Abstract

I develop a second-order ray-tracing model of the light scattered by a cloud of randomly oriented facets having sizes much larger than the incident wavelength. My results suggest that both symmetric and asymmetric branches of the polarization opposition effect can be produced by the same mechanism responsible for the photometric opposition effect, i.e., constructive interference of light rays traversing reciprocal paths that is associated with coherent backscattering enhancement. The model provides a greatly simplified representation of the physical phenomena to isolate the two mechanisms that may be responsible for the effect. The shapes and positions of the two branches of the polarization opposition effect calculated with the model are consistent with observation, so the model may provide a rapid technique to characterize the optical and physical properties of a scattering system. I note, however, that the model is a gross simplification containing only two physical mechanisms, Fresnel reflections and coherent interference, and it is possible that it represents a nonphysical description of particles smaller than the wavelength or that other mechanisms contributing to the polarization opposition effect are not included.

© 2002 Optical Society of America

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  1. V. K. Rosenbush, V. V. Avramchuk, A. E. Rosenbush, M. I. Mishchenko, “Polarization properties of the Galilean satellites of Jupiter: observations and preliminary analysis,” Astrophys. J. 487, 402–414 (1997).
    [CrossRef]
  2. K. Muinonen, “Coherent backscattering by solar system dust particles,” in Asteroids, Comets and Meteors, A. Milani, M. Di Martino, A. Cellino, eds. (Kluwer, Dordrecht, The Netherlands, 1974), pp. 271–296.
  3. Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).
  4. M. I. Mishchenko, “On the nature of the polarization opposition effect exhibited by Saturn’s rings,” Astrophys. J. 411, 351–361 (1993).
    [CrossRef]
  5. V. D. Ozrin, “Exact solution for the coherent backscattering of polarized light from a random medium of Rayleigh scatterers,” Waves Random Media 2, 141–164 (1992).
    [CrossRef]
  6. M. I. Mishchenko, “Polarization effects in weak localization of light: calculation of the copolarized and depolarized backscattering enhancement factors,” Phys. Rev. B 44, 12579–12600 (1991).
    [CrossRef]
  7. M. I. Mishchenko, “Enhanced backscattering of polarized light from discrete random media,” J. Opt. Soc. Am. A 9, 978–982 (1992).
    [CrossRef]
  8. M. I. Mishchenko, J.-M. Luck, T. M. Nieuwenhuizen, “Full angular profile of the coherent polarization opposition effect,” J. Opt. Soc. Am. A 17, 888–891 (2000).
    [CrossRef]
  9. I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. W. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
    [CrossRef]
  10. K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. I. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
    [CrossRef]
  11. K. Muinonen, “Coherent backscattering by absorbing and scattering media,” in Light Scattering by Nonspherical Particles, B. Gustafson, L. Kolokolova, G. Videen, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2002) 223–226.
  12. Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
    [CrossRef]
  13. J. E. Geake, M. Geake, “A remote-sensing method for sub-wavelength grains on planetary surfaces by optical polarimetry,” Mon. Notes R. Astron. Soc. 245, 46–55 (1990).
  14. G. Videen, M. Kocifaj, eds., Optics of Cosmic Dust (Kluwer Academic, Dordrecht, The Netherlands, 2002).
    [CrossRef]
  15. M. Wolff, “Polarization of light reflected from rough planetary surface,” Appl. Opt. 14, 1395–1405 (1975).
    [CrossRef] [PubMed]
  16. Yu. Shkuratov, “New mechanism of the negative polarization of light scattered by atmosphereless cosmic bodies,” Astron. Vestn. 23, 176–180 (1989).
  17. K. Muinonen, “Scattering of light by solar system dust: the coherent backscatter phenomenon,” in the 1990 Proceedings of the Finnish Astronomical Society, K. Muinonen, M. Kokku, P. Pohjolainen, P. Hakala, eds. (Observatory and Astrophysics Laboratory, University of Helsinki, Helsinki, Finland, 1990), Vol. 12, pp. 12–15.
  18. Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1991), Vol. 24, pp. 67–197.
  19. N. T. Zakharova, M. I. Mishchenko, “Scattering properties of needlelike and platelike ice spheroids with moderate size parameters,” Appl. Opt. 39, 5052–5057 (2000); see, for example, Fig. 3 for a/b = 2.
    [CrossRef]
  20. H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
    [CrossRef]
  21. O. Muñoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm,” J. Geophys. Res. 106 (D19), 22833–22844 (2001).
    [CrossRef]

