Abstract

Lateral light scattering in fibrous media is investigated by computing the modulation transfer function (MTF) of 22 paper samples using a Monte Carlo model. The simulation tool uses phase functions from infinitely long homogenous cylinders and the directional inhomogeneity of paper is achieved by aligning the cylinders in the plane. The inverse frequency at half maximum of the MTF is compared to both measurements and previous simulations with isotropic and strongly forward single scattering phase functions. It is found that the conical scattering by cylinders enhances the lateral scattering and therefore predicts a larger extent of lateral light scattering than models using rotationally invariant single scattering phase functions. However, it does not fully reach the levels of lateral scattering observed in measurements. It is argued that the hollow lumen of a wood fiber or dependent scattering effects must be considered for a complete description of lateral light scattering in paper.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proceedings of TAGA3, 65–67 (1951).
  2. T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Pap. Res. J.27, 500–506 (2012).
    [CrossRef]
  3. M. Neuman, L. G. Coppel, and P. Edstrom, “Point spreading in turbid media with anisotropic single scattering,” Opt. Express19, 1915–1920 (2011).
    [CrossRef] [PubMed]
  4. J. Arney, C. Arney, M. Katsube, and P. Engeldrum, “An MTF analysis of papers,” J. Imaging Sci. Technol.40, 19–25 (1996).
  5. J. S. Arney, J. Chauvin, J. Nauman, and P. G. Anderson, “Kubelka-Munk theory and the MTF of paper,” J. Imaging Sci. Technol.47, 339–345 (2003).
  6. L. G. Coppel, M. Neuman, and P. Edström, “Lateral light scattering in paper - MTF simulation and measurement,” Opt. Express19, 25181–25187 (2011).
    [CrossRef]
  7. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, 1983).
  8. A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol.48, N7–N14 (2003).
    [CrossRef] [PubMed]
  9. A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett.29, 2617–2619 (2004).
    [CrossRef] [PubMed]
  10. H. He, N. Zeng, R. Liao, T. Yun, W. Li, Y. He, and H. Ma, “Application of sphere-cylinder scattering model to skeletal muscle,” Opt. Express18, 15104–15112 (2010).
    [CrossRef] [PubMed]
  11. A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
    [CrossRef] [PubMed]
  12. A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express16, 9895–9906 (2008).
    [CrossRef] [PubMed]
  13. B. Peng, T. Ding, and P. Wang, “Propagation of polarized light through textile material,” Appl. Opt.51, 6325–6334 (2012).
    [CrossRef] [PubMed]
  14. T. Yun, N. Zeng, W. Li, D. Li, X. Jiang, and H. Ma, “Monte Carlo simulation of polarized photon scattering in anisotropic media,” Opt. Express17, 16590–16602 (2009).
    [CrossRef] [PubMed]
  15. C. Fellers and B. Norman, Pappersteknik, 3rd ed. (Department of Pulp and Paper Chemistry and Technology, Royal Institute of Technology, 1996).
  16. M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

2012

T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Pap. Res. J.27, 500–506 (2012).
[CrossRef]

B. Peng, T. Ding, and P. Wang, “Propagation of polarized light through textile material,” Appl. Opt.51, 6325–6334 (2012).
[CrossRef] [PubMed]

2011

2010

2009

2008

2007

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
[CrossRef] [PubMed]

2004

2003

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol.48, N7–N14 (2003).
[CrossRef] [PubMed]

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

1996

J. Arney, C. Arney, M. Katsube, and P. Engeldrum, “An MTF analysis of papers,” J. Imaging Sci. Technol.40, 19–25 (1996).

1951

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proceedings of TAGA3, 65–67 (1951).

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. Technol.47, 339–345 (2003).

Arney, C.

J. Arney, C. Arney, M. Katsube, and P. Engeldrum, “An MTF analysis of papers,” J. Imaging Sci. Technol.40, 19–25 (1996).

Arney, J.

J. Arney, C. Arney, M. Katsube, and P. Engeldrum, “An MTF analysis of papers,” J. Imaging Sci. Technol.40, 19–25 (1996).

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. Technol.47, 339–345 (2003).

Bassi, A.

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, 1983).

Chauvin, J.

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

Comelli, D.

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
[CrossRef] [PubMed]

Coppel, L. G.

D’Andrea, C.

Diebolder, R.

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol.48, N7–N14 (2003).
[CrossRef] [PubMed]

Ding, T.

Edstrom, P.

Edström, P.

Engeldrum, P.

