Abstract

We use the numerically exact superposition T-matrix method to compute electromagnetic scattering characteristics of a macroscopic volume of a discrete random medium filled with wavelength-sized spherical particles with a refractive index typical of water ice at centimeter wavelengths. Our analysis demonstrates relative strengths of various optical observables in terms of their potential remote-sensing content. In particular, it illustrates the importance of accounting for the forward-scattering interference effect in the interpretation of occultation measurements of planetary rings. We show that among the most robust indicators of the amount of multiple scattering inside a particulate medium are the cross- polarized scattered intensity, the same-helicity scattered intensity, and the circular polarization ratio. We also demonstrate that many predictions of the low-packing-density theories of radiative transfer and coherent backscattering are applicable, both qualitatively and semi-quantitatively, to densely packed media.

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  1. E. Rignot, “Backscatter model for the unusual radar properties of the Greenland Ice Sheet,” J. Geophys. Res. 100, 9389-9400 (1995).
    [CrossRef]
  2. S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
    [CrossRef]
  3. J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
    [CrossRef]
  4. S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235-1279 (1993).
    [CrossRef]
  5. P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
    [CrossRef]
  6. V. Rosenbush, N. Kiselev, V. Avramchuk, and M. Mishchenko, “Photometric and polarimetric opposition phenomena exhibited by solar system bodies,” in Optics of Cosmic Dust, G. Videen and M. Kocifaj, eds. (Kluwer Academic, 2002), pp. 191-224.
  7. G.Videen, Ya.Yatskiv, and M.Mishchenko, eds., Photopolarimetry in Remote Sensing (Kluwer Academic, 2004).
  8. 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]
  9. Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
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    [CrossRef]
  13. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).
  14. V. P. Tishkovets, “Incoherent and coherent backscattering of light by a layer of densely packed random medium,” J. Quant. Spectrosc. Radiat. Transfer 108, 454-463 (2007).
    [CrossRef]
  15. K. K. Tse, L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, “Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow,” Radio Sci. 42, RS5001 (2007).
    [CrossRef]
  16. M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, “Multiple scattering by random particulate media: exact 3D results,” Opt. Express 15, 2822-2836 (2007).
    [CrossRef] [PubMed]
  17. S. Tseng, “Optical characteristics of a cluster of closely-packed dielectric spheres,” Opt. Commun. 281, 1986-1990 (2008).
    [CrossRef]
  18. Y. Okada and A. A. Kokhanovsky, “Light scattering and absorption by densely packed groups of spherical particles,” J. Quant. Spectrosc. Radiat. Transfer (to be published).
  19. Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, “Enhanced backscattering in optics,” Prog. Opt. 29, 65-197 (1991).
    [CrossRef]
  20. V. L. Kuz'min and V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Phys.-Usp. 39, 231-260 (1996).
    [CrossRef]
  21. C.Mätzler, ed., Thermal Microwave Radiation: Applications for Remote Sensing (IET Press, 2006).
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  22. D. W. Mackowski, “A simplified model to predict the effects of aggregation on the absorption properties of soot particles,” J. Quant. Spectrosc. Radiat. Transfer 100, 237-249 (2006).
    [CrossRef]
  23. D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266-2278 (1996).
    [CrossRef]
  24. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002), http://www.giss.nasa.gov/~crmim/books.html.
  25. J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres--Basic Concepts and Practical Methods (Springer, 2004).
  26. M. I. Mishchenko, “Multiple scattering, radiative transfer, and weak localization in discrete random media: unified microphysical approach,” Rev. Geophys. 46, RG2003 (2008).
    [CrossRef]
  27. A. P. Ivanov, A. Ya. Khairullina, and T. N. Kharkova, “Experimental detection of cooperative effects in a scattering volume,” Opt. Spectrosc. 28, 204-207 (1970).
  28. C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
    [CrossRef]
  29. J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
    [CrossRef]
  30. J. M. Dlugach and M. I. Mishchenko, “Diffuse and coherent backscattering of polarized light: polarization ratios for a discrete random medium composed of nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 21-32(2007).
    [CrossRef]
  31. E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering of agglomerate particles,” J. Quant. Spectrosc. Radiat. Transfer 88, 163-171 (2004).
    [CrossRef]