2001 (2)

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
[CrossRef]

O. Muñoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm,” J. Geophys. Res. 106 (D19), 22833–22844 (2001).
[CrossRef]

2000 (2)

1999 (1)

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

1997 (1)

V. K. Rosenbush, V. V. Avramchuk, A. E. Rosenbush, M. I. Mishchenko, “Polarization properties of the Galilean satellites of Jupiter: observations and preliminary analysis,” Astrophys. J. 487, 402–414 (1997).
[CrossRef]

1993 (1)

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

1992 (2)

V. D. Ozrin, “Exact solution for the coherent backscattering of polarized light from a random medium of Rayleigh scatterers,” Waves Random Media 2, 141–164 (1992).
[CrossRef]

M. I. Mishchenko, “Enhanced backscattering of polarized light from discrete random media,” J. Opt. Soc. Am. A 9, 978–982 (1992).
[CrossRef]

1991 (3)

1990 (1)

J. E. Geake, M. Geake, “A remote-sensing method for sub-wavelength grains on planetary surfaces by optical polarimetry,” Mon. Notes R. Astron. Soc. 245, 46–55 (1990).

1989 (1)

Yu. Shkuratov, “New mechanism of the negative polarization of light scattered by atmosphereless cosmic bodies,” Astron. Vestn. 23, 176–180 (1989).

1975 (1)

Arnold, G.

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

Avramchuk, V. V.

V. K. Rosenbush, V. V. Avramchuk, A. E. Rosenbush, M. I. Mishchenko, “Polarization properties of the Galilean satellites of Jupiter: observations and preliminary analysis,” Astrophys. J. 487, 402–414 (1997).
[CrossRef]

Barabanenkov, Yu. N.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1991), Vol. 24, pp. 67–197.

Barber, P. W.

Geake, J. E.

J. E. Geake, M. Geake, “A remote-sensing method for sub-wavelength grains on planetary surfaces by optical polarimetry,” Mon. Notes R. Astron. Soc. 245, 46–55 (1990).

Geake, M.

J. E. Geake, M. Geake, “A remote-sensing method for sub-wavelength grains on planetary surfaces by optical polarimetry,” Mon. Notes R. Astron. Soc. 245, 46–55 (1990).

Haan, J. F. de

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
[CrossRef]

O. Muñoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm,” J. Geophys. Res. 106 (D19), 22833–22844 (2001).
[CrossRef]

Helfenstein, P.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Hoovenier, J. W.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
[CrossRef]

O. Muñoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm,” J. Geophys. Res. 106 (D19), 22833–22844 (2001).
[CrossRef]

Kaasalainen, S.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Kaydash, V.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Kravtsov, Yu. A.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1991), Vol. 24, pp. 67–197.

Kreslavsky, M.

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

Lindell, I. V.

Luck, J.-M.

Lumme, K. A.

Miloslavskaya, O.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Mishchenko, M. I.

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

N. T. Zakharova, M. I. Mishchenko, “Scattering properties of needlelike and platelike ice spheroids with moderate size parameters,” Appl. Opt. 39, 5052–5057 (2000); see, for example, Fig. 3 for a/b = 2.
[CrossRef]

V. K. Rosenbush, V. V. Avramchuk, A. E. Rosenbush, M. I. Mishchenko, “Polarization properties of the Galilean satellites of Jupiter: observations and preliminary analysis,” Astrophys. J. 487, 402–414 (1997).
[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, “Enhanced backscattering of polarized light from discrete random media,” J. Opt. Soc. Am. A 9, 978–982 (1992).
[CrossRef]

M. I. Mishchenko, “Polarization effects in weak localization of light: calculation of the copolarized and depolarized backscattering enhancement factors,” Phys. Rev. B 44, 12579–12600 (1991).
[CrossRef]

Muinonen, K.

K. Muinonen, “Coherent backscattering by solar system dust particles,” in Asteroids, Comets and Meteors, A. Milani, M. Di Martino, A. Cellino, eds. (Kluwer, Dordrecht, The Netherlands, 1974), pp. 271–296.

