Abstract

We present results for the bidirectional reflectance distribution function (BRDF) for samples of uniform rectangular and triangular grooves constructed from polydimethylsilicone replicas. The measurements are performed with the detector in the plane of incidence, but with varying groove orientations with respect to that plane. The samples are opaque in some cases and semitransparent in others. By measuring the BRDF for colored samples over a wide spectral range, we explicitly probe the effect of sample albedo, which is important for inter-reflections. For the opaque samples, we compare the results with exact theoretical results either taken from the literature (for the triangular geometry) or worked out here (for the rectangular geometry). For both geometries, we also extend the theoretical results to finite length grooves. There is generally very good agreement between theory and the experiment. Shadowing, masking, and inter-reflection are clearly observed, as well as effects that may be due to polarization and asperity scattering. For semitransparent samples, we observe the effect of increasing transparency on the BRDF.

© 2011 Optical Society of America

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  1. G. V. G. Baranoski and A. Krishnaswamy, “An introduction to light interaction with human skin,” RITA 11, 33-62 (2004).
  2. A. Krishnaswamy and G. V. G. Baranoski, “A biophysically-based spectral model of light interaction with human skin,” Comput. Graph. Forum 23, 331-340 (2004).
    [CrossRef]
  3. J. Dozier and T. H. Painter, “Multispectral and hyperspectral remote sensing of alpine snow properties,” Annu. Rev. Earth Planet. Sci. 32, 465-494 (2004).
    [CrossRef]
  4. R. L. Thompson, “A snapshot of canopy reflectance models and a universal model for the radiation regime,” Remote Sens. Rev. 18, 197-225 (2000).
    [CrossRef]
  5. J. Dorsey and H. Rushmeier, “Advanced material appearance modeling,” in Proceedings of ACM SIGGRAPH 2009 Courses (ACM, 2009), article 3.
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  6. K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105-1112 (1967).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227-251 (1995).
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  9. J. J. Koenderink, A. J. van Doorn, K. J. Dana, and S. K. Nayar, “Bidirectional reflection distribution function of thoroughly pitted surfaces,” Int. J. Comput. Vis. 31, 129-144 (1999).
    [CrossRef]
  10. S. C. Pont and J. J. Koenderink, “Bidirectional reflectance distribution function of specular surfaces with hemispherical pits,” J. Opt. Soc. Am. A 19, 2456-2466 (2002).
    [CrossRef]
  11. S. Pont and J. J. Koenderink, “Reflectance from locally glossy thoroughly pitted surfaces,” Comput. Vis. Image Underst. 98, 211-222 (2005).
    [CrossRef]
  12. J. E. Geake, M. Geake, and B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Not. R. Astron. Soc. 210, 89-112. (1984).
  13. S. Bondarenko, A. Ovcharenko, Y. Shkuratov, G. Videen, J. Eversol, and M. Hart, “Backscatter by surfaces composed of small spherical particles,” Appl. Opt. 45, 3871-3877 (2006).
    [CrossRef] [PubMed]
  14. A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
    [CrossRef]
  15. Y. G. Shkuratov and Y. S. Grynko, “Scattering by semitransparent particles of different shapes and media consisting of these particles in geometric optics approximation: consequences for photometry and spectroscopy of the planetary regoliths,” Icarus 173, 16-28. (2005).
    [CrossRef]
  16. Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
    [CrossRef]
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    [CrossRef]
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  19. J. Koenderink and S. Pont, “The secret of velvety skin,” Mach. Vis. Appl. 14, 260-268 (2003).
    [CrossRef]
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    [CrossRef]
  21. M. Hašan, M. Fuchs, W. Matusik, H. Pfister, and S. Rusinkiewicz, “Physical reproduction of materials with specified subsurface scattering,” ACM Trans. Graph. 29, 61 (2010).
    [CrossRef]
  22. Y. Shkuratov, D. V. Petrov, and G. Videen, “Classical photometry of pre-fractal surfaces,” J. Opt. Soc. Am. 20, 2081-2092 (2003).
    [CrossRef]
  23. D. A. Haner, B. T. McGuckin, and C. J. Bruegge, “Polarization characteristics of spectralon illuminated by coherent light,” Appl. Opt. 38, 6350-6356 (1999).
    [CrossRef]
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2010 (1)

