Abstract

Subsurface light transport can affect the visual appearance of materials significantly. Measuring and modeling this phenomenon is crucial for accurately reproducing colors in printing or for rendering translucent objects on displays. In this paper, we propose an apparatus to measure subsurface light transport employing a reference material to cancel out adverse signals that may bias the results. In contrast to other approaches, the setup enables improved focusing on rough surfaces (e.g. uncoated paper). We derive a measurement equation that may be used to deduce the point spread function (PSF) of subsurface light transport. Main contributions are the usage of spectrally-narrowband exchangeable LEDs allowing spectrally-resolved measurements and an approach based on quadratic programming for reconstructing PSFs in the case of isotropic light transport.

© 2014 Optical Society of America

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  1. J. A. C. Yule, W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Tech. Assn. Graphic Arts, 4, 65–76 (1951).
  2. G. L. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41(6), 643–656 (1997).
  3. G. Rogers, “Optical dot gain: lateral scattering probabilities,” J. Imaging Sci. Technol. 42(4), 341–345 (1998).
  4. J. S. Arney, T. Wu, C. Blehm, “Modeling the Yule-Nielsen Effect on Color Halftones,” J. Imaging Sci. Technol. 42(4), 335–340 (1998).
  5. J. A. S. Viggiano, “New models for the reflectance spectra produced by halftone-based hardcopy,” Ph.D. thesis, Center for Imaging Science, Rochester Institute of Technology, Rochester, NY, USA (2010).
  6. M. Hašan, M. Fuchs, W. Matusik, H. Pfister, S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graphics 29, 61 (2010).
    [CrossRef]
  7. Y. Dong, J. Wang, F. Pellacini, X. Tong, B. Guo, “Fabricating spatially-varying subsurface scattering,” ACM Trans. Graphics 29, 62 (2010).
    [CrossRef]
  8. M. Goesele, H. Lensch, J. Lang, C. Fuchs, H. Seidel, “Disco: acquisition of translucent objects,” ACM Trans. Graphics 23, 835–844 (2004).
    [CrossRef]
  9. X. Tong, J. Wang, S. Lin, B. Guo, H. Shum, “Modeling and rendering of quasi-homogeneous materials,” ACM Trans. Graphics 24, 1054–1061 (2005).
    [CrossRef]
  10. P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
    [CrossRef]
  11. J. Yule, D. Howe, J. Altman, “The Effect of the Spread-Function of Paper on Halftone Reproduction,” TAPPI Journal 7, 337–344 (1967).
  12. P. G. Engeldrum, B. Pridham, “Application of turbid medium theory to paper spread function measurements,” TAGA Proceedings 1, 339–352 (1995).
  13. C. Ackermann, H. Praast, L. Göttsching, “Einfluss von Lichtstreuung und Lichtabsorption auf die Bildwiedergabe gedruckter Rasterflächen,” Tech. Rep. 12395N, AiF (2002).
  14. H. Wakeshima, T. Kunishi, “Light scattering in paper and its effect on halftone reproduction,” J. Opt. Soc. Am. 58(2), 272–273 (1968).
    [CrossRef]
  15. S. Inoue, N. Tsumura, Y. Miyake, “Measuring mtf of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41(6), 657–661 (1997).
  16. G. L. Rogers, “Measurement of the modulation transfer function of paper,” Appl. Opt. 37, 7235–7240 (1998).
    [CrossRef]
  17. J. Arney, C. D. Arney, M. Katsube, P. G. Engeldrum, “An mtf analysis of papers,” J. Imaging Sci. Technol. 40, 19–25 (1996).
  18. K. Happel, M. Walter, P. Urban, E. Dörsam, “Measuring anisotropic light scatter within graphic arts papers for modeling optical dot gain,” “IS&T/SID, 18th Color and Imaging Conference,” San Antonio, Texas, 347–352 (2010).
  19. M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
    [CrossRef]
  20. M. Walter, “Methode zur Messung orthotroper Lichtstreuung in grafischen Papieren,” Master’s thesis, Technische Universität Darmstadt (2009).
  21. K. Happel, “Led-based light scattering measurements of papers for printing applications,” Ph.D. thesis, Technische Universität Darmstadt, Germany (2011).
  22. E. S. 1288, “Standard for Characterization of Image Sensors and Cameras,” European Machine Vision Association (2010).
  23. K. Happel, P. Urban, E. Dörsam, X. Ludewig, “Classifying Papers According to their Light Scatter Properties,” “Midterm Meeting of the International Colour Association (AIC),” Zurich, Switzerland, 138–141 (2011).
  24. B. Jähne, Digital Image Processing, 6 (Springer, 2005).
  25. F. Berg, “Isotrope Lichtstreuung in Papier - Neue Überlegungen zur Kubelka-Munk-Theorie,” Ph.D. thesis, Technische Hochschule Darmstadt (1997).
  26. F. Ruckdeschel, O. Hauser, “Yule-nielsen effect in printing: a physical analysis,” Applied Optics, 17, 3376–3383 (1978).
    [CrossRef] [PubMed]
  27. G. Fischer, J. Rodriguez-Giles, K. R. Scheuter, “Ein physikalisches modell für die beschreibung von licht-streuprozessen,” Die Farbe 30, 199–220 (1982).
  28. S. Gustavson, “Dot gain in colour halftones,” Ph.D. thesis, Sweden (1997).
  29. F. P. Callahan, “Light scattering in halftone prints,” J. Opt. Soc. Am. 42(2), 104–105 (1952).
    [CrossRef]
  30. A. Murray, “Monochrome reproduction in photoengraving,” Journal of the Franklin Institute, 221, 721–744 (1936).
    [CrossRef]
  31. J. Viggiano, “The Color of Halftone Tints,” in “TAGA Proceedings,” 647–661 (1985).
  32. E. Marchand, “Derivation of the point spread function from the line spread function,” J. Opt. Soc. Am. 54(7), 915–919 (1964).
    [CrossRef]