K. Muinonen, “Coherent backscattering by absorbing and scattering media,” in Light Scattering by Nonspherical Particles, B. Gustafson, L. Kolokolova, G. Videen, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2002) 223–226.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

K. Muinonen, “Scattering of light by solar system dust: the coherent backscatter phenomenon,” in the 1990 Proceedings of the Finnish Astronomical Society, K. Muinonen, M. Kokku, P. Pohjolainen, P. Hakala, eds. (Observatory and Astrophysics Laboratory, University of Helsinki, Helsinki, Finland, 1990), Vol. 12, pp. 12–15.

Muinonen, K. O.

Muñoz, O.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
[CrossRef]

O. Muñoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm,” J. Geophys. Res. 106 (D19), 22833–22844 (2001).
[CrossRef]

Nelson, R.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Nieuwenhuizen, T. M.

Omelchenko, V.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Ovcharenko, A.

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Ozrin, V. D.

V. D. Ozrin, “Exact solution for the coherent backscattering of polarized light from a random medium of Rayleigh scatterers,” Waves Random Media 2, 141–164 (1992).
[CrossRef]

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1991), Vol. 24, pp. 67–197.

Pieters, C.

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

Piironen, J.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Rol, E.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
[CrossRef]

Rosenbush, A. E.

V. K. Rosenbush, V. V. Avramchuk, A. E. Rosenbush, M. I. Mishchenko, “Polarization properties of the Galilean satellites of Jupiter: observations and preliminary analysis,” Astrophys. J. 487, 402–414 (1997).
[CrossRef]

Rosenbush, V.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Rosenbush, V. K.

V. K. Rosenbush, V. V. Avramchuk, A. E. Rosenbush, M. I. Mishchenko, “Polarization properties of the Galilean satellites of Jupiter: observations and preliminary analysis,” Astrophys. J. 487, 402–414 (1997).
[CrossRef]

Saichev, A. I.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1991), Vol. 24, pp. 67–197.

Shkuratov, Yu.

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

Yu. Shkuratov, “New mechanism of the negative polarization of light scattered by atmosphereless cosmic bodies,” Astron. Vestn. 23, 176–180 (1989).

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Sihvola, A. H.

Smythe, W.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Stankevich, D.

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Vassen, W.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
[CrossRef]

O. Muñoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm,” J. Geophys. Res. 106 (D19), 22833–22844 (2001).
[CrossRef]

Volten, H.

O. Muñoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm,” J. Geophys. Res. 106 (D19), 22833–22844 (2001).
[CrossRef]

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
[CrossRef]

Wolff, M.

Zakharova, N. T.

Zubko, E.

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

Appl. Opt. (2)

Astron. Vestn. (1)

Yu. Shkuratov, “New mechanism of the negative polarization of light scattered by atmosphereless cosmic bodies,” Astron. Vestn. 23, 176–180 (1989).

Astrophys. J. (2)

V. K. Rosenbush, V. V. Avramchuk, A. E. Rosenbush, M. I. Mishchenko, “Polarization properties of the Galilean satellites of Jupiter: observations and preliminary analysis,” Astrophys. J. 487, 402–414 (1997).
[CrossRef]

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

Icarus (1)

Yu. Shkuratov, M. Kreslavsky, A. Ovcharenko, D. Stankevich, E. Zubko, C. Pieters, G. Arnold, “Opposition effect from Clementine data and mechanisms of backscatter,” Icarus 141, 132–155 (1999).
[CrossRef]

J. Geophys. Res. (2)

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106 (D15), 17375–17401 (2001).
[CrossRef]

O. Muñoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hoovenier, “Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm,” J. Geophys. Res. 106 (D19), 22833–22844 (2001).
[CrossRef]

J. Opt. Soc. Am. A (4)

Mon. Notes R. Astron. Soc. (1)

J. E. Geake, M. Geake, “A remote-sensing method for sub-wavelength grains on planetary surfaces by optical polarimetry,” Mon. Notes R. Astron. Soc. 245, 46–55 (1990).