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

2009 (2)

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28, 32 (2009).
[CrossRef]

J. Dorsey and H. Rushmeier, “Advanced material appearance modeling,” in Proceedings of ACM SIGGRAPH 2009 Courses (ACM, 2009), article 3.
[CrossRef]

2006 (2)

S. Bondarenko, A. Ovcharenko, Y. Shkuratov, G. Videen, J. Eversol, and M. Hart, “Backscatter by surfaces composed of small spherical particles,” Appl. Opt. 45, 3871-3877 (2006).
[CrossRef] [PubMed]

A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
[CrossRef]

2005 (3)

Y. G. Shkuratov and Y. S. Grynko, “Scattering by semitransparent particles of different shapes and media consisting of these particles in geometric optics approximation: consequences for photometry and spectroscopy of the planetary regoliths,” Icarus 173, 16-28. (2005).
[CrossRef]

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

S. Pont and J. J. Koenderink, “Reflectance from locally glossy thoroughly pitted surfaces,” Comput. Vis. Image Underst. 98, 211-222 (2005).
[CrossRef]

2004 (3)

G. V. G. Baranoski and A. Krishnaswamy, “An introduction to light interaction with human skin,” RITA 11, 33-62 (2004).

A. Krishnaswamy and G. V. G. Baranoski, “A biophysically-based spectral model of light interaction with human skin,” Comput. Graph. Forum 23, 331-340 (2004).
[CrossRef]

J. Dozier and T. H. Painter, “Multispectral and hyperspectral remote sensing of alpine snow properties,” Annu. Rev. Earth Planet. Sci. 32, 465-494 (2004).
[CrossRef]

2003 (2)

J. Koenderink and S. Pont, “The secret of velvety skin,” Mach. Vis. Appl. 14, 260-268 (2003).
[CrossRef]

Y. Shkuratov, D. V. Petrov, and G. Videen, “Classical photometry of pre-fractal surfaces,” J. Opt. Soc. Am. 20, 2081-2092 (2003).
[CrossRef]

2002 (1)

2000 (1)

R. L. Thompson, “A snapshot of canopy reflectance models and a universal model for the radiation regime,” Remote Sens. Rev. 18, 197-225 (2000).
[CrossRef]

1999 (2)

J. J. Koenderink, A. J. van Doorn, K. J. Dana, and S. K. Nayar, “Bidirectional reflection distribution function of thoroughly pitted surfaces,” Int. J. Comput. Vis. 31, 129-144 (1999).
[CrossRef]

D. A. Haner, B. T. McGuckin, and C. J. Bruegge, “Polarization characteristics of spectralon illuminated by coherent light,” Appl. Opt. 38, 6350-6356 (1999).
[CrossRef]

1998 (1)

Y. Xia and G. Whitesides, “Soft lithography,” Annu. Rev. Mater. Sci. 28, 153-184 (1998).
[CrossRef]

1995 (2)

S. K. Nayar and M. Oren, “Visual appearance of matte surfaces,” Science 267, 1153-1156 (1995).
[CrossRef] [PubMed]

M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227-251 (1995).
[CrossRef]

1984 (1)

J. E. Geake, M. Geake, and B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Not. R. Astron. Soc. 210, 89-112. (1984).

1977 (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, 1977).

1967 (1)

Baranoski, G. V. G.

A. Krishnaswamy and G. V. G. Baranoski, “A biophysically-based spectral model of light interaction with human skin,” Comput. Graph. Forum 23, 331-340 (2004).
[CrossRef]

G. V. G. Baranoski and A. Krishnaswamy, “An introduction to light interaction with human skin,” RITA 11, 33-62 (2004).

Bondarenko, S.

Bondarenko, S. Y.

A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
[CrossRef]

Bruegge, C. J.

Chevrel, S. D.

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

Cord, A. M.

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

Dana, K. J.

J. J. Koenderink, A. J. van Doorn, K. J. Dana, and S. K. Nayar, “Bidirectional reflection distribution function of thoroughly pitted surfaces,” Int. J. Comput. Vis. 31, 129-144 (1999).
[CrossRef]

Daydou, Y. H.

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

Dorsey, J.