2010 (2)

M. Hašan, M. Fuchs, W. Matusik, H. Pfister, S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graphics 29, 61 (2010).
[CrossRef]

Y. Dong, J. Wang, F. Pellacini, X. Tong, B. Guo, “Fabricating spatially-varying subsurface scattering,” ACM Trans. Graphics 29, 62 (2010).
[CrossRef]

2009 (1)

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
[CrossRef]

2006 (1)

P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
[CrossRef]

2005 (1)

X. Tong, J. Wang, S. Lin, B. Guo, H. Shum, “Modeling and rendering of quasi-homogeneous materials,” ACM Trans. Graphics 24, 1054–1061 (2005).
[CrossRef]

2004 (1)

M. Goesele, H. Lensch, J. Lang, C. Fuchs, H. Seidel, “Disco: acquisition of translucent objects,” ACM Trans. Graphics 23, 835–844 (2004).
[CrossRef]

1998 (3)

G. Rogers, “Optical dot gain: lateral scattering probabilities,” J. Imaging Sci. Technol. 42(4), 341–345 (1998).

J. S. Arney, T. Wu, C. Blehm, “Modeling the Yule-Nielsen Effect on Color Halftones,” J. Imaging Sci. Technol. 42(4), 335–340 (1998).

G. L. Rogers, “Measurement of the modulation transfer function of paper,” Appl. Opt. 37, 7235–7240 (1998).
[CrossRef]

1997 (2)

G. L. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41(6), 643–656 (1997).

S. Inoue, N. Tsumura, Y. Miyake, “Measuring mtf of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41(6), 657–661 (1997).

1996 (1)

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

1995 (1)

P. G. Engeldrum, B. Pridham, “Application of turbid medium theory to paper spread function measurements,” TAGA Proceedings 1, 339–352 (1995).

1982 (1)

G. Fischer, J. Rodriguez-Giles, K. R. Scheuter, “Ein physikalisches modell für die beschreibung von licht-streuprozessen,” Die Farbe 30, 199–220 (1982).

1978 (1)

F. Ruckdeschel, O. Hauser, “Yule-nielsen effect in printing: a physical analysis,” Applied Optics, 17, 3376–3383 (1978).
[CrossRef] [PubMed]

1968 (1)

1967 (1)

J. Yule, D. Howe, J. Altman, “The Effect of the Spread-Function of Paper on Halftone Reproduction,” TAPPI Journal 7, 337–344 (1967).

1964 (1)

1952 (1)

1951 (1)

J. A. C. Yule, W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Tech. Assn. Graphic Arts, 4, 65–76 (1951).

1936 (1)

A. Murray, “Monochrome reproduction in photoengraving,” Journal of the Franklin Institute, 221, 721–744 (1936).
[CrossRef]

Ackermann, C.

