Abstract

Laboratory bidirectional reflectance and polarization measurements were carried out on packed layers of both natural sediments and manufactured spherical particles. The results indicate that among the natural sediments showing a strong backscattering peak (“hotspot”), the rough platelets are the only sediments with a branch of negative polarization. Measurements of circular and linear polarization ratios indicate that both smooth ooids and rough platelets are strongly depolarizing. Measurements of perfect spherical grains show both negative polarization and strong backscattering as a remnant of the single scattering process.

© 2009 Optical Society of America

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    [CrossRef]
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  3. Y. G. Shkuratov, K. Muinonen, E. Bowell et al. "A critical review of theoretical models of negatively polarized light scattered by atmosphereless solar system bodies," Earth, Moon and Planets 65, 201-246 (1994).
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    [CrossRef]
  6. M. I. Mishchenko, V. K. Rosenbush, and N. N. Kiselev, "Weak localization of electromagnetic waves and opposition phenomena exhibited by high-albedo atmosphereless solar system objects," Appl. Opt. 45, 4459-4463 (2006).
    [CrossRef] [PubMed]
  7. P. M. Saulnier, M. P. Zinkin, and G. H. Watson, "Scatterer correlation effects on photon transport in dense random media," Phys. Rev. B 42, 2621-2623 (1990).
    [CrossRef]
  8. B. W. Hapke, R. M. Nelson, and W. D. Smythe, "The opposition effect of the moon: the contribution of coherent backscatter," Science 260, 5107-5109 (1993).
    [CrossRef]
  9. Y. G. Shkuratov, M. A. Kreslavsky, A. A. Ovcharenko, D. G. Stankevich, and E. S. Zubko, "Opposition effect from Clementine data and mechanisms of backscatter," Icarus 141,132-155 (1999).
    [CrossRef]
  10. Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
    [CrossRef]
  11. M. I. Mishchenko, J. M. Luck, and T. M. Nieuwenhiuzen, "Full angular profile of the coherent polarization opposition effect," J. Opt. Soc. Am. A 17, 888-891 (2000).
    [CrossRef]
  12. M. I. Mishchenko, "The angular width of the coherent back-scatter opposition effect: an application to icy outer planet satellites," Astrophys. Space Sci. 194, 327-333 (1992).
    [CrossRef]
  13. B. Hapke, D. DiMucci, R. Nelson, and W. Smythe, "The cause of the hot spot in vegetation canopies and soils: shadow hiding versus coherent backscattering," Remote Sens. Environ. 53, 63-68 (1996).
    [CrossRef]
  14. B. Hapke, R. Nelson, and W. Smythe, "The opposition effect of the moon: Coherent backscatter and shadow hiding," Icarus 133, 89-97 (1998).
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    [CrossRef]
  23. S. Bondarenko, A. Ovcharenko, Y. Shkuratov, G. Videen, J. Eversole, and M. Hart, "Light backscatter by surfaces composed of small spherical particles," Appl. Opt. 45, 3871-3877 (2006).
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2006 (4)

2005 (2)

H. Zhang and K. J. Voss, "Comparisons of bidirectional reflectance distribution function measurements on prepared particulate surfaces and radiative-transfer models," Appl. Opt. 44, 597-610 (2005).
[CrossRef] [PubMed]

Y. Shkuratov and Y. S. Grynko, "Light scattering by media composed of semitransparent particles of different shapes in ray optics approximation: consequences for spectroscopy, photometry and polarimetry of planetary regoliths," Icarus 173, 16-28 (2005).
[CrossRef]

2003 (1)

H. Zhang, K. J. Voss, R. P Reid, and E. M. Louchard, "Bidirectional reflectance measurements of sediments in the vicinity of Lee Stocking Island, Bahamas," Limnol. Oceanogr. 48, 380-389 (2003).
[CrossRef]

2002 (1)

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

2001 (1)

C. Bruegge, N. Chrien, and D. Haner, "Spectralon BRF data for MISR calibration applications," Remote Sens. Environ. 76, 354-366 (2001).
[CrossRef]

2000 (1)

1999 (3)

G. D. Lewis, D. L. Jordan, and P. J. Roberts, "Backscattering target detection in a turbid medium by polarization discrimination," Appl. Opt. 38, 3937 - 3944 (1999).
[CrossRef]