J. Dorsey and H. Rushmeier, “Advanced material appearance modeling,” in Proceedings of ACM SIGGRAPH 2009 Courses (ACM, 2009), article 3.
[CrossRef]

Dozier, J.

J. Dozier and T. H. Painter, “Multispectral and hyperspectral remote sensing of alpine snow properties,” Annu. Rev. Earth Planet. Sci. 32, 465-494 (2004).
[CrossRef]

Eversol, J.

Fuchs, M.

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

Geake, J. E.

J. E. Geake, M. Geake, and B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Not. R. Astron. Soc. 210, 89-112. (1984).

Geake, M.

J. E. Geake, M. Geake, and B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Not. R. Astron. Soc. 210, 89-112. (1984).

Ginsburg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, 1977).

Grynko, Y. S.

Y. G. Shkuratov and Y. S. Grynko, “Scattering by semitransparent particles of different shapes and media consisting of these particles in geometric optics approximation: consequences for photometry and spectroscopy of the planetary regoliths,” Icarus 173, 16-28. (2005).
[CrossRef]

Haner, D. A.

Hart, M.

Hašan, M.

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

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, 1977).

Koenderink, J.

J. Koenderink and S. Pont, “The secret of velvety skin,” Mach. Vis. Appl. 14, 260-268 (2003).
[CrossRef]

Koenderink, J. J.

S. Pont and J. J. Koenderink, “Reflectance from locally glossy thoroughly pitted surfaces,” Comput. Vis. Image Underst. 98, 211-222 (2005).
[CrossRef]

S. C. Pont and J. J. Koenderink, “Bidirectional reflectance distribution function of specular surfaces with hemispherical pits,” J. Opt. Soc. Am. A 19, 2456-2466 (2002).
[CrossRef]

J. J. Koenderink, A. J. van Doorn, K. J. Dana, and S. K. Nayar, “Bidirectional reflection distribution function of thoroughly pitted surfaces,” Int. J. Comput. Vis. 31, 129-144 (1999).
[CrossRef]

Krishnaswamy, A.

G. V. G. Baranoski and A. Krishnaswamy, “An introduction to light interaction with human skin,” RITA 11, 33-62 (2004).

A. Krishnaswamy and G. V. G. Baranoski, “A biophysically-based spectral model of light interaction with human skin,” Comput. Graph. Forum 23, 331-340 (2004).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, 1977).

Matusik, W.

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

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28, 32 (2009).
[CrossRef]

McGuckin, B. T.

Nayar, S. K.

J. J. Koenderink, A. J. van Doorn, K. J. Dana, and S. K. Nayar, “Bidirectional reflection distribution function of thoroughly pitted surfaces,” Int. J. Comput. Vis. 31, 129-144 (1999).
[CrossRef]

S. K. Nayar and M. Oren, “Visual appearance of matte surfaces,” Science 267, 1153-1156 (1995).
[CrossRef] [PubMed]

M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227-251 (1995).
[CrossRef]

Nelson, R. M.

A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, 1977).

Oren, M.

S. K. Nayar and M. Oren, “Visual appearance of matte surfaces,” Science 267, 1153-1156 (1995).
[CrossRef] [PubMed]

M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227-251 (1995).
[CrossRef]

Ovcharenko, A.

Ovcharenko, A. A.

A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
[CrossRef]

Painter, T. H.

J. Dozier and T. H. Painter, “Multispectral and hyperspectral remote sensing of alpine snow properties,” Annu. Rev. Earth Planet. Sci. 32, 465-494 (2004).
[CrossRef]

Peers, P.

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28, 32 (2009).
[CrossRef]

Petrov, D. V.

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

Y. Shkuratov, D. V. Petrov, and G. Videen, “Classical photometry of pre-fractal surfaces,” J. Opt. Soc. Am. 20, 2081-2092 (2003).
[CrossRef]

Pfister, H.

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

Pinet, P. C.

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

Pont, S.

S. Pont and J. J. Koenderink, “Reflectance from locally glossy thoroughly pitted surfaces,” Comput. Vis. Image Underst. 98, 211-222 (2005).
[CrossRef]

J. Koenderink and S. Pont, “The secret of velvety skin,” Mach. Vis. Appl. 14, 260-268 (2003).
[CrossRef]

Pont, S. C.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, 1977).