C. Ackermann, H. Praast, L. Göttsching, “Einfluss von Lichtstreuung und Lichtabsorption auf die Bildwiedergabe gedruckter Rasterflächen,” Tech. Rep. 12395N, AiF (2002).

Altman, J.

J. Yule, D. Howe, J. Altman, “The Effect of the Spread-Function of Paper on Halftone Reproduction,” TAPPI Journal 7, 337–344 (1967).

Arney, C. D.

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

Arney, J.

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

Arney, J. S.

J. S. Arney, T. Wu, C. Blehm, “Modeling the Yule-Nielsen Effect on Color Halftones,” J. Imaging Sci. Technol. 42(4), 335–340 (1998).

Berg, F.

F. Berg, “Isotrope Lichtstreuung in Papier - Neue Überlegungen zur Kubelka-Munk-Theorie,” Ph.D. thesis, Technische Hochschule Darmstadt (1997).

Blehm, C.

J. S. Arney, T. Wu, C. Blehm, “Modeling the Yule-Nielsen Effect on Color Halftones,” J. Imaging Sci. Technol. 42(4), 335–340 (1998).

Callahan, F. P.

Dong, Y.

Y. Dong, J. Wang, F. Pellacini, X. Tong, B. Guo, “Fabricating spatially-varying subsurface scattering,” ACM Trans. Graphics 29, 62 (2010).
[CrossRef]

Dörsam, E.

K. Happel, M. Walter, P. Urban, E. Dörsam, “Measuring anisotropic light scatter within graphic arts papers for modeling optical dot gain,” “IS&T/SID, 18th Color and Imaging Conference,” San Antonio, Texas, 347–352 (2010).

K. Happel, P. Urban, E. Dörsam, X. Ludewig, “Classifying Papers According to their Light Scatter Properties,” “Midterm Meeting of the International Colour Association (AIC),” Zurich, Switzerland, 138–141 (2011).

Dutré, P.

P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
[CrossRef]

Engeldrum, P. G.

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

P. G. Engeldrum, B. Pridham, “Application of turbid medium theory to paper spread function measurements,” TAGA Proceedings 1, 339–352 (1995).

Fischer, G.

G. Fischer, J. Rodriguez-Giles, K. R. Scheuter, “Ein physikalisches modell für die beschreibung von licht-streuprozessen,” Die Farbe 30, 199–220 (1982).

Fuchs, C.

M. Goesele, H. Lensch, J. Lang, C. Fuchs, H. Seidel, “Disco: acquisition of translucent objects,” ACM Trans. Graphics 23, 835–844 (2004).
[CrossRef]

Fuchs, M.

M. Hašan, M. Fuchs, W. Matusik, H. Pfister, S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graphics 29, 61 (2010).
[CrossRef]

Goesele, M.

M. Goesele, H. Lensch, J. Lang, C. Fuchs, H. Seidel, “Disco: acquisition of translucent objects,” ACM Trans. Graphics 23, 835–844 (2004).
[CrossRef]

Göttsching, L.

C. Ackermann, H. Praast, L. Göttsching, “Einfluss von Lichtstreuung und Lichtabsorption auf die Bildwiedergabe gedruckter Rasterflächen,” Tech. Rep. 12395N, AiF (2002).

Guo, B.

Y. Dong, J. Wang, F. Pellacini, X. Tong, B. Guo, “Fabricating spatially-varying subsurface scattering,” ACM Trans. Graphics 29, 62 (2010).
[CrossRef]

X. Tong, J. Wang, S. Lin, B. Guo, H. Shum, “Modeling and rendering of quasi-homogeneous materials,” ACM Trans. Graphics 24, 1054–1061 (2005).
[CrossRef]

Gustavson, S.

S. Gustavson, “Dot gain in colour halftones,” Ph.D. thesis, Sweden (1997).

Happel, K.

K. Happel, M. Walter, P. Urban, E. Dörsam, “Measuring anisotropic light scatter within graphic arts papers for modeling optical dot gain,” “IS&T/SID, 18th Color and Imaging Conference,” San Antonio, Texas, 347–352 (2010).

K. Happel, “Led-based light scattering measurements of papers for printing applications,” Ph.D. thesis, Technische Universität Darmstadt, Germany (2011).

