Abstract

An experimental set-up was devised to record the transmission of red and green HeNe lasers through different types of paper. The measured data was compared with data obtained using the Henyey-Greenstein function (often employed in paper optics models to represent the bulk scattering of material samples) and data obtained using an alternative exponentiated cosine function. The comparisons are used to qualitatively assess the degree of fidelity of the bulk scattering approximations provided by both functions.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Casey, Pulp and Paper, 2nd ed. (Interscience Publishers, Inc., New York, 1961) Vol. 3,.
  2. A. Oksman, R. Silvennoinen, K. Peiponen, M. Avikainen, and H. Komulainen, "Reflectance study of compressed paper," Appl. Spectrosc. 58, 481-485 (2004).
    [CrossRef]
  3. T. Lettieri, E. Marx, J. Song, and T. Vorburger, "Light scattering from glossy coatings on paper," Appl. Opt. 30, 4439 (1991).
    [CrossRef] [PubMed]
  4. K. Green, L. Lamberg, and K. Lumme, "Stochastic modeling of paper structure and Monte Carlo simulation of light scattering," Appl. Opt. 39, 4669-4683 (2000).
    [CrossRef]
  5. J. Carlsson, A. Persson, W. Persson, C. Wahlstrom, P. Hellentin, and L. Malmqvist, "Time-resolved studies of light propagation in paper," Appl. Opt. 34, 1528 (1995).
    [CrossRef] [PubMed]
  6. P. Edstrom, "Comparison of the DORT2002 radiative transfer solution method and the Kubelka-Munk model," Nordic Pulp and Paper Research Journal 19, 397-403 (2004).
    [CrossRef]
  7. W. Bruls and J. van der Leun, "Forward scattering properties of human epidermal layers," Photochemistry and Photobiology 40, 231-242 (1984).
    [CrossRef] [PubMed]
  8. L. Henyey and J. Greenstein, "Diffuse radiation in galaxy," Astrophys. J. 93, 70-83 (1941).
    [CrossRef]
  9. S. Jacques, C. Alter, and S. Prahl, "Angular dependence of HeNe laser light scattering by human dermis," Lasers Life Sci. 1, 309-333 (1987).
  10. S. Prahl, M. Keijzer, S. Jacques, and A. Welch, "A Monte Carlo model of light propagation in tissue," SPIE Institute Series IS 5, 102-111 (1989).
  11. J. Hammerley and D. Handscomb, Monte Carlo Methods (Wiley, New York, 1964).
    [CrossRef]
  12. M. Neuman, "Anisotropic reflectance from paper - measurements, simulations and analysis," Master’s thesis, Department of Physics, UMEA University (2005).
  13. M. B’eland and J. M. Bennett, "Effect of local microroughness on the gloss uniformity of printed paper surfaces," Appl. Opt. 39, 2719-2726 (2000).
    [CrossRef]
  14. J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, Inc., 1990).
  15. G. Baranoski and J. Rokne, Light Interaction with Plants: A Computer Graphics Perspective (Horwood Publishing, Chichester, UK, 2004).
  16. G. Baranoski, A. Krishnaswamy, and B. Kimmel, "Increasing the predictability of tissue subsurface scattering simulations," The Visual Computer 21, 265-278 (2005).
    [CrossRef]
  17. E. Lafortune and Y. D. Willems, "Using the modified Phong reflectance model for physically based rendering," Tech. Rep., Department of Computer Science, K. U. Leuven (1994).
  18. P. Edstrom, "Fast and stable solution method for angle-resolved light scattering simulation," Tech. Rep. R-02 35, Mid Sweden University (2002).
  19. A. Krishnaswamy, G. Baranoski, and J. Rokne, "Improving the reliability/cost ratio of goniophotometric comparisons," Journal of Graphics Tools 9, 1-20 (2004).
  20. M. Spiegel, Schaum’s Outline of Theory and Problems of Statistics, 2nd ed. (McGraw-Hill, Inc., 1991).

2005 (1)

G. Baranoski, A. Krishnaswamy, and B. Kimmel, "Increasing the predictability of tissue subsurface scattering simulations," The Visual Computer 21, 265-278 (2005).
[CrossRef]

2004 (3)

A. Krishnaswamy, G. Baranoski, and J. Rokne, "Improving the reliability/cost ratio of goniophotometric comparisons," Journal of Graphics Tools 9, 1-20 (2004).

A. Oksman, R. Silvennoinen, K. Peiponen, M. Avikainen, and H. Komulainen, "Reflectance study of compressed paper," Appl. Spectrosc. 58, 481-485 (2004).
[CrossRef]

P. Edstrom, "Comparison of the DORT2002 radiative transfer solution method and the Kubelka-Munk model," Nordic Pulp and Paper Research Journal 19, 397-403 (2004).
[CrossRef]

2000 (2)

1995 (1)

1991 (1)

1989 (1)

S. Prahl, M. Keijzer, S. Jacques, and A. Welch, "A Monte Carlo model of light propagation in tissue," SPIE Institute Series IS 5, 102-111 (1989).