Rushmeier, H.

J. Dorsey and H. Rushmeier, “Advanced material appearance modeling,” in Proceedings of ACM SIGGRAPH 2009 Courses (ACM, 2009), article 3.
[CrossRef]

Rusinkiewicz, S.

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

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28, 32 (2009).
[CrossRef]

Shkuratov, Y.

Shkuratov, Y. G.

A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
[CrossRef]

Y. G. Shkuratov and Y. S. Grynko, “Scattering by semitransparent particles of different shapes and media consisting of these particles in geometric optics approximation: consequences for photometry and spectroscopy of the planetary regoliths,” Icarus 173, 16-28. (2005).
[CrossRef]

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

Smythe, W. D.

A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
[CrossRef]

Sparrow, E. M.

Stankevich, D. G.

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

Thompson, R. L.

R. L. Thompson, “A snapshot of canopy reflectance models and a universal model for the radiation regime,” Remote Sens. Rev. 18, 197-225 (2000).
[CrossRef]

Torrance, K. E.

van Doorn, A. J.

J. J. Koenderink, A. J. van Doorn, K. J. Dana, and S. K. Nayar, “Bidirectional reflection distribution function of thoroughly pitted surfaces,” Int. J. Comput. Vis. 31, 129-144 (1999).
[CrossRef]

Videen, G.

A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
[CrossRef]

S. Bondarenko, A. Ovcharenko, Y. Shkuratov, G. Videen, J. Eversol, and M. Hart, “Backscatter by surfaces composed of small spherical particles,” Appl. Opt. 45, 3871-3877 (2006).
[CrossRef] [PubMed]

Y. Shkuratov, D. V. Petrov, and G. Videen, “Classical photometry of pre-fractal surfaces,” J. Opt. Soc. Am. 20, 2081-2092 (2003).
[CrossRef]

Weyrich, T.

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28, 32 (2009).
[CrossRef]

Whitesides, G.

Y. Xia and G. Whitesides, “Soft lithography,” Annu. Rev. Mater. Sci. 28, 153-184 (1998).
[CrossRef]

Xia, Y.

Y. Xia and G. Whitesides, “Soft lithography,” Annu. Rev. Mater. Sci. 28, 153-184 (1998).
[CrossRef]

Zellner, B. H.

J. E. Geake, M. Geake, and B. H. Zellner, “Experiments to test theoretical models of the polarization of light by rough surfaces,” Mon. Not. R. Astron. Soc. 210, 89-112. (1984).

Zubko, E. S.

A. A. Ovcharenko, S. Y. Bondarenko, E. S. Zubko, Y. G. Shkuratov, G. Videen, R. M. Nelson, and W. D. Smythe, “Particle size effect on the opposition spike and negative polarization,” J. Quant. Spectrosc. Radiat. Transfer 101, 394-403 (2006).
[CrossRef]

ACM Trans. Graph. (2)

T. Weyrich, P. Peers, W. Matusik, and S. Rusinkiewicz, “Fabricating microgeometry for custom surface reflectance,” ACM Trans. Graph. 28, 32 (2009).
[CrossRef]

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

Annu. Rev. Earth Planet. Sci. (1)

J. Dozier and T. H. Painter, “Multispectral and hyperspectral remote sensing of alpine snow properties,” Annu. Rev. Earth Planet. Sci. 32, 465-494 (2004).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

Y. Xia and G. Whitesides, “Soft lithography,” Annu. Rev. Mater. Sci. 28, 153-184 (1998).
[CrossRef]

Appl. Opt. (2)

Comput. Graph. Forum (1)

A. Krishnaswamy and G. V. G. Baranoski, “A biophysically-based spectral model of light interaction with human skin,” Comput. Graph. Forum 23, 331-340 (2004).
[CrossRef]

Comput. Vis. Image Underst. (1)

S. Pont and J. J. Koenderink, “Reflectance from locally glossy thoroughly pitted surfaces,” Comput. Vis. Image Underst. 98, 211-222 (2005).
[CrossRef]

Icarus (2)

Y. G. Shkuratov and Y. S. Grynko, “Scattering by semitransparent particles of different shapes and media consisting of these particles in geometric optics approximation: consequences for photometry and spectroscopy of the planetary regoliths,” Icarus 173, 16-28. (2005).
[CrossRef]