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transfer 63, 409-432 (1999).
[CrossRef]

Y. G. Shkuratov, M. A. Kreslavsky, A. A. Ovcharenko, D. G. Stankevich, and E. S. Zubko, "Opposition effect from Clementine data and mechanisms of backscatter," Icarus 141,132-155 (1999).
[CrossRef]

1998 (1)

B. Hapke, R. Nelson, and W. Smythe, "The opposition effect of the moon: Coherent backscatter and shadow hiding," Icarus 133, 89-97 (1998).
[CrossRef]

1996 (1)

B. Hapke, D. DiMucci, R. Nelson, and W. Smythe, "The cause of the hot spot in vegetation canopies and soils: shadow hiding versus coherent backscattering," Remote Sens. Environ. 53, 63-68 (1996).
[CrossRef]

1994 (1)

Y. G. Shkuratov, K. Muinonen, E. Bowell et al. "A critical review of theoretical models of negatively polarized light scattered by atmosphereless solar system bodies," Earth, Moon and Planets 65, 201-246 (1994).
[CrossRef]

1993 (3)

M. I. Mishchenko, "On the nature of the polarization opposition effect exhibited by Saturn’s rings", Astrophys. J. 411, 351-361 (1993).
[CrossRef]

K. Muinonen, "Coherent backscattering by solar system dust particles," Asteroids, Comets, Meteors 160, 271-296 (1993).

B. W. Hapke, R. M. Nelson, and W. D. Smythe, "The opposition effect of the moon: the contribution of coherent backscatter," Science 260, 5107-5109 (1993).
[CrossRef]

1992 (1)

M. I. Mishchenko, "The angular width of the coherent back-scatter opposition effect: an application to icy outer planet satellites," Astrophys. Space Sci. 194, 327-333 (1992).
[CrossRef]

1990 (1)

P. M. Saulnier, M. P. Zinkin, and G. H. Watson, "Scatterer correlation effects on photon transport in dense random media," Phys. Rev. B 42, 2621-2623 (1990).
[CrossRef]

1984 (1)

K. J. Voss and E. S. Fry, "Measurement of the Mueller matrix for ocean water," Applied Opt. 23, 4427-4439 (1984).
[CrossRef]

1967 (1)

Azubko, E.

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

Bondarenko, S.

Bowell, E.

Y. G. Shkuratov, K. Muinonen, E. Bowell et al. "A critical review of theoretical models of negatively polarized light scattered by atmosphereless solar system bodies," Earth, Moon and Planets 65, 201-246 (1994).
[CrossRef]

Bruegge, C.

C. Bruegge, N. Chrien, and D. Haner, "Spectralon BRF data for MISR calibration applications," Remote Sens. Environ. 76, 354-366 (2001).
[CrossRef]

Chrien, N.

C. Bruegge, N. Chrien, and D. Haner, "Spectralon BRF data for MISR calibration applications," Remote Sens. Environ. 76, 354-366 (2001).
[CrossRef]

DiMucci, D.

B. Hapke, D. DiMucci, R. Nelson, and W. Smythe, "The cause of the hot spot in vegetation canopies and soils: shadow hiding versus coherent backscattering," Remote Sens. Environ. 53, 63-68 (1996).
[CrossRef]

Dlugach, J. M.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transfer 63, 409-432 (1999).
[CrossRef]

Eversole, J.

Fry, E. S.

K. J. Voss and E. S. Fry, "Measurement of the Mueller matrix for ocean water," Applied Opt. 23, 4427-4439 (1984).
[CrossRef]

Gilbert, G. D.

Grynko, Y. S.

Y. Shkuratov and Y. S. Grynko, "Light scattering by media composed of semitransparent particles of different shapes in ray optics approximation: consequences for spectroscopy, photometry and polarimetry of planetary regoliths," Icarus 173, 16-28 (2005).
[CrossRef]

Haner, D.

C. Bruegge, N. Chrien, and D. Haner, "Spectralon BRF data for MISR calibration applications," Remote Sens. Environ. 76, 354-366 (2001).
[CrossRef]

Hapke, B.

