Abstract

Point spreading is investigated using general radiative transfer theory. We find that the single scattering anisotropy plays a significant role for point spreading together with the medium mean free path, single scattering albedo and thickness. When forward scattering dominates, the light will on average undergo more scattering events to give a specific optical response in reflectance measurements. This will significantly increase point spreading if the medium is low absorbing with large mean free path. Any fundamental and generic model of point spreading must capture the dependence on all of these medium characteristics.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Oittinen, "Limits of microscopic print quality," in Advances in Printing Science and Technology, W. H. Banks, ed. (Pentech, London, 1982), Vol. 16, pp 121-128.
  2. P. Kubelka, and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).
  3. P. G. Engeldrum, and B. Pridham, "Application of turbid medium theory to paper spread function measurements," Tech. Assoc. Graphic Arts Proc. 47, 339-352 (1995).
  4. 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).
  5. S. Gustavson, "Dot Gain in Colour Halftones," Doctoral thesis, Linköping university (1997).
  6. P. Emmel, "Modèles de Prédiction Couleur Appliqués à l’Impression Jet d’Encre," Doctoral thesis, Ecole Polytechnique Fédérale de Lausanne (1998).
  7. S. Mourad, "Improved Calibration of Optical Characteristics of Paper by an Adapted Paper-MTF Model," J. Imaging Sci. Technol. 51, 283-292 (2007).
    [CrossRef]
  8. A. S. Glassner, Principles of Digital Image Synthesis, Vol. 2, (Morgan Kauffman, 1995).
  9. J. M. Schmitt, "Optical coherence tomography (OCT): A review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
    [CrossRef]
  10. S. Chandrasekhar, Radiative Transfer, (Dover, 1960).
  11. L. G. Henyey, and J. L. Greenstein, "Diffuse Radiation in the Galaxy," Astrophys. J. 93, 70-83 (1941).
    [CrossRef]
  12. W.-F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
    [CrossRef]
  13. S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, "Determining the optical properties of turbid media by using the adding-doubling method," Appl. Opt. 32, 559-568 (1993).
    [CrossRef] [PubMed]
  14. N. Joshi, C. Donner, and H. W. Jensen, "Noninvasive measurement of scattering anisotropy in turbid materials by nonnormal incident illumination," Opt. Lett. 31, 936-938 (2006).
    [CrossRef] [PubMed]
  15. P. Edström, "A fast and stable solution method for the radiative transfer problem," SIAM Rev. 47, 447-468 (2005).
    [CrossRef]
  16. 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).
  17. 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]
  18. T. F. Chen, G. V. G. Baranoski, and K. F. Lin, "Bulk scattering approximations for HeNe laser transmitted through paper," Opt. Express 16, 21762-21771 (2008).
    [CrossRef] [PubMed]
  19. M. Neuman, and P. Edström, "Anisotropic reflectance from turbid media. I. Theory," J. Opt. Soc. Am. A 27, 1032-1039 (2010).
    [CrossRef]
  20. M. Neuman, and P. Edström, "Anisotropic reflectance from turbid media. II. Measurements," J. Opt. Soc. Am. A 27, 1040-1045 (2010).
    [CrossRef]
  21. ISO 2469: Paper, Board and Pulps - Measurement of Diffuse Reflectance Factor, (International Organization for Standardization, 1994).
  22. P. Edström, "A Two-Phase Parameter Estimation Method for Radiative Transfer Problems in Paper Industry Applications," J. Comput. Appl. Math. 16, 927-951 (2008).

2010 (2)

M. Neuman, and P. Edström, "Anisotropic reflectance from turbid media. I. Theory," J. Opt. Soc. Am. A 27, 1032-1039 (2010).
[CrossRef]

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

2009 (1)

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]

2008 (2)

T. F. Chen, G. V. G. Baranoski, and K. F. Lin, "Bulk scattering approximations for HeNe laser transmitted through paper," Opt. Express 16, 21762-21771 (2008).
[CrossRef] [PubMed]

P. Edström, "A Two-Phase Parameter Estimation Method for Radiative Transfer Problems in Paper Industry Applications," J. Comput. Appl. Math. 16, 927-951 (2008).