2008 (3)

S. Tseng, “Optical characteristics of a cluster of closely-packed dielectric spheres,” Opt. Commun. 281, 1986-1990 (2008).
[CrossRef]

M. I. Mishchenko, “Multiple scattering, radiative transfer, and weak localization in discrete random media: unified microphysical approach,” Rev. Geophys. 46, RG2003 (2008).
[CrossRef]

C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
[CrossRef]

2007 (5)

Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
[CrossRef]

V. P. Tishkovets, “Incoherent and coherent backscattering of light by a layer of densely packed random medium,” J. Quant. Spectrosc. Radiat. Transfer 108, 454-463 (2007).
[CrossRef]

K. K. Tse, L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, “Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow,” Radio Sci. 42, RS5001 (2007).
[CrossRef]

J. M. Dlugach and M. I. Mishchenko, “Diffuse and coherent backscattering of polarized light: polarization ratios for a discrete random medium composed of nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 21-32(2007).
[CrossRef]

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, “Multiple scattering by random particulate media: exact 3D results,” Opt. Express 15, 2822-2836 (2007).
[CrossRef] [PubMed]

2006 (2)

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]

D. W. Mackowski, “A simplified model to predict the effects of aggregation on the absorption properties of soot particles,” J. Quant. Spectrosc. Radiat. Transfer 100, 237-249 (2006).
[CrossRef]

2005 (1)

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

2004 (1)

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering of agglomerate particles,” J. Quant. Spectrosc. Radiat. Transfer 88, 163-171 (2004).
[CrossRef]

2003 (1)

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 775-824 (2003).
[CrossRef]

2001 (1)

S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
[CrossRef]

1996 (2)

V. L. Kuz'min and V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Phys.-Usp. 39, 231-260 (1996).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266-2278 (1996).
[CrossRef]

1995 (1)

E. Rignot, “Backscatter model for the unusual radar properties of the Greenland Ice Sheet,” J. Geophys. Res. 100, 9389-9400 (1995).
[CrossRef]

1994 (1)

J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
[CrossRef]

1993 (1)

S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235-1279 (1993).
[CrossRef]

1991 (1)

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, “Enhanced backscattering in optics,” Prog. Opt. 29, 65-197 (1991).
[CrossRef]

1974 (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

1970 (1)

A. P. Ivanov, A. Ya. Khairullina, and T. N. Kharkova, “Experimental detection of cooperative effects in a scattering volume,” Opt. Spectrosc. 28, 204-207 (1970).

Avramchuk, V.

V. Rosenbush, N. Kiselev, V. Avramchuk, and M. Mishchenko, “Photometric and polarimetric opposition phenomena exhibited by solar system bodies,” in Optics of Cosmic Dust, G. Videen and M. Kocifaj, eds. (Kluwer Academic, 2002), pp. 191-224.

Barabanenkov, Yu. N.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, “Enhanced backscattering in optics,” Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Black, G. J.

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

Bondarenko, S.

Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
[CrossRef]

Bonner, R.

S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
[CrossRef]

Bussey, D.

S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
[CrossRef]

Cairns, B.

Campbell, D. B.

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

Chan, C. H.

K. K. Tse, L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, “Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow,” Radio Sci. 42, RS5001 (2007).
[CrossRef]

Crespo, A.

J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
[CrossRef]

Ding, K. H.

K. K. Tse, L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, “Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow,” Radio Sci. 42, RS5001 (2007).
[CrossRef]

Dlugach, J. M.

J. M. Dlugach and M. I. Mishchenko, “Diffuse and coherent backscattering of polarized light: polarization ratios for a discrete random medium composed of nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 21-32(2007).
[CrossRef]

Domke, H.

J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres--Basic Concepts and Practical Methods (Springer, 2004).

Dones, L.

C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
[CrossRef]

Dryer, M. J.

J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
[CrossRef]

Eversole, J.

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering of agglomerate particles,” J. Quant. Spectrosc. Radiat. Transfer 88, 163-171 (2004).
[CrossRef]

French, R. G.

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

Hansen, J. E.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

Harmon, J. K.

J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
[CrossRef]

Hart, M.