Y. G. Shkuratov, D. G. Stankevich, D. V. Petrov, P. C. Pinet, A. M. Cord, Y. H. Daydou, and S. D. Chevrel, “Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scatter,” Icarus 173, 3-15 (2005).
[CrossRef]

Int. J. Comput. Vis. (2)

M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227-251 (1995).
[CrossRef]

J. J. Koenderink, A. J. van Doorn, K. J. Dana, and S. K. Nayar, “Bidirectional reflection distribution function of thoroughly pitted surfaces,” Int. J. Comput. Vis. 31, 129-144 (1999).
[CrossRef]

J. Opt. Soc. Am. (2)

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Figures (17)

Fig. 1
Fig. 1

Clockwise from top left: PDMS replica of painted triangular grooves, painted rectangular grooves, magnified image of painted rectangular grooves showing microscale texture on surface, and top view of triangular grooves.

Fig. 2
Fig. 2

(a) Geometry and dimensions for the rectangular (top) and triangular (bottom) geometries. The dimensions for rectangular samples are h = 0.55 mm , t = 0.94 mm , w = 0.65 mm for painted samples and h = 0.48 mm , t = 0.84 mm , w = 0.75 mm for pigmented samples. For triangular samples, h = 0.52 mm . (b) Schematic showing the definition of the incident and viewing angles and the azimuthal orientation of grooves with respect to the plane of incidence. In the diagram on the left the grooves are oriented perpendicular to the plane of incidence. In the diagram on the right, the sample is rotated in steps from an orientation where the grooves are parallel to the plane of incidence ( ϕ = 90 ° ) to an orientation where the grooves are perpendicular to the plane of incidence ( ϕ = 0 ° ).

Fig. 3
Fig. 3

(a) Reflectance factor for the painted rectangular (squares) and triangular (circles) grooved samples. (b) Reflectance factor for the pigmented rectangular grooved samples having pigment concentration (by weight) of 1.0% (squares), 2.7% (circles), 5.0% (triangles), and 10% (diamonds). The data are taken from the flat region of the samples at the “standard” setting, i.e., incident angle is 0 ° and viewing angle is 20 ° . For clarity every second, fourth and eight points are plotted for the 1, 5 and 10   wt. % pigmented sample. (c) Absorbance spectra for 1   wt. % pigmented rectangular grooved sample.

Fig. 4
Fig. 4

Reflectance factor divided by albedo ( RF / ρ ) for painted rectangular grooved samples at two different albedos, low (left panel) and high (right panel), for three incident angles: (a)  0 ° , (b)  10 ° , and (c)  20 ° . In all plots the solid line denotes a theoretical Lambertian. Data from the flat region, grooves oriented parallel, and grooves oriented perpendicular, are denoted using open triangles, squares, and circles, respectively (groove orientations are specified with respect to the plane of incidence).

Fig. 5
Fig. 5

Reflectance factor normalized by the flat equivalent ( RF NFE ) of painted rectangular grooved samples at low (left) and high (right) albedo values for (a)  0 ° , (b)  10 ° , and (c)  20 ° incident angles for grooves oriented parallel (squares) and per pendicular (circles) to the plane of incidence. The solid and dashed lines are theoretical predictions for parallel and perpendicular grooves, respectively.

Fig. 6
Fig. 6

Reflectance factor normalized by the flat equivalent ( RF NFE ) of painted rectangular grooved samples measured at different viewing angles for varying azimuthal orientations at (a) low and (b) high albedo values for light incident at 20 ° . Measurements taken at different azimuthal angles are shown using symbols, and the different line styles are theoretical plots. 0 ° corresponds to perpendicular while 90 ° corresponds to parallel orientation of the grooves.

Fig. 7
Fig. 7

Reflectance factor normalized by the flat equivalent ( RF NFE ) versus albedo for painted rectangular grooved samples at 0 ° incident angle. The different viewing angles are plotted using different symbols.

Fig. 8
Fig. 8

Normalized reflectance factor ( RF / ρ ) for 90 ° painted triangular grooved samples at low (left) and high (right) albedo values for three incident angles: (a)  0 ° , (b)  10 ° , and (c)  20 ° . In all plots the solid line denotes a theoretical Lambertian. Data from the flat region, grooves oriented parallel, and grooves oriented perpendicular are denoted using open triangles, squares, and circles, respectively (groove orientations are specified with respect to the plane of incidence).