Phys. Rev. B (1)

M. I. Mishchenko, “Polarization effects in weak localization of light: calculation of the copolarized and depolarized backscattering enhancement factors,” Phys. Rev. B 44, 12579–12600 (1991).
[CrossRef]

Waves Random Media (1)

V. D. Ozrin, “Exact solution for the coherent backscattering of polarized light from a random medium of Rayleigh scatterers,” Waves Random Media 2, 141–164 (1992).
[CrossRef]

Other (6)

K. Muinonen, “Coherent backscattering by solar system dust particles,” in Asteroids, Comets and Meteors, A. Milani, M. Di Martino, A. Cellino, eds. (Kluwer, Dordrecht, The Netherlands, 1974), pp. 271–296.

Yu. Shkuratov, A. Ovcharenko, E. Zubko, V. Kaydash, D. Stankevich, V. Omelchenko, O. Miloslavskaya, K. Muinonen, J. Piironen, S. Kaasalainen, R. Nelson, W. Smythe, V. Rosenbush, P. Helfenstein, “The opposition effect and negative polarization of structural analogs of planetary regoliths,” Icarus (to be published).

K. Muinonen, “Coherent backscattering by absorbing and scattering media,” in Light Scattering by Nonspherical Particles, B. Gustafson, L. Kolokolova, G. Videen, eds. (U.S. Army Research Laboratory, Adelphi, Md., 2002) 223–226.

G. Videen, M. Kocifaj, eds., Optics of Cosmic Dust (Kluwer Academic, Dordrecht, The Netherlands, 2002).
[CrossRef]

K. Muinonen, “Scattering of light by solar system dust: the coherent backscatter phenomenon,” in the 1990 Proceedings of the Finnish Astronomical Society, K. Muinonen, M. Kokku, P. Pohjolainen, P. Hakala, eds. (Observatory and Astrophysics Laboratory, University of Helsinki, Helsinki, Finland, 1990), Vol. 12, pp. 12–15.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, A. I. Saichev, “Enhanced backscattering in optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1991), Vol. 24, pp. 67–197.

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Figures (3)

Fig. 1
Fig. 1

Polarization properties of a Rayleigh scatterer and of large facets, whose scatter into the far field is calculated by a single Fresnel reflection. Zero degrees is the forward scatter, measured from the specular direction, and 180° is the backscatter direction. Although the polarization properties of a Rayleigh sphere is independent of material, those calculated with Fresnel reflections are dependent on material properties of the crystal. The refractive indices used in this simulation are m water = 1.33 + 10-5 i and m aluminum = 0.5 + 5.0i.

Fig. 2
Fig. 2

Geometry of the scattering system.

Fig. 3
Fig. 3

Polarization state of scattered light resulting from second-order ray tracing. Three different spatial distributions of facets are chosen. For large separations, the POE dip is asymmetric and its minima are located at approximately 1°. As the facets are brought closer together, the position of the peak moves to larger scattering angles and becomes more symmetric.

Equations (13)

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qmin1.68kl.
D0=sin γ, 0, -cos γ, D1=-sin θ cos ϕ, -sin θ sin ϕ, -cos θ, D2=0, 0, 1.
α01=12π-arccosD0 · D1 =12π-arccos-sin θ cos ϕ sin γ+cos θ cos γ, α12=θ/2.
cos θ12=D0×D1|D0×D1| · D1×D2|D1×D2|=sin θ cos γ+cos θ cos ϕ sin γsin2 θ sin2 ϕ+sin θ cos ϕ cos γ+cos θ sin γ21/2.
θ20=ϕ.
EsEpcos ϕsin ϕ-sin ϕcos ϕrsα1200rpα12×cos θ12sin θ12-sin θ12cos θ12rsα01E0rpα01E0,
IsIpEs*EsEp*EpPzPx cos α12 cos α01×sin α12dxdα12dϕ.
I2=I1 exp-β|D1|,
IsIp Es*EsEp*Epexp-βxcos α12 cos α01×sin α12dα12dxdϕ.
Es=Es1+Es2; Ep=Ep1+Ep2,
Es*Es=2Es1*Es11+cos Φ, Ep*Ep=2Ep1*Ep11+cos Φ,
Φ=k|D1|-cos θ+sin γ sin θ cos ϕ+cos γ cos θ=α|D1|.
IsIp2 Es1*Es1Ep1*Ep12β2+α2β2+α2cos α12 cos α01×sin α12dα12dϕ.

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