B. Hapke, R. Nelson, and W. Smythe, "The opposition effect of the moon: Coherent backscatter and shadow hiding," Icarus 133, 89-97 (1998).
[CrossRef]

B. Hapke, D. DiMucci, R. Nelson, and W. Smythe, "The cause of the hot spot in vegetation canopies and soils: shadow hiding versus coherent backscattering," Remote Sens. Environ. 53, 63-68 (1996).
[CrossRef]

Hapke, B. W.

B. W. Hapke, R. M. Nelson, and W. D. Smythe, "The opposition effect of the moon: the contribution of coherent backscatter," Science 260, 5107-5109 (1993).
[CrossRef]

Hart, M.

Helfenstein, P.

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

Jordan, D. L.

Kiselev, N. N.

Kreslavsky, M. A.

Y. G. Shkuratov, M. A. Kreslavsky, A. A. Ovcharenko, D. G. Stankevich, and E. S. Zubko, "Opposition effect from Clementine data and mechanisms of backscatter," Icarus 141,132-155 (1999).
[CrossRef]

Lewis, G. D.

Louchard, E. M.

H. Zhang, K. J. Voss, R. P Reid, and E. M. Louchard, "Bidirectional reflectance measurements of sediments in the vicinity of Lee Stocking Island, Bahamas," Limnol. Oceanogr. 48, 380-389 (2003).
[CrossRef]

Luck, J. M.

Miloslavskaya, O.

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, V. K. Rosenbush, and N. N. Kiselev, "Weak localization of electromagnetic waves and opposition phenomena exhibited by high-albedo atmosphereless solar system objects," Appl. Opt. 45, 4459-4463 (2006).
[CrossRef] [PubMed]

M. I. Mishchenko, J. M. Luck, and T. M. Nieuwenhiuzen, "Full angular profile of the coherent polarization opposition effect," J. Opt. Soc. Am. A 17, 888-891 (2000).
[CrossRef]

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transfer 63, 409-432 (1999).
[CrossRef]

M. I. Mishchenko, "On the nature of the polarization opposition effect exhibited by Saturn’s rings", Astrophys. J. 411, 351-361 (1993).
[CrossRef]

M. I. Mishchenko, "The angular width of the coherent back-scatter opposition effect: an application to icy outer planet satellites," Astrophys. Space Sci. 194, 327-333 (1992).
[CrossRef]

Muinonen, K.

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

Y. G. Shkuratov, K. Muinonen, E. Bowell et al. "A critical review of theoretical models of negatively polarized light scattered by atmosphereless solar system bodies," Earth, Moon and Planets 65, 201-246 (1994).
[CrossRef]

K. Muinonen, "Coherent backscattering by solar system dust particles," Asteroids, Comets, Meteors 160, 271-296 (1993).

Nelson, R.

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

B. Hapke, R. Nelson, and W. Smythe, "The opposition effect of the moon: Coherent backscatter and shadow hiding," Icarus 133, 89-97 (1998).
[CrossRef]

B. Hapke, D. DiMucci, R. Nelson, and W. Smythe, "The cause of the hot spot in vegetation canopies and soils: shadow hiding versus coherent backscattering," Remote Sens. Environ. 53, 63-68 (1996).
[CrossRef]

Nelson, R. M.

B. W. Hapke, R. M. Nelson, and W. D. Smythe, "The opposition effect of the moon: the contribution of coherent backscatter," Science 260, 5107-5109 (1993).
[CrossRef]

Nieuwenhiuzen, T. M.

Ovcharenko, A.

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

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

Ovcharenko, A. A.

Y. G. Shkuratov, M. A. Kreslavsky, A. A. Ovcharenko, D. G. Stankevich, and E. S. Zubko, "Opposition effect from Clementine data and mechanisms of backscatter," Icarus 141,132-155 (1999).
[CrossRef]

Pernicka, J. C.

Piironen, J.

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

Reid, R. P

H. Zhang, K. J. Voss, R. P Reid, and E. M. Louchard, "Bidirectional reflectance measurements of sediments in the vicinity of Lee Stocking Island, Bahamas," Limnol. Oceanogr. 48, 380-389 (2003).
[CrossRef]

Roberts, P. J.

Rosenbush, V.

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

Rosenbush, V. K.

Saulnier, P. M.

P. M. Saulnier, M. P. Zinkin, and G. H. Watson, "Scatterer correlation effects on photon transport in dense random media," Phys. Rev. B 42, 2621-2623 (1990).
[CrossRef]

Shkuratov, Y.

