[CrossRef]

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Gustavson, S.

S. Gustavson, “Dot Gain in Colour Halftones,” Ph. D. thesis, Linköping university (1997).

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hersch, R. D.

R. D. Hersch, “Spectral prediction model for color prints on paper with fluorescent additives,” Appl. Opt. 47, 6710–6722 (2008).
[CrossRef] [PubMed]

S. Mourad, P. Emmel, K. Simon, and R. D. Hersch, “Extending Kubelka-Munk’s theory with lateral light scattering,” in IS&T’s NIP17: International Conference on Digital Printing Technologies, Lauderdale, Florida, USA, (2001), pp. 469–473.

Jenny, P.

Kubelka, P.

Lindquister, M.

L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H. Niskanen, and J. Hämäläinen, eds. (Kuopio, 2009).

Mourad, S.

M. Sormaz, T. Stamm, S. Mourad, and P. Jenny, “Stochastic modeling of light scattering with fluorescence using a Monte Carlo-based multiscale approach,” J. Opt. Soc. Am. A 26, 1403–1413 (2009).
[CrossRef]

S. Mourad, “Improved Calibration of Optical Characteristics of Paper by an Adapted Paper-MTF Model,” J. Imaging Sci. Techn. 51, 283–292 (2007).
[CrossRef]

S. Mourad, P. Emmel, K. Simon, and R. D. Hersch, “Extending Kubelka-Munk’s theory with lateral light scattering,” in IS&T’s NIP17: International Conference on Digital Printing Technologies, Lauderdale, Florida, USA, (2001), pp. 469–473.

Nauman, J.

J.S. Arney, J. Chauvin, J. Nauman, and P.G. Anderson, “Kubelka-Munk theory and the MTF of paper,” J. Imaging Sci. Techn.47, 339–345 (2003).

Neilsen, W.

J. Yule and W. Neilsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of TAGA ,vol.  3 (1951), pp. 65–67.

Neuman, M.

Oittinen, P.

P. Oittinen, “Limits of microscopic print quality,” in Advances in Printing Science and Technology, L. . W. H. Banks, ed. (Pentech, London, 1982), Vol. 16, pp. 121–128.

Schmitt, J. M.

J. M. Schmitt, “Optical coherence tomography (OCT): A review,” IEEE J. Sel. Top. Quant. 5, 1205–1215 (1999).
[CrossRef]

Simon, K.

S. Mourad, P. Emmel, K. Simon, and R. D. Hersch, “Extending Kubelka-Munk’s theory with lateral light scattering,” in IS&T’s NIP17: International Conference on Digital Printing Technologies, Lauderdale, Florida, USA, (2001), pp. 469–473.

Sormaz, M.

Stamm, T.

Ukishima, M.

M. Ukishima, “Prediction and evaluation of color halftone print quality based on microscopic measurement,” Ph.D. thesis, University of Eastern Finland (2010).

Williams, F. C.

Yang, L.

Yule, J.

J. Yule and W. Neilsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of TAGA ,vol.  3 (1951), pp. 65–67.

Appl. Opt.

Astrophys. J.

L. G. Henyey and J. L. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

IEEE J. Sel. Top. Quant.

J. M. Schmitt, “Optical coherence tomography (OCT): A review,” IEEE J. Sel. Top. Quant. 5, 1205–1215 (1999).
[CrossRef]

Inverse Probl. Sci. En.

P. Edström, “A two-phase parameter estimation method for radiative transfer problems in paper industry applications,” Inverse Probl. Sci. En. 16, 927–951 (2008).
[CrossRef]

IS&T’s NIP17: International Conference on Digital Printing Technologies, Lauderdale, Florida, USA

S. Mourad, P. Emmel, K. Simon, and R. D. Hersch, “Extending Kubelka-Munk’s theory with lateral light scattering,” in IS&T’s NIP17: International Conference on Digital Printing Technologies, Lauderdale, Florida, USA, (2001), pp. 469–473.

J. Imaging Sci. Techn.

S. Mourad, “Improved Calibration of Optical Characteristics of Paper by an Adapted Paper-MTF Model,” J. Imaging Sci. Techn. 51, 283–292 (2007).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nord. Pulp Pap. Res. J.

H. Granberg and M.-C. Béland, “Modelling the angle-dependent light scattering from sheets of pulp fiber fragments,” Nord. Pulp Pap. Res. J. 19, 354–359 (2004).
[CrossRef]

Opt. Express

Principles of Digital Image Synthesis

A. S. Glassner, Principles of Digital Image Synthesis, Volume Two, (Morgan Kauffman, 1995).

Proceedings of TAGA

J. Yule and W. Neilsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of TAGA ,vol.  3 (1951), pp. 65–67.

SIAM Rev.

P. Edström, “A fast and stable solution method for the radiative transfer problem,” SIAM Rev. 47, 447–468 (2005).
[CrossRef]

Other

L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H. Niskanen, and J. Hämäläinen, eds. (Kuopio, 2009).

S. Gustavson, “Dot Gain in Colour Halftones,” Ph. D. thesis, Linköping university (1997).

P. Oittinen, “Limits of microscopic print quality,” in Advances in Printing Science and Technology, L. . W. H. Banks, ed. (Pentech, London, 1982), Vol. 16, pp. 121–128.

M. Ukishima, “Prediction and evaluation of color halftone print quality based on microscopic measurement,” Ph.D. thesis, University of Eastern Finland (2010).

J.S. Arney, J. Chauvin, J. Nauman, and P.G. Anderson, “Kubelka-Munk theory and the MTF of paper,” J. Imaging Sci. Techn.47, 339–345 (2003).

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Figures (3)

Fig. 1
Fig. 1

(a) Simulated reflectance image. (b) Averaged edge response and its derivative, the LSF, here shown for sample 2 and 17. (c) Fourier transform of the LSF gives the MTF from which kp can be obtained.

Fig. 2
Fig. 2

Simulated kp versus kp obtained from Eq. (2), for single sheet (left) and opaque pad of sheets (right), and two values of the asymmetry factor g. The Arney value is close to the MC value for single sheets, and for opaque pads of sheets when kp is low. The asymmetry factor has a negligible impact, except for the single sheet samples with low S (and thus larger kp).

Fig. 3
Fig. 3

Simulated kp versus measured kp. Bold line shows a one to one relationship. The MC simulations underestimate kp.

Tables (1)

Tables Icon

Table 1 Sample type, thickness, and scattering and absorption coefficients determined for the three models used.

Equations (2)

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MTF ( w ) = 1 1 + 5.4 w / S .
k p = 5.4 S ,

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