1987 (1)

S. Jacques, C. Alter, and S. Prahl, "Angular dependence of HeNe laser light scattering by human dermis," Lasers Life Sci. 1, 309-333 (1987).

1984 (1)

W. Bruls and J. van der Leun, "Forward scattering properties of human epidermal layers," Photochemistry and Photobiology 40, 231-242 (1984).
[CrossRef] [PubMed]

1941 (1)

L. Henyey and J. Greenstein, "Diffuse radiation in galaxy," Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Alter, C.

S. Jacques, C. Alter, and S. Prahl, "Angular dependence of HeNe laser light scattering by human dermis," Lasers Life Sci. 1, 309-333 (1987).

Avikainen, M.

Baranoski, G.

G. Baranoski, A. Krishnaswamy, and B. Kimmel, "Increasing the predictability of tissue subsurface scattering simulations," The Visual Computer 21, 265-278 (2005).
[CrossRef]

A. Krishnaswamy, G. Baranoski, and J. Rokne, "Improving the reliability/cost ratio of goniophotometric comparisons," Journal of Graphics Tools 9, 1-20 (2004).

Bruls, W.

W. Bruls and J. van der Leun, "Forward scattering properties of human epidermal layers," Photochemistry and Photobiology 40, 231-242 (1984).
[CrossRef] [PubMed]

Carlsson, J.

Edstr¨om, P.

P. Edstrom, "Comparison of the DORT2002 radiative transfer solution method and the Kubelka-Munk model," Nordic Pulp and Paper Research Journal 19, 397-403 (2004).
[CrossRef]

Green, K.

Greenstein, J.

L. Henyey and J. Greenstein, "Diffuse radiation in galaxy," Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Hellentin, P.

Henyey, L.

L. Henyey and J. Greenstein, "Diffuse radiation in galaxy," Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Jacques, S.

S. Prahl, M. Keijzer, S. Jacques, and A. Welch, "A Monte Carlo model of light propagation in tissue," SPIE Institute Series IS 5, 102-111 (1989).

S. Jacques, C. Alter, and S. Prahl, "Angular dependence of HeNe laser light scattering by human dermis," Lasers Life Sci. 1, 309-333 (1987).

Keijzer, M.

S. Prahl, M. Keijzer, S. Jacques, and A. Welch, "A Monte Carlo model of light propagation in tissue," SPIE Institute Series IS 5, 102-111 (1989).

Kimmel, B.

G. Baranoski, A. Krishnaswamy, and B. Kimmel, "Increasing the predictability of tissue subsurface scattering simulations," The Visual Computer 21, 265-278 (2005).
[CrossRef]

Komulainen, H.

Krishnaswamy, A.

G. Baranoski, A. Krishnaswamy, and B. Kimmel, "Increasing the predictability of tissue subsurface scattering simulations," The Visual Computer 21, 265-278 (2005).
[CrossRef]

A. Krishnaswamy, G. Baranoski, and J. Rokne, "Improving the reliability/cost ratio of goniophotometric comparisons," Journal of Graphics Tools 9, 1-20 (2004).

Lamberg, L.

Lettieri, T.

Lumme, K.

Malmqvist, L.

Marx, E.

Oksman, A.

Peiponen, K.

Persson, A.

Persson, W.

Prahl, S.

S. Prahl, M. Keijzer, S. Jacques, and A. Welch, "A Monte Carlo model of light propagation in tissue," SPIE Institute Series IS 5, 102-111 (1989).

S. Jacques, C. Alter, and S. Prahl, "Angular dependence of HeNe laser light scattering by human dermis," Lasers Life Sci. 1, 309-333 (1987).

Rokne, J.

A. Krishnaswamy, G. Baranoski, and J. Rokne, "Improving the reliability/cost ratio of goniophotometric comparisons," Journal of Graphics Tools 9, 1-20 (2004).

Silvennoinen, R.

Song, J.

van der Leun, J.

W. Bruls and J. van der Leun, "Forward scattering properties of human epidermal layers," Photochemistry and Photobiology 40, 231-242 (1984).
[CrossRef] [PubMed]

Vorburger, T.

Wahlstrom, C.

Welch, A.

S. Prahl, M. Keijzer, S. Jacques, and A. Welch, "A Monte Carlo model of light propagation in tissue," SPIE Institute Series IS 5, 102-111 (1989).

Appl. Opt. (4)

Appl. Spectrosc. (1)

Astrophys. J. (1)

L. Henyey and J. Greenstein, "Diffuse radiation in galaxy," Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Journal of Graphics Tools (1)

A. Krishnaswamy, G. Baranoski, and J. Rokne, "Improving the reliability/cost ratio of goniophotometric comparisons," Journal of Graphics Tools 9, 1-20 (2004).