Fig. 9
Fig. 9

Reflectance factor normalized by the flat equivalent ( RF NFE ) of painted triangular grooved samples at low (left) and high (right) albedo values for (a)  0 ° , (b)  10 ° , and (c)  20 ° incident angles for grooves oriented parallel (square) and perpendicular (circles) to the plane of incidence. The solid and dashed lines are theoretical predictions for parallel and perpendicular cases, respectively. For the perpendicular orientation case in (b) and (c) some viewing angles are absent, as described in the text.

Fig. 10
Fig. 10

Reflectance factor normalized by the flat equivalent ( RF NFE ) versus albedo for painted triangular grooved samples at 0 ° incident angle. The different viewing angles are plotted using different symbols.

Fig. 11
Fig. 11

Reflectance factor for four different polarization combinations at two viewing angles, (a)  45 ° and (b)  0 ° , both for a 45 ° incident angle. The source and detector polarizations used are ps (squares), pp (circles), sp (up-triangles), and ss (down triangles), where s and p refer to polarization perpendicular and parallel, respectivley, to the plane of incidence. For clarity every second data point is plotted in (a), apart from the sp polarization, where every seventh data point is plotted. Similarly for (b), every seventh data point is plotted for sp and ss, while every second data point is plotted for pp and ps polarization.

Fig. 12
Fig. 12

Reflectance factor divided by albedo ( RF / ρ ) for pigmented rectangular grooved samples for two different pigment concentrations, (a)  10   wt. % and (b)  1   wt. % , each for an incident angle of 20 ° . In all plots the solid line denotes a theoretical Lambertian. Data from the flat region, grooves oriented parallel, and grooves oriented perpendicular are denoted using open triangles, squares, and circles, respectively (groove orientations are specified with respect to the plane of incidence). The plots on the left are for low albedo and those on the right are for high albedo values.

Fig. 13
Fig. 13

Reflectance factor normalized by the flat equivalent ( RF NFE ) of pigmented rectangular grooved samples at low (left) and high (right) albedo values for (a)  10   wt. % and (b)  1   wt. % pigment concentrations for grooves oriented parallel (square) and perpendicular (circles) to the plane of incidence. The solid and dashed lines are theoretical predictions for parallel and perpendicular grooves, respectively, for light incident at 20 ° .

Fig. 14
Fig. 14

Comparison of sp polarized BRDF data from Haner et al. [23] (triangles) and our setup (squares) for light incident at (a)  0 ° and (b)  45 ° for two albedo values. We used 442 and 632 nm from Haner to compare with our low ( 500 nm ) and high ( 600 nm ) albedo values.

Fig. 15
Fig. 15

Shadowing and masking combinations for rectangular grooves that are relevant for the different incident and viewing angles measured. Bold lines represent areas that are not shadowed by the incident beam or masked to the detector.

Fig. 16
Fig. 16

Shadowing and masking combinations for triangular grooves that are relevant for the different incident and viewing angles measured. Bold lines represent areas that are not shadowed by the incident beam or masked to the detector.

Fig. 17
Fig. 17

Finite results divided by the infinite results for a few incident/viewing angle conditions (a) as a function of the length/width ( L / w ) for painted rectangular grooves and (b) as a function of length/height ( L / h ) for painted triangular grooves.

Tables (1)

Tables Icon

Table 1 List of PDMS Samples Prepared and Measured

Equations (31)