J. Arney, C. Arney, M. Katsube, and P. Engeldrum, “An MTF analysis of papers,” J. Imaging Sci. Technol.40, 19–25 (1996).

Fellers, C.

C. Fellers and B. Norman, Pappersteknik, 3rd ed. (Department of Pulp and Paper Chemistry and Technology, Royal Institute of Technology, 1996).

Forster, F. K.

A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett.29, 2617–2619 (2004).
[CrossRef] [PubMed]

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol.48, N7–N14 (2003).
[CrossRef] [PubMed]

Foschum, F.

Hauta-Kasari, M.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

He, H.

He, Y.

Hibst, R.

A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett.29, 2617–2619 (2004).
[CrossRef] [PubMed]

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol.48, N7–N14 (2003).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, 1983).

Jiang, X.

Kaneko, H.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

Katsube, M.

J. Arney, C. Arney, M. Katsube, and P. Engeldrum, “An MTF analysis of papers,” J. Imaging Sci. Technol.40, 19–25 (1996).

Kienle, A.

A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express16, 9895–9906 (2008).
[CrossRef] [PubMed]

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
[CrossRef] [PubMed]

A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett.29, 2617–2619 (2004).
[CrossRef] [PubMed]

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol.48, N7–N14 (2003).
[CrossRef] [PubMed]

Li, D.

Li, W.

Liao, R.

Linder, T.

T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Pap. Res. J.27, 500–506 (2012).
[CrossRef]

Löfqvist, T.

T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Pap. Res. J.27, 500–506 (2012).
[CrossRef]

Ma, H.

Miyake, Y.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

Nakaguchi, T.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

Nauman, J.

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

Neuman, M.

Nielsen, W. J.

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proceedings of TAGA3, 65–67 (1951).

Norman, B.

C. Fellers and B. Norman, Pappersteknik, 3rd ed. (Department of Pulp and Paper Chemistry and Technology, Royal Institute of Technology, 1996).

Parkkinen, J.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

Peng, B.

Pifferi, A.

A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express16, 9895–9906 (2008).
[CrossRef] [PubMed]

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
[CrossRef] [PubMed]

Taroni, P.

A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express16, 9895–9906 (2008).
[CrossRef] [PubMed]

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
[CrossRef] [PubMed]

Tsumura, N.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

Ukishima, M.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

Wang, P.

Wetzel, C.

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
[CrossRef] [PubMed]

Yule, J. A. C.

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proceedings of TAGA3, 65–67 (1951).

Yun, T.

Zeng, N.

Appl. Opt.

IEICE Trans. Fundam. Electron. Commun. Comput. Sci.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A Simple Method to Measure MTF of Paper and Its Application for Dot Gain Analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.E92A, 3328–3335.

J. Biomed. Opt.

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12 (2007).
[CrossRef] [PubMed]

J. Imaging Sci. Technol.

J. Arney, C. Arney, M. Katsube, and P. Engeldrum, “An MTF analysis of papers,” J. Imaging Sci. Technol.40, 19–25 (1996).

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

Nord. Pulp Pap. Res. J.

T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Pap. Res. J.27, 500–506 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol.48, N7–N14 (2003).
[CrossRef] [PubMed]

Proceedings of TAGA

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Proceedings of TAGA3, 65–67 (1951).

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, 1983).

C. Fellers and B. Norman, Pappersteknik, 3rd ed. (Department of Pulp and Paper Chemistry and Technology, Royal Institute of Technology, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Simulated ESF and corresponding LSF in (a) and simulated MTFs for single paper sheet sample 2 in (b) and sample 17 in (c). The main difference between the samples is that sample 17 has a about four times larger scattering coefficient compared to sample 2. The red dots indicate the measured value of kp presented by Arney et al.

Fig. 2
Fig. 2

Measured values of kp versus simulated values for a single sheet (a) and an opaque pad of sheets (b).

Fig. 3
Fig. 3

Measured and simulated values of kp for a single paper sheet (a) and an opaque pad of paper sheets (b) plotted against the density of cylinders Ca.

Tables (1)

Tables Icon

Table 1 Sample thickness t, cylinder density Ca, scattering coefficient μs(), absorption coefficient μa and simulated values of kp for a single sheet and an opaque pad ( k p ).

Equations (3)

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

μ s ( ζ ) = C a d Q s ( ζ ) .
E S F ( x , y ) = P S F ( x , y ) * i ( x , y ) .
M T F ( 1 k p ) = 0.5.

Metrics