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering of agglomerate particles,” J. Quant. Spectrosc. Radiat. Transfer 88, 163-171 (2004).
[CrossRef]

Hovenier, J. W.

J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres--Basic Concepts and Practical Methods (Springer, 2004).

Ivanov, A. P.

A. P. Ivanov, A. Ya. Khairullina, and T. N. Kharkova, “Experimental detection of cooperative effects in a scattering volume,” Opt. Spectrosc. 28, 204-207 (1970).

Johnson, J. M.

J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
[CrossRef]

Kahnert, F. M.

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 775-824 (2003).
[CrossRef]

Kaydash, V.

Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
[CrossRef]

Khairullina, A. Ya.

A. P. Ivanov, A. Ya. Khairullina, and T. N. Kharkova, “Experimental detection of cooperative effects in a scattering volume,” Opt. Spectrosc. 28, 204-207 (1970).

Kharkova, T. N.

A. P. Ivanov, A. Ya. Khairullina, and T. N. Kharkova, “Experimental detection of cooperative effects in a scattering volume,” Opt. Spectrosc. 28, 204-207 (1970).

Kiselev, N.

V. Rosenbush, N. Kiselev, V. Avramchuk, and M. Mishchenko, “Photometric and polarimetric opposition phenomena exhibited by solar system bodies,” in Optics of Cosmic Dust, G. Videen and M. Kocifaj, eds. (Kluwer Academic, 2002), pp. 191-224.

Kiselev, N. N.

Kokhanovsky, A. A.

Y. Okada and A. A. Kokhanovsky, “Light scattering and absorption by densely packed groups of spherical particles,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

Kravtsov, Yu. A.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, “Enhanced backscattering in optics,” Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Kuz'min, V. L.

V. L. Kuz'min and V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Phys.-Usp. 39, 231-260 (1996).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002), http://www.giss.nasa.gov/~crmim/books.html.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).

Leung, K. W.

K. K. Tse, L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, “Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow,” Radio Sci. 42, RS5001 (2007).
[CrossRef]

Lichtenberg, C.

S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
[CrossRef]

Liu, L.

Mackowski, D. W.

Margot, J.-L.

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

Mishchenko, M.

V. Rosenbush, N. Kiselev, V. Avramchuk, and M. Mishchenko, “Photometric and polarimetric opposition phenomena exhibited by solar system bodies,” in Optics of Cosmic Dust, G. Videen and M. Kocifaj, eds. (Kluwer Academic, 2002), pp. 191-224.

Mishchenko, M. I.

M. I. Mishchenko, “Multiple scattering, radiative transfer, and weak localization in discrete random media: unified microphysical approach,” Rev. Geophys. 46, RG2003 (2008).
[CrossRef]

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, “Multiple scattering by random particulate media: exact 3D results,” Opt. Express 15, 2822-2836 (2007).
[CrossRef] [PubMed]

J. M. Dlugach and M. I. Mishchenko, “Diffuse and coherent backscattering of polarized light: polarization ratios for a discrete random medium composed of nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 21-32(2007).
[CrossRef]

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]

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266-2278 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002), http://www.giss.nasa.gov/~crmim/books.html.

Muñoz, O.

Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
[CrossRef]

Nicholson, P. D.

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

Nolan, M. C.

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

Nozette, S.

S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
[CrossRef]

Okada, Y.

Y. Okada and A. A. Kokhanovsky, “Light scattering and absorption by densely packed groups of spherical particles,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

Ostro, S. J.

S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235-1279 (1993).
[CrossRef]

Ozrin, V. D.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, “Enhanced backscattering in optics,” Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Porco, C. C.

C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
[CrossRef]

Quinn, T.

C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
[CrossRef]

Richardson, D. C.

C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
[CrossRef]

Rignot, E.

E. Rignot, “Backscatter model for the unusual radar properties of the Greenland Ice Sheet,” J. Geophys. Res. 100, 9389-9400 (1995).
[CrossRef]

Robinson, M.

S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
[CrossRef]

Romanov, V. P.

V. L. Kuz'min and V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Phys.-Usp. 39, 231-260 (1996).
[CrossRef]

Rosenbush, V.

V. Rosenbush, N. Kiselev, V. Avramchuk, and M. Mishchenko, “Photometric and polarimetric opposition phenomena exhibited by solar system bodies,” in Optics of Cosmic Dust, G. Videen and M. Kocifaj, eds. (Kluwer Academic, 2002), pp. 191-224.