K. Happel, P. Urban, E. Dörsam, X. Ludewig, “Classifying Papers According to their Light Scatter Properties,” “Midterm Meeting of the International Colour Association (AIC),” Zurich, Switzerland, 138–141 (2011).

Hašan, M.

M. Hašan, M. Fuchs, W. Matusik, H. Pfister, S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graphics 29, 61 (2010).
[CrossRef]

Hauser, O.

F. Ruckdeschel, O. Hauser, “Yule-nielsen effect in printing: a physical analysis,” Applied Optics, 17, 3376–3383 (1978).
[CrossRef] [PubMed]

Hauta-Kasari, M.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
[CrossRef]

Howe, D.

J. Yule, D. Howe, J. Altman, “The Effect of the Spread-Function of Paper on Halftone Reproduction,” TAPPI Journal 7, 337–344 (1967).

Inoue, S.

S. Inoue, N. Tsumura, Y. Miyake, “Measuring mtf of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41(6), 657–661 (1997).

Jähne, B.

B. Jähne, Digital Image Processing, 6 (Springer, 2005).

Kaneko, H.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
[CrossRef]

Katsube, M.

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

Kunishi, T.

Lang, J.

M. Goesele, H. Lensch, J. Lang, C. Fuchs, H. Seidel, “Disco: acquisition of translucent objects,” ACM Trans. Graphics 23, 835–844 (2004).
[CrossRef]

Lawrence, J.

P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
[CrossRef]

Lensch, H.

M. Goesele, H. Lensch, J. Lang, C. Fuchs, H. Seidel, “Disco: acquisition of translucent objects,” ACM Trans. Graphics 23, 835–844 (2004).
[CrossRef]

Lin, S.

X. Tong, J. Wang, S. Lin, B. Guo, H. Shum, “Modeling and rendering of quasi-homogeneous materials,” ACM Trans. Graphics 24, 1054–1061 (2005).
[CrossRef]

Ludewig, X.

K. Happel, P. Urban, E. Dörsam, X. Ludewig, “Classifying Papers According to their Light Scatter Properties,” “Midterm Meeting of the International Colour Association (AIC),” Zurich, Switzerland, 138–141 (2011).

Marchand, E.

Matusik, W.

M. Hašan, M. Fuchs, W. Matusik, H. Pfister, S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graphics 29, 61 (2010).
[CrossRef]

P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
[CrossRef]

Miyake, Y.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
[CrossRef]

S. Inoue, N. Tsumura, Y. Miyake, “Measuring mtf of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41(6), 657–661 (1997).

Murray, A.

A. Murray, “Monochrome reproduction in photoengraving,” Journal of the Franklin Institute, 221, 721–744 (1936).
[CrossRef]

Nakaguchi, T.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
[CrossRef]

Nielsen, W. J.

J. A. C. Yule, W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Tech. Assn. Graphic Arts, 4, 65–76 (1951).

Parkkinen, J.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
[CrossRef]

Peers, P.

P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
[CrossRef]

Pellacini, F.

Y. Dong, J. Wang, F. Pellacini, X. Tong, B. Guo, “Fabricating spatially-varying subsurface scattering,” ACM Trans. Graphics 29, 62 (2010).
[CrossRef]

Pfister, H.

M. Hašan, M. Fuchs, W. Matusik, H. Pfister, S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graphics 29, 61 (2010).
[CrossRef]

Praast, H.

C. Ackermann, H. Praast, L. Göttsching, “Einfluss von Lichtstreuung und Lichtabsorption auf die Bildwiedergabe gedruckter Rasterflächen,” Tech. Rep. 12395N, AiF (2002).

Pridham, B.

P. G. Engeldrum, B. Pridham, “Application of turbid medium theory to paper spread function measurements,” TAGA Proceedings 1, 339–352 (1995).

Ramamoorthi, R.

P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
[CrossRef]

Rodriguez-Giles, J.

G. Fischer, J. Rodriguez-Giles, K. R. Scheuter, “Ein physikalisches modell für die beschreibung von licht-streuprozessen,” Die Farbe 30, 199–220 (1982).

Rogers, G.

G. Rogers, “Optical dot gain: lateral scattering probabilities,” J. Imaging Sci. Technol. 42(4), 341–345 (1998).

Rogers, G. L.

G. L. Rogers, “Measurement of the modulation transfer function of paper,” Appl. Opt. 37, 7235–7240 (1998).
[CrossRef]

G. L. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41(6), 643–656 (1997).

Ruckdeschel, F.