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

Y. Shkuratov and Y. S. Grynko, "Light scattering by media composed of semitransparent particles of different shapes in ray optics approximation: consequences for spectroscopy, photometry and polarimetry of planetary regoliths," Icarus 173, 16-28 (2005).
[CrossRef]

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

Shkuratov, Y. G.

Y. G. Shkuratov, M. A. Kreslavsky, A. A. Ovcharenko, D. G. Stankevich, and E. S. Zubko, "Opposition effect from Clementine data and mechanisms of backscatter," Icarus 141,132-155 (1999).
[CrossRef]

Y. G. Shkuratov, K. Muinonen, E. Bowell et al. "A critical review of theoretical models of negatively polarized light scattered by atmosphereless solar system bodies," Earth, Moon and Planets 65, 201-246 (1994).
[CrossRef]

Smythe, W.

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

B. Hapke, R. Nelson, and W. Smythe, "The opposition effect of the moon: Coherent backscatter and shadow hiding," Icarus 133, 89-97 (1998).
[CrossRef]

B. Hapke, D. DiMucci, R. Nelson, and W. Smythe, "The cause of the hot spot in vegetation canopies and soils: shadow hiding versus coherent backscattering," Remote Sens. Environ. 53, 63-68 (1996).
[CrossRef]

Smythe, W. D.

B. W. Hapke, R. M. Nelson, and W. D. Smythe, "The opposition effect of the moon: the contribution of coherent backscatter," Science 260, 5107-5109 (1993).
[CrossRef]

Stankevich, D. G.

Y. G. Shkuratov, M. A. Kreslavsky, A. A. Ovcharenko, D. G. Stankevich, and E. S. Zubko, "Opposition effect from Clementine data and mechanisms of backscatter," Icarus 141,132-155 (1999).
[CrossRef]

Videen, G.

Voss, K. J.

Watson, G. H.

P. M. Saulnier, M. P. Zinkin, and G. H. Watson, "Scatterer correlation effects on photon transport in dense random media," Phys. Rev. B 42, 2621-2623 (1990).
[CrossRef]

Yanovitskij, E. G.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transfer 63, 409-432 (1999).
[CrossRef]

Zakharova, N. T.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transfer 63, 409-432 (1999).
[CrossRef]

Zhang, H.

Zinkin, M. P.

P. M. Saulnier, M. P. Zinkin, and G. H. Watson, "Scatterer correlation effects on photon transport in dense random media," Phys. Rev. B 42, 2621-2623 (1990).
[CrossRef]

Zubko, E. S.

Y. G. Shkuratov, M. A. Kreslavsky, A. A. Ovcharenko, D. G. Stankevich, and E. S. Zubko, "Opposition effect from Clementine data and mechanisms of backscatter," Icarus 141,132-155 (1999).
[CrossRef]

Appl. Opt. (7)

Applied Opt. (1)

K. J. Voss and E. S. Fry, "Measurement of the Mueller matrix for ocean water," Applied Opt. 23, 4427-4439 (1984).
[CrossRef]

Astrophys. J. (1)

M. I. Mishchenko, "On the nature of the polarization opposition effect exhibited by Saturn’s rings", Astrophys. J. 411, 351-361 (1993).
[CrossRef]

Astrophys. Space Sci. (1)

M. I. Mishchenko, "The angular width of the coherent back-scatter opposition effect: an application to icy outer planet satellites," Astrophys. Space Sci. 194, 327-333 (1992).
[CrossRef]

Earth, Moon and Planets (1)

Y. G. Shkuratov, K. Muinonen, E. Bowell et al. "A critical review of theoretical models of negatively polarized light scattered by atmosphereless solar system bodies," Earth, Moon and Planets 65, 201-246 (1994).
[CrossRef]

Icarus (4)

Y. G. Shkuratov, M. A. Kreslavsky, A. A. Ovcharenko, D. G. Stankevich, and E. S. Zubko, "Opposition effect from Clementine data and mechanisms of backscatter," Icarus 141,132-155 (1999).
[CrossRef]

Y. Shkuratov, A. Ovcharenko, E. Azubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, "The opposition effect and negative polarization of structural analogs for planetary regoliths," Icarus 159, 396-416 (2002).
[CrossRef]