2007 (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]

2006 (1)

N. Joshi, C. Donner, and H. W. Jensen, "Noninvasive measurement of scattering anisotropy in turbid materials by nonnormal incident illumination," Opt. Lett. 31, 936-938 (2006).
[CrossRef] [PubMed]

2005 (1)

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

2003 (1)

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).

1999 (1)

J. M. Schmitt, "Optical coherence tomography (OCT): A review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

1995 (1)

P. G. Engeldrum, and B. Pridham, "Application of turbid medium theory to paper spread function measurements," Tech. Assoc. Graphic Arts Proc. 47, 339-352 (1995).

1993 (1)

S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, "Determining the optical properties of turbid media by using the adding-doubling method," Appl. Opt. 32, 559-568 (1993).
[CrossRef] [PubMed]

1990 (1)

W.-F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

1941 (1)

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

1931 (1)

P. Kubelka, and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).

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, 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).

Baranoski, G. V. G.

T. F. Chen, G. V. G. Baranoski, and K. F. Lin, "Bulk scattering approximations for HeNe laser transmitted through paper," Opt. Express 16, 21762-21771 (2008).
[CrossRef] [PubMed]

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).

Chen, T. F.

T. F. Chen, G. V. G. Baranoski, and K. F. Lin, "Bulk scattering approximations for HeNe laser transmitted through paper," Opt. Express 16, 21762-21771 (2008).
[CrossRef] [PubMed]

Cheong, W.-F.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Donner, C.

N. Joshi, C. Donner, and H. W. Jensen, "Noninvasive measurement of scattering anisotropy in turbid materials by nonnormal incident illumination," Opt. Lett. 31, 936-938 (2006).
[CrossRef] [PubMed]

Edström, P.

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

M. Neuman, and P. Edström, "Anisotropic reflectance from turbid media. I. Theory," J. Opt. Soc. Am. A 27, 1032-1039 (2010).
[CrossRef]

P. Edström, "A Two-Phase Parameter Estimation Method for Radiative Transfer Problems in Paper Industry Applications," J. Comput. Appl. Math. 16, 927-951 (2008).

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

Engeldrum, P. G.

P. G. Engeldrum, and B. Pridham, "Application of turbid medium theory to paper spread function measurements," Tech. Assoc. Graphic Arts Proc. 47, 339-352 (1995).

Greenstein, J. L.

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

Henyey, L. G.

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

Jenny, P.

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]

Jensen, H. W.

N. Joshi, C. Donner, and H. W. Jensen, "Noninvasive measurement of scattering anisotropy in turbid materials by nonnormal incident illumination," Opt. Lett. 31, 936-938 (2006).
[CrossRef] [PubMed]

Joshi, N.

N. Joshi, C. Donner, and H. W. Jensen, "Noninvasive measurement of scattering anisotropy in turbid materials by nonnormal incident illumination," Opt. Lett. 31, 936-938 (2006).
[CrossRef] [PubMed]

Kubelka, P.

P. Kubelka, and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).

Lin, K. F.

T. F. Chen, G. V. G. Baranoski, and K. F. Lin, "Bulk scattering approximations for HeNe laser transmitted through paper," Opt. Express 16, 21762-21771 (2008).
[CrossRef] [PubMed]

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. Technol. 51, 283-292 (2007).
[CrossRef]

Munk, F.

P. Kubelka, and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).

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.

M. Neuman, and P. Edström, "Anisotropic reflectance from turbid media. I. Theory," J. Opt. Soc. Am. A 27, 1032-1039 (2010).
[CrossRef]

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

Prahl, S. A.

S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, "Determining the optical properties of turbid media by using the adding-doubling method," Appl. Opt. 32, 559-568 (1993).
[CrossRef] [PubMed]

W.-F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Pridham, B.

P. G. Engeldrum, and B. Pridham, "Application of turbid medium theory to paper spread function measurements," Tech. Assoc. Graphic Arts Proc. 47, 339-352 (1995).

Schmitt, J. M.