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I ( single   groove ) = ρ π E 0 [ cos θ i cos ( θ r ) ( t + D I ) L ] + α ( ρ π ) 2 E 0 { cos ( 90 θ r ) cos ( 90 θ i ) cos 2 ( φ ) IF rl h L + cos ( 90 θ r ) cos ( θ i ) cos ( φ ) IF bl h L + cos ( θ r ) cos ( 90 θ i ) cos ( φ ) IF rb w L } .
a max [ h tan θ i cos φ w tan θ i cos φ , 0 ] ,
b max [ h tan θ r cos φ w tan θ r cos φ , 0 ] ,
a min [ h tan θ i cos φ , w ] ,
b min [ h tan θ r cos φ , w ] ,
D I max [ w h ( tan θ i cos φ + tan θ r cos φ ) , 0 ] ,
IF rl = π 2 w 2 + ( a h ) 2 + w 2 + ( b h ) 2 w w 2 + ( a b ) 2 h ,
IF bl = π 2 h 2 + a 2 + b 2 + w 2 h 2 + w 2 b 2 + a 2 h ,
IF rb = π 2 w 2 + a 2 + b 2 + h 2 w 2 + h 2 b 2 + a 2 w .
BRDF = I ( single   groove ) E 0 ( t + w ) L cos θ i cos θ r .
I ( flat   equiv ) = ρ π E 0 A [ cos θ i cos θ r ] .
BRDF = I ( flat   equiv ) E 0 ( t + w ) L cos θ i cos θ r = ρ π .
I ( single   groove ) = ρ π E 0 [ cos ( 45 + θ i ) cos ( 45 θ r ) ( h b h ) ( h b h ) h L + cos ( 45 θ i ) cos ( 45 + θ r ) ( h a h ) ( h a h ) h L ] + α ( ρ π ) 2 E 0 { cos ( 45 θ r ) cos ( 45 θ i ) IF rl h L + cos ( 45 + θ r ) cos ( 45 + θ i ) IF lr ( h a h ) ( h b h ) h L } ,
a max [ h tan ( θ i 45 ) , 0 ] ,
b max [ h tan ( θ r 45 ) , 0 ] ,
If     θ r < 45 , then     a = 0 , else     a = h ,
If     θ i < 45 , then     b = 0 , else     b = h ,
IF rl = π 2 h 2 + a 2 + b 2 + h 2 2 h 2 b 2 + a 2 h ,
IF lr = π 2 ( 2 2 ) .
I ( flat   equiv ) = ρ π E 0 [ cos ( 45 + θ i ) cos ( 45 θ r ) ( h b h ) h L + cos ( 45 θ i ) cos ( 45 + θ r ) ( h a h ) h L ] .
I ( single   groove ) = ρ π E 0 { 2 cos θ i cos θ r cos 2 ( 45 ) h L } + α ( ρ π ) 2 E 0 { 2 cos θ i cos θ r cos 2 ( 45 ) IF lr h L } .
I ( flat   equiv ) = ρ π E 0 { 2 cos θ i cos θ r cos 2 ( 45 ) h L } .
BRDF = I E 0 2 h L cos θ i cos θ r .
RF NFE rect ( θ i , θ r ) = BRDF rect   grooves ( θ i , θ r ) BRDF flat ( θ i , θ r ) .
RF NFE tri ( θ i , 0 θ r 45 ) = BRDF tri ( θ i , θ r ) cos θ i cos θ r 2 [ cos ( 45 + θ i ) cos ( 45 θ r ) BRDF flat + tilt ( θ i , θ r ) + cos ( 45 θ i ) cos ( 45 + θ r ) BRDF flat tilt ( θ i , θ r ) ] , RF NFE tri ( θ i , 45 < θ r ) = BRDF tri ( θ i , θ r ) cos θ i cos θ r 2 cos ( 45 + θ i ) cos ( 45 θ r ) BRDF flat + tilt ( θ i , θ r ) .
RF NFE tri | | ( θ i , θ r ) = BRDF tri | | ( θ i , θ r ) cos θ i cos θ r 2 BRDF flat   out   tilt ( θ i , θ r ) 2 cos θ i cos θ r cos 2 ( 45 ) .
IF rb = 1 w a h d y b w d x d z x y [ x 2 + y 2 + z 2 ] 2 ,
IF bl = 1 h a w d y b h d x d z x y [ x 2 + y 2 + z 2 ] 2 .
IF rl = w 2 h b h d y a h d y d z 1 [ w 2 + ( y y ) 2 + z 2 ] 2 .
IF rl = w 2 h L b h d y a h d y L / 2 L / 2 d z L / 2 L / 2 d z 1 [ w 2 + ( y y ) 2 + ( z z ) 2 ] 2 .
IF = 1 h L a h d y b h d x L / 2 L / 2 d z L / 2 L / 2 d z x y [ x 2 + y 2 + ( z z ) 2 ] 2 .

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