B. Hapke, R. Nelson, and W. Smythe, "The opposition effect of the moon: Coherent backscatter and shadow hiding," Icarus 133, 89-97 (1998).
[CrossRef]

Y. Shkuratov and Y. S. Grynko, "Light scattering by media composed of semitransparent particles of different shapes in ray optics approximation: consequences for spectroscopy, photometry and polarimetry of planetary regoliths," Icarus 173, 16-28 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transfer 63, 409-432 (1999).
[CrossRef]

Limnol. Oceanogr. (1)

H. Zhang, K. J. Voss, R. P Reid, and E. M. Louchard, "Bidirectional reflectance measurements of sediments in the vicinity of Lee Stocking Island, Bahamas," Limnol. Oceanogr. 48, 380-389 (2003).
[CrossRef]

Meteors (1)

K. Muinonen, "Coherent backscattering by solar system dust particles," Asteroids, Comets, Meteors 160, 271-296 (1993).

Phys. Rev. B (1)

P. M. Saulnier, M. P. Zinkin, and G. H. Watson, "Scatterer correlation effects on photon transport in dense random media," Phys. Rev. B 42, 2621-2623 (1990).
[CrossRef]

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C. Bruegge, N. Chrien, and D. Haner, "Spectralon BRF data for MISR calibration applications," Remote Sens. Environ. 76, 354-366 (2001).
[CrossRef]

B. Hapke, D. DiMucci, R. Nelson, and W. Smythe, "The cause of the hot spot in vegetation canopies and soils: shadow hiding versus coherent backscattering," Remote Sens. Environ. 53, 63-68 (1996).
[CrossRef]

Science (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the polarized goniometric system. LP-linear polarizer; QWP-quarter wave plate. In reality, LP1 and QWP1 are inside the incident tube assembly and LP2 and QWP2 are inside the viewing tube assembly. The y axis is the normal of the scattering plane and the direction of perpendicular (“S”) liner polarization, and x is the parallel (“P”) direction.

Fig. 2.
Fig. 2.

(a) REFF (b) degree of polarization (DOP) and (c) μc of sample Rough at normal and 60° illuminations. To aid the identification of the BNP, DOP=0 is shown as the green line in (b).

Fig. 3.
Fig. 3.

Same as Fig. 2 but for Sample A.

Fig. 4.
Fig. 4.

Same as Fig. 2 but for Volcanic.

Fig. 5.
Fig. 5.

Linear polarization ratios μ and μ // of sample Rough at 8° illumination.

Fig. 6.
Fig. 6.

Linear polarization ratios μ and μ // of Sample A at 8° illumination.

Fig. 7.
Fig. 7.

Same as Fig. 2 but for Spheres. Negative phase angle stands for 180° relative azimuth angle between incident and viewing directions. Note the denser data points around the rainbows around 15° and 102°, see Figs. 89 for more detailed angular structures.

Fig. 8.
Fig. 8.

Comparisons of gonio measurement at 60° illumination and single scattering calculations for Spheres: REFF (top), DOP (middle) and circular polarization ratio μc (bottom).

Fig. 9.
Fig. 9.

Measured Spheres μc at incident angles at normal, 20°, 30°, 40°, 50° and 60°, with calculated μc for single scattering, (a) overall comparison (b) comparisons near the first order rainbow and (c) measured μc near the opposition.

Fig. 10
Fig. 10

(a) Linear polarization ratios μ and μ //, (b) single scattering factor (SS Factor) and (c) comparisons of measured REFF (Data REFF), the SS Factor corrected REFF (Data REFF*SS Factor) and single scattering REFF (Eq.(6)) (Model SS REFF), under 60° illumination.

Equations (7)

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

DOP = I I / / I + I / / ,
Δg 0.72 k l * ,
l * = 1 Q sca ( 1 cos θ ) ,
M ij = M 11 M 12 0 0 M 12 M 11 0 0 0 0 M 33 M 34 0 0 M 34 M 33 .
μ c = M 11 + M 33 M 11 M 33
REFF = ω ¯ 0 4 ( μ 0 + μ ) P ( g ) .
Fraction = I PP I PS I PP + I PS = 1 μ / / 1 + μ / / .

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