Rosenbush, V. K.

Saichev, A. I.

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, “Enhanced backscattering in optics,” Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Salo, H. J.

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

Shkuratov, Yu.

Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
[CrossRef]

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering of agglomerate particles,” J. Quant. Spectrosc. Radiat. Transfer 88, 163-171 (2004).
[CrossRef]

Slade, M. A.

J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
[CrossRef]

Spudis, P.

S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
[CrossRef]

Throop, H.

C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
[CrossRef]

Tishkovets, V. P.

V. P. Tishkovets, “Incoherent and coherent backscattering of light by a layer of densely packed random medium,” J. Quant. Spectrosc. Radiat. Transfer 108, 454-463 (2007).
[CrossRef]

Travis, L. D.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002), http://www.giss.nasa.gov/~crmim/books.html.

Tsang, L.

K. K. Tse, L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, “Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow,” Radio Sci. 42, RS5001 (2007).
[CrossRef]

Tse, K. K.

K. K. Tse, L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, “Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow,” Radio Sci. 42, RS5001 (2007).
[CrossRef]

Tseng, S.

S. Tseng, “Optical characteristics of a cluster of closely-packed dielectric spheres,” Opt. Commun. 281, 1986-1990 (2008).
[CrossRef]

van der Mee, C.

J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres--Basic Concepts and Practical Methods (Springer, 2004).

Vélez, R. A.

J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
[CrossRef]

Videen, G.

Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
[CrossRef]

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, “Multiple scattering by random particulate media: exact 3D results,” Opt. Express 15, 2822-2836 (2007).
[CrossRef] [PubMed]

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering of agglomerate particles,” J. Quant. Spectrosc. Radiat. Transfer 88, 163-171 (2004).
[CrossRef]

Volten, H.

Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
[CrossRef]

Voss, K. J.

H. Zhang and K. J. Voss, “Bidirectional reflectance measurements of closely packed natural and prepared particulate surfaces,” in Light Scattering Reviews 3, Springer Praxis Books (Springer, 2008), pp. 279-327.
[CrossRef]

Weiss, J. W.

C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
[CrossRef]

Zhang, H.

H. Zhang and K. J. Voss, “Bidirectional reflectance measurements of closely packed natural and prepared particulate surfaces,” in Light Scattering Reviews 3, Springer Praxis Books (Springer, 2008), pp. 279-327.
[CrossRef]

Zubko, E.

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering of agglomerate particles,” J. Quant. Spectrosc. Radiat. Transfer 88, 163-171 (2004).
[CrossRef]

Appl. Opt. (1)

Astron. J. (1)

C. C. Porco, J. W. Weiss, D. C. Richardson, L. Dones, T. Quinn, and H. Throop, “Simulations of the dynamical and lighT-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties,” Astron. J. 136, 2172-2200(2008).
[CrossRef]

Icarus (1)

P. D. Nicholson, R. G. French, D. B. Campbell, J.-L. Margot, M. C. Nolan, G. J. Black, and H. J. Salo, “Radar imaging of Saturn's rings,” Icarus 177, 32-62 (2005).
[CrossRef]

J. Geophys. Res. (2)

E. Rignot, “Backscatter model for the unusual radar properties of the Greenland Ice Sheet,” J. Geophys. Res. 100, 9389-9400 (1995).
[CrossRef]

S. Nozette, P. Spudis, M. Robinson, D. Bussey, C. Lichtenberg, and R. Bonner, “Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole,” J. Geophys. Res. 106, 23253-23266 (2001).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer (7)

D. W. Mackowski, “A simplified model to predict the effects of aggregation on the absorption properties of soot particles,” J. Quant. Spectrosc. Radiat. Transfer 100, 237-249 (2006).
[CrossRef]

J. M. Dlugach and M. I. Mishchenko, “Diffuse and coherent backscattering of polarized light: polarization ratios for a discrete random medium composed of nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 21-32(2007).
[CrossRef]

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering of agglomerate particles,” J. Quant. Spectrosc. Radiat. Transfer 88, 163-171 (2004).
[CrossRef]