F. Ruckdeschel, O. Hauser, “Yule-nielsen effect in printing: a physical analysis,” Applied Optics, 17, 3376–3383 (1978).
[CrossRef] [PubMed]

Rusinkiewicz, S.

M. Hašan, M. Fuchs, W. Matusik, H. Pfister, S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graphics 29, 61 (2010).
[CrossRef]

P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
[CrossRef]

Scheuter, K. R.

G. Fischer, J. Rodriguez-Giles, K. R. Scheuter, “Ein physikalisches modell für die beschreibung von licht-streuprozessen,” Die Farbe 30, 199–220 (1982).

Seidel, H.

M. Goesele, H. Lensch, J. Lang, C. Fuchs, H. Seidel, “Disco: acquisition of translucent objects,” ACM Trans. Graphics 23, 835–844 (2004).
[CrossRef]

Shum, H.

X. Tong, J. Wang, S. Lin, B. Guo, H. Shum, “Modeling and rendering of quasi-homogeneous materials,” ACM Trans. Graphics 24, 1054–1061 (2005).
[CrossRef]

Tong, X.

Y. Dong, J. Wang, F. Pellacini, X. Tong, B. Guo, “Fabricating spatially-varying subsurface scattering,” ACM Trans. Graphics 29, 62 (2010).
[CrossRef]

X. Tong, J. Wang, S. Lin, B. Guo, H. Shum, “Modeling and rendering of quasi-homogeneous materials,” ACM Trans. Graphics 24, 1054–1061 (2005).
[CrossRef]

Tsumura, N.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
[CrossRef]

S. Inoue, N. Tsumura, Y. Miyake, “Measuring mtf of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41(6), 657–661 (1997).

Ukishima, M.

M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences 92, 3328–3335 (2009).
[CrossRef]

Urban, P.

K. Happel, M. Walter, P. Urban, E. Dörsam, “Measuring anisotropic light scatter within graphic arts papers for modeling optical dot gain,” “IS&T/SID, 18th Color and Imaging Conference,” San Antonio, Texas, 347–352 (2010).

K. Happel, P. Urban, E. Dörsam, X. Ludewig, “Classifying Papers According to their Light Scatter Properties,” “Midterm Meeting of the International Colour Association (AIC),” Zurich, Switzerland, 138–141 (2011).

Viggiano, J.

J. Viggiano, “The Color of Halftone Tints,” in “TAGA Proceedings,” 647–661 (1985).

Viggiano, J. A. S.

J. A. S. Viggiano, “New models for the reflectance spectra produced by halftone-based hardcopy,” Ph.D. thesis, Center for Imaging Science, Rochester Institute of Technology, Rochester, NY, USA (2010).

vom Berge, K.

P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, P. Dutré, “A compact factored representation of heterogeneous subsurface scattering,” ACM Trans. Graphics 25, 746–753 (2006).
[CrossRef]

Wakeshima, H.

Walter, M.

K. Happel, M. Walter, P. Urban, E. Dörsam, “Measuring anisotropic light scatter within graphic arts papers for modeling optical dot gain,” “IS&T/SID, 18th Color and Imaging Conference,” San Antonio, Texas, 347–352 (2010).

M. Walter, “Methode zur Messung orthotroper Lichtstreuung in grafischen Papieren,” Master’s thesis, Technische Universität Darmstadt (2009).

Wang, J.

Y. Dong, J. Wang, F. Pellacini, X. Tong, B. Guo, “Fabricating spatially-varying subsurface scattering,” ACM Trans. Graphics 29, 62 (2010).
[CrossRef]

X. Tong, J. Wang, S. Lin, B. Guo, H. Shum, “Modeling and rendering of quasi-homogeneous materials,” ACM Trans. Graphics 24, 1054–1061 (2005).
[CrossRef]

Wu, T.

J. S. Arney, T. Wu, C. Blehm, “Modeling the Yule-Nielsen Effect on Color Halftones,” J. Imaging Sci. Technol. 42(4), 335–340 (1998).

Yule, J.

J. Yule, D. Howe, J. Altman, “The Effect of the Spread-Function of Paper on Halftone Reproduction,” TAPPI Journal 7, 337–344 (1967).

Yule, J. A. C.