J. M. Schmitt, "Optical coherence tomography (OCT): A review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

Sormaz, M.

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]

Stamm, T.

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]

van Gemert, M. J. C.

S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, "Determining the optical properties of turbid media by using the adding-doubling method," Appl. Opt. 32, 559-568 (1993).
[CrossRef] [PubMed]

Welch, A. J.

S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, "Determining the optical properties of turbid media by using the adding-doubling method," Appl. Opt. 32, 559-568 (1993).
[CrossRef] [PubMed]

W.-F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Appl. Opt. (1)

S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, "Determining the optical properties of turbid media by using the adding-doubling method," Appl. Opt. 32, 559-568 (1993).
[CrossRef] [PubMed]

Astrophys. J. (1)

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

IEEE J. Quantum Electron. (1)

W.-F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. M. Schmitt, "Optical coherence tomography (OCT): A review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

J. Comput. Appl. Math. (1)

P. Edström, "A Two-Phase Parameter Estimation Method for Radiative Transfer Problems in Paper Industry Applications," J. Comput. Appl. Math. 16, 927-951 (2008).

J. Imaging Sci. Technol. (2)

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. 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).

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

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]

M. Neuman, and P. Edström, "Anisotropic reflectance from turbid media. I. Theory," J. Opt. Soc. Am. A 27, 1032-1039 (2010).
[CrossRef]

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

Opt. Express (1)

T. F. Chen, G. V. G. Baranoski, and K. F. Lin, "Bulk scattering approximations for HeNe laser transmitted through paper," Opt. Express 16, 21762-21771 (2008).
[CrossRef] [PubMed]

Opt. Lett. (1)

N. Joshi, C. Donner, and H. W. Jensen, "Noninvasive measurement of scattering anisotropy in turbid materials by nonnormal incident illumination," Opt. Lett. 31, 936-938 (2006).
[CrossRef] [PubMed]

SIAM Rev. (1)

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

Tech. Assoc. Graphic Arts Proc. (1)

P. G. Engeldrum, and B. Pridham, "Application of turbid medium theory to paper spread function measurements," Tech. Assoc. Graphic Arts Proc. 47, 339-352 (1995).

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

P. Kubelka, and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).

Other (7)

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

S. Gustavson, "Dot Gain in Colour Halftones," Doctoral thesis, Linköping university (1997).

P. Emmel, "Modèles de Prédiction Couleur Appliqués à l’Impression Jet d’Encre," Doctoral thesis, Ecole Polytechnique Fédérale de Lausanne (1998).

A. S. Glassner, Principles of Digital Image Synthesis, Vol. 2, (Morgan Kauffman, 1995).

S. Chandrasekhar, Radiative Transfer, (Dover, 1960).

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).

ISO 2469: Paper, Board and Pulps - Measurement of Diffuse Reflectance Factor, (International Organization for Standardization, 1994).

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 (2)

Fig. 1
Fig. 1

Point spreading as represented by for two thicknesses of media M1–4 when g is varied. Point spreading increases with g for all media. M1 (high albedo and large mean free path) has the largest point spreading and the most noticeable difference when varying the thickness. M4 (low albedo and short mean free path) has the smallest point spreading.

Fig. 2
Fig. 2

The mean number of scattering events that the wave packets undergo before exiting the medium. We see that the asymmetry factor g affects the number of scattering events, and that increasing the albedo leads to more scattering events in opaque media.

Tables (1)

Tables Icon

Table 1 Albedo (a) and mean free path (e) of the media at 620 nm obtained from d/0 measurements when the asymmetry factor g is varied. Parameters here are used in the Monte Carlo simulations

Equations (5)

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

D ( x , y ) = Δ v Δ u P S F ( x , y ; u , v ) I ( u , v ) d u d v
d I ( x , y , z ; θ , φ ) d s = σ e [ I ( x , y , z ; θ , φ ) + S ] .
S = a 4 π 4 π p ( cos Θ ) I ( x , y , z ; θ , φ ) d ω ,
r ¯ = [ i P S F ( r i ) ] 1 i r i P S F ( r i ) .
P S F ( r ) = i α i exp ( β i r )

Metrics