Y. Okada and A. A. Kokhanovsky, “Light scattering and absorption by densely packed groups of spherical particles,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

Yu. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Muñoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Radiat. Transfer 106, 487-508 (2007).
[CrossRef]

V. P. Tishkovets, “Incoherent and coherent backscattering of light by a layer of densely packed random medium,” J. Quant. Spectrosc. Radiat. Transfer 108, 454-463 (2007).
[CrossRef]

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 775-824 (2003).
[CrossRef]

Nature (1)

J. K. Harmon, M. A. Slade, R. A. Vélez, A. Crespo, M. J. Dryer, and J. M. Johnson, “Radar mapping of Mercury's polar anomalies,” Nature 369, 213-215 (1994).
[CrossRef]

Opt. Commun. (1)

S. Tseng, “Optical characteristics of a cluster of closely-packed dielectric spheres,” Opt. Commun. 281, 1986-1990 (2008).
[CrossRef]

Opt. Express (1)

Opt. Spectrosc. (1)

A. P. Ivanov, A. Ya. Khairullina, and T. N. Kharkova, “Experimental detection of cooperative effects in a scattering volume,” Opt. Spectrosc. 28, 204-207 (1970).

Phys.-Usp. (1)

V. L. Kuz'min and V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Phys.-Usp. 39, 231-260 (1996).
[CrossRef]

Prog. Opt. (1)

Yu. N. Barabanenkov, Yu. A. Kravtsov, V. D. Ozrin, and A. I. Saichev, “Enhanced backscattering in optics,” Prog. Opt. 29, 65-197 (1991).
[CrossRef]

Radio Sci. (1)

K. K. Tse, L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, “Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow,” Radio Sci. 42, RS5001 (2007).
[CrossRef]

Rev. Geophys. (1)

M. I. Mishchenko, “Multiple scattering, radiative transfer, and weak localization in discrete random media: unified microphysical approach,” Rev. Geophys. 46, RG2003 (2008).
[CrossRef]

Rev. Mod. Phys. (1)

S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235-1279 (1993).
[CrossRef]

Space Sci. Rev. (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

Other (8)

C.Mätzler, ed., Thermal Microwave Radiation: Applications for Remote Sensing (IET Press, 2006).
[CrossRef]

H. Zhang and K. J. Voss, “Bidirectional reflectance measurements of closely packed natural and prepared particulate surfaces,” in Light Scattering Reviews 3, Springer Praxis Books (Springer, 2008), pp. 279-327.
[CrossRef]

M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

V. Rosenbush, N. Kiselev, V. Avramchuk, and M. Mishchenko, “Photometric and polarimetric opposition phenomena exhibited by solar system bodies,” in Optics of Cosmic Dust, G. Videen and M. Kocifaj, eds. (Kluwer Academic, 2002), pp. 191-224.

G.Videen, Ya.Yatskiv, and M.Mishchenko, eds., Photopolarimetry in Remote Sensing (Kluwer Academic, 2004).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002), http://www.giss.nasa.gov/~crmim/books.html.

J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres--Basic Concepts and Practical Methods (Springer, 2004).

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Figures (1)

Fig. 1
Fig. 1

(a) Macroscopic spherical scattering volume filled with N randomly positioned spherical ice particles. (b) Scattering geometry. (c)–(l) Scattering characteristics of the macroscopic volume as functions of the particle filling factor and scattering angle.

Equations (4)

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

[ I sca Q sca U sca V sca ] [ a 1 ( Θ ) b 1 ( Θ ) 0 0 b 1 ( Θ ) a 2 ( Θ ) 0 0 0 0 a 3 ( Θ ) b 2 ( Θ ) 0 0 b 2 ( Θ ) a 4 ( Θ ) ] [ I inc Q inc U inc V inc ] ,
1 2 0 π d Θ sin Θ a 1 ( Θ ) = 1.
μ L = I sca Q sca I sca + Q sca = a 1 ( Θ ) a 2 ( Θ ) a 1 ( Θ ) + 2 b 1 ( Θ ) + a 2 ( Θ ) ,
μ C = I sca + V sca I sca V sca = a 1 ( Θ ) + a 4 ( Θ ) a 1 ( Θ ) a 4 ( Θ ) .

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