J. A. C. Yule, W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” Tech. Assn. Graphic Arts, 4, 65–76 (1951).

ACM Trans. Graphics (5)

M. Hašan, M. Fuchs, W. Matusik, H. Pfister, S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graphics 29, 61 (2010).
[CrossRef]

Y. Dong, J. Wang, F. Pellacini, X. Tong, B. Guo, “Fabricating spatially-varying subsurface scattering,” ACM Trans. Graphics 29, 62 (2010).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Measurement setup with illumination unit, sample unit, and observation unit.

Fig. 2
Fig. 2

Relative spectral power distribution of blue, green, and red LED.

Fig. 3
Fig. 3

Sample holding unit (schematic and CAD rendering): The focus is adjusted using the reference (first surface mirror) and is maintained for the sample material by mechanical shifting. The unit allows rotating the sample around the optical axis of the microscope to detect anisotropic subsurface light transport.

Fig. 4
Fig. 4

ESFs (top left), LSFs (top right), PSFs (bottom left) and cutout (bottom right) for the green LED. The circles in the cutout (bottom right) indicate the average distance of subsurface light transport. Resolution: 0.54μm/Pixel.

Fig. 5
Fig. 5

LSFs of OG (opal glas). Resolution: 0.54μm/Pixel.

Fig. 6
Fig. 6

Measured ESF and ESFs reconstructed from the computed LSF and from the two-dimensional PSF. The curves shown in this Figure correspond to the largest RMSEs listed in Table 2 (see rows: Red LED, column: IC). Resolution: 0.54μm/Pixel.

Fig. 7
Fig. 7

Optical dot gain model.

Fig. 8
Fig. 8

Spectral RMSE of model predictions including and excluding PSF filtering. The red stars indicate the spectral RMSEs of the Yule-Nielsen modified Murray-Davies model fitted to the test samples (ground truth spectral measurements).

Tables (2)

Tables Icon

Table 1 Selected samples.

Tables Icon

Table 2 RMSEa and RMSEb.

Equations (27)

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V = V total V dark = K η λ A h c E camera t E
k = K η λ A h c t E ,
V ( i , j ) = k E camera ( i , j )
E camera ( i , j ) = ( E * 𝒫 * 𝒫 o ) ( i , j ) .
V ( i , j ) = k ( E * 𝒫 * 𝒫 o ) ( i , j )
V M ( i , j ) = k ( ( M E ) * 𝒫 o * 𝒫 ) ( i , j )
V ( i , j ) = k E ( i , j )
V M ( i , j ) = k E ( i , j ) ( 𝒫 o * 𝒫 * M ) ( i , j )
V M ( i , j ) V ( i , j ) = ( 𝒫 o * 𝒫 * M ) ( i , j )
V M , ref ( i , j ) V ref ( i , j ) = ( 𝒫 o * M ) ( i , j )
V M ( i , j ) V ( i , j ) = ( 𝒫 * V M , ref V ref ) ( i , j )
a ( i ) = ( * a ref ) ( i ) ,
a ( i ) = 1 n j = 1 n V M ( i , j ) V ( i , j )
a ref ( i ) = 1 n j = 1 n V M , ref ( i , j ) V ref ( i , j )
( x ) = 1 [ ( a ( i ) ) ( a ref ( i ) ) ] .
= argmin ´ i = 1 m [ a ( i ) ( ´ * a ref ) ( i ) ] 2
= argmin ´ ( a A ref ´ ) T ( a A ref ´ )
´ 0
´ ( i 0 i ) = ´ ( i 0 + i ) , i > 0
´ ( i ) ´ ( i + 1 ) 0 , i i 0
´ ( i 1 ) 2 ´ ( i ) + ´ ( i + 1 ) 0 , i > i 0
´ 1 = 1
RMSE a = 1 m i = 1 m ( a ( i ) ( * a ref ) ( i ) ) 2
RMSE b = 1 n m j = 1 n i = 1 m ( V M ( i , j ) V ( i , j ) ( 𝒫 * V M , ref V ref ) ( i , j ) ) 2
R = 1 Vol ( A ) A ( T 45 ° * 𝒫 ) ( z ) R s T 0 ° ( z ) d z
( x ) = 𝒫 ( x 2 + y 2 ) d y
𝒫 ( r ) = 2 π 0 A ( v 2 + r 2 ) d v A ( x ) = ( x 2 )

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