Lasers Life Sci. (1)

S. Jacques, C. Alter, and S. Prahl, "Angular dependence of HeNe laser light scattering by human dermis," Lasers Life Sci. 1, 309-333 (1987).

Nordic Pulp and Paper Research Journal (1)

P. Edstrom, "Comparison of the DORT2002 radiative transfer solution method and the Kubelka-Munk model," Nordic Pulp and Paper Research Journal 19, 397-403 (2004).
[CrossRef]

Photochemistry and Photobiology (1)

W. Bruls and J. van der Leun, "Forward scattering properties of human epidermal layers," Photochemistry and Photobiology 40, 231-242 (1984).
[CrossRef] [PubMed]

SPIE Institute Series IS (1)

S. Prahl, M. Keijzer, S. Jacques, and A. Welch, "A Monte Carlo model of light propagation in tissue," SPIE Institute Series IS 5, 102-111 (1989).

The Visual Computer (1)

G. Baranoski, A. Krishnaswamy, and B. Kimmel, "Increasing the predictability of tissue subsurface scattering simulations," The Visual Computer 21, 265-278 (2005).
[CrossRef]

Other (8)

E. Lafortune and Y. D. Willems, "Using the modified Phong reflectance model for physically based rendering," Tech. Rep., Department of Computer Science, K. U. Leuven (1994).

P. Edstrom, "Fast and stable solution method for angle-resolved light scattering simulation," Tech. Rep. R-02 35, Mid Sweden University (2002).

J. Hammerley and D. Handscomb, Monte Carlo Methods (Wiley, New York, 1964).
[CrossRef]

M. Neuman, "Anisotropic reflectance from paper - measurements, simulations and analysis," Master’s thesis, Department of Physics, UMEA University (2005).

J. Casey, Pulp and Paper, 2nd ed. (Interscience Publishers, Inc., New York, 1961) Vol. 3,.

J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, Inc., 1990).

G. Baranoski and J. Rokne, Light Interaction with Plants: A Computer Graphics Perspective (Horwood Publishing, Chichester, UK, 2004).

M. Spiegel, Schaum’s Outline of Theory and Problems of Statistics, 2nd ed. (McGraw-Hill, Inc., 1991).

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 (7)

Fig. 1.
Fig. 1.

Sketch of the physical measurement set-up used to collect the scattering data used in this investigation.

Fig. 2.
Fig. 2.

Normalized intensity profiles of the paper samples using the red HeNe laser (633 nm). Top left: lined paper. Top right: printer paper. Bottom left: sketch paper. Bottom right: water paper. The dashed lines indicate the beginning of region of interest, and each data set is normalized to the maximum in the region. The distance is given in terms of the number of pixels between the position and the center of the laser beam in the image.

Fig. 3.
Fig. 3.

Normalized intensity profiles of the paper samples using the green HeNe laser (543 nm). Top left: lined paper. Top right: printer paper. Bottom left: sketch paper. Bottom right: water paper. The dashed lines indicate the beginning of region of interest, and each data set is normalized to the maximum in the region. The distance is given in terms of the number of pixels between the position and the center of the laser beam in the image.

Fig. 4.
Fig. 4.

Comparison of measured data using the red HeNe laser (633 nm) and simulated scattering profiles obtained using the HGWF and ECWF. Top left: lined paper. Top right: printer paper. Bottom left: sketch paper. Bottom right: water paper.

Fig. 5.
Fig. 5.

Comparison of measured data using the green HeNe laser (543 nm) and simulated scattering profiles obtained using the HGWF and ECWF. Top left: lined paper. Top right: printer paper. Bottom left: sketch paper. Bottom right: water paper.

Fig. 6.
Fig. 6.

Comparison of orthogonal projections of the actual data using the red HeNe laser (633 nm) and simulated scattering profiles obtained using the HGWF and ECWF. First row: lined paper. Second row: Printer paper. Third row: Sketch paper. Fourth row: Water paper.

Fig. 7.
Fig. 7.

Comparison of orthogonal projections of the actual data using the green HeNe laser (543 nm) and simulated scattering profiles obtained using the HGWF and ECWF. First row: lined paper. Second row: Printer paper. Third row: Sketch paper. Fourth row: Water paper.

Tables (2)

Tables Icon

Table 1. RMS errors associated with the approximations for the red HeNe laser (633 nm) corresponding to plots in Figs. 4 and 6.

Tables Icon

Table 2. RMS errors associated with the approximations for the green HeNe laser (543 nm) corresponding to plots in Figs. 5 and 7.

Equations (5)

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

Γ HG ( g , θ ) = 1 g 2 ( 1 + g 2 2 g cos θ ) 3 2 ,
θ = cos 1 ( 1 2 g [ 1 + g 2 { 1 g 2 1 + g 2 g ξ 1 } 2 ] ) .
Γ EC ( n , θ ) = n + 1 2 π cos n θ ,
θ = cos 1 ( ( 1 ξ 1 ) 1 n + 1 ) .
ϕ = 2 π ξ 2 .

Metrics