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Coherent Backscattering by Solar System Dust Particles

Published online by Cambridge University Press:  19 July 2016

Karri Muinonen
Karri Muinonen*
Affiliation:
Observatory, P.O. Box 14 FIN-00014 University of Helsinki, Finland E-mail [email protected]

Abstract

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I review progress in interpreting the opposition effect and negative linear polarization observed for solar system dust particles. The so–called coherent backscattering mechanism has recently been introduced to explain the observations. However, fundamental difficulties in theoretical modeling still prevent quantitative interpretation. I also review some of the key observations that questioned the hitherto widely accepted mutual–shadowing explanation for the opposition effect. I summarize previous theoretical and experimental work on the opposition effect and negative polarization.

Type
Physical Observations and Modeling
Information
Symposium - International Astronomical Union , Volume 160: Asteroids, Comets, Meteors 1993 , 1994 , pp. 271 - 296
Copyright
Copyright © Kluwer 1994 

References

Akimov, L. A.: 1980, “O prirode oppozicionnogo effekta”. Vestnik Kharkovskogo Univ. 204, 3–12.Google Scholar
Bahar, E., and Fitzwater, M. A.: 1988, “Enhancement of backscattered diffuse specific intensities from random distributions of finitely conducting particles with rough surfaces”. J. Opt. Soc. Am. A 5, 89–98.Google Scholar
Bahar, E., and Fitzwater, M. A.: 1989, “Depolarization and backscatter enhancement in light scattering from random rough surfaces: comparison of full–wave theory with experiment”. J. Opt. Soc. Am. A 6, 33–43.Google Scholar
Barabanenkov, Yu. N., Kravtsov, Yu. A., Ozrin, V. D., and Saichev, A. I.: 1991, “Enhanced backscattering in optics”. In Progress in Optics XXIX (Wolf, E., Ed.), 67–197, Elsevier.Google Scholar
Barabashev, N. P.: 1922, “Bestimmung der Erdalbedo und des Reflexionsgesetzes für die Oberfläche der Mondmeere. Theorie der Rillen”. Astron. Nachr. 217, 445–452.CrossRefGoogle Scholar
Bobrov, M. S.: 1940, “On the physical interpretation of the phase curve of Saturn's rings”. Astron. Zh. 17, 1–8.Google Scholar
Bobrov, M. S.: 1961, “A generalisation of the theory of the shadow effect on Saturn's rings for the case of particles of unequal size”. Astron. Zh. 38, 669–680.Google Scholar
Born, M., and Wolf, E.: 1970, Principles of Optics (4th edition), Pergamon.Google Scholar
Bowell, E., Dollfus, A., and Geake, J. E.: 1972, “Polarimetric properties of the lunar surface and its interpretation. Part 5: Apollo 14 and Luna 16 samples”. In Proc. 3rd Lunar Sci. Conf. (Supplement 3, Geochimica et Cosmochimica Acta) 3, 3103–3126, The M.I.T. Press.Google Scholar
Bowell, E., Hapke, B., Lumme, K., Harris, A. W., Domingue, D., and Peltoniemi, J. I.: 1989, “Application of photometric models to asteroids”. In Asteroids II (Binzel, R. P., Gehrels, T., and Matthews, M., Eds.), 524–556, Univ. of Arizona Press.Google Scholar
Brown, R. H., and Cruikshank, D. P.: 1983, “The Uranian satellites: surface compositions and opposition brightness surges”. Icarus 55, 83–92.CrossRefGoogle Scholar
Bruce, N. C., and Dainty, J. C.: 1991a, “Multiple scattering from random rough surfaces using the Kirchhoff approximation”. Journal of Modern Optics 38, 579–590.Google Scholar
Bruce, N. C., and Dainty, J. C.: 1991b, “Multiple scattering from rough dielectric and metal surfaces using the Kirchhoff approximation”. Journal of Modern Optics 38, 1471–1481.Google Scholar
Celli, V., Maradudin, A. A., Marvin, A. M., and McGurn, A. R.: 1985, “Some aspects of light scattering from a randomly rough metal surface”. J. Opt. Soc. Am. A 2, 2225–2239.CrossRefGoogle Scholar
Chandrasekhar, S.: 1960, Radiative Transfer, Dover.Google Scholar
de Wolf, D. A.: 1971, “Electromagnetic reflections from an extended turbulent medium: cumulative forward–scatter single backscatter approximation”. IEEE Trans. Antennas Propag. 19, 254–262.Google Scholar
Dollfus, A.: 1975, “Optical polarimetry of the Galilean satellites of Jupiter”. Icarus 25, 416–431.Google Scholar
Dollfus, A., and Bowell, E.: 1970, “Polarimetric properties of the lunar surface and its interpretation. Part I. Telescopic observations,” Astron. Astrophys. 10, 29–53.Google Scholar
Dollfus, A., and Titulaer, C.: 1971, “Polarimetric properties of the lunar surface and its interpretation. Part III. Volcanic samples in several wavelengths”. Astron. Astrophys. 12, 199–209.Google Scholar
Dollfus, A., Bowell, E., and Titulaer, C.: 1971, “Polarimetric properties of the lunar surface and its interpretation. Part II. Terrestrial samples in orange light.” Astron. Astrophys. 10, 450–466.Google Scholar
Domingue, D. L., Hapke, B. W., Lockwood, G. W., and Thompson, D. T.: 1991, “Europa's phase curve: implications for surface structure”. Icarus 90, 30–42.CrossRefGoogle Scholar
Egan, W. G.: 1967, “Polarimetric measurements of simulated lunar surfaces”. J. Geophys. Res. 72, 3233–3245.Google Scholar
Esposito, L. W.: 1979, “Extensions to the classical calculation of the effect of mutual shadowing in diffuse reflection”. Icarus 39, 69–80.CrossRefGoogle Scholar
Franklin, F. A., and Cook, A. F.: 1965, “Optical properties of Saturn's rings. II. Two-color phase curves of the two bright rings”. Astron. J. 70, 704–720.Google Scholar
Geake, J. E., and Geake, M.: 1990, “A remote–sensing method for sub–wavelength grains on planetary surfaces by optical polarimetry”. Mon. Not. Royal Astron. Soc. 245, 46–55.Google Scholar
Geake, J. E., Geake, M., and Zellner, B. H.: 1984, “Experiments to test theoretical models of the polarization of light by rough surfaces”. Mon. Not. R. Astr. Soc. 210, 89–112.CrossRefGoogle Scholar
Gehrels, T.: 1956, “Photometric studies of asteroids. V. The light–curve and phase function of 20 Massalia”. Ap. J. 123, 331–338.Google Scholar
Gehrels, T.: 1977, “The physical basis of the polarimetric method for deriving asteroid albedos”. In The Interrelated Origin of Comets, Asteroids, and Meteorites (Delsemme, A. H., Ed.), 253–256, Univ. of Toledo Publs.Google Scholar
Gehrels, T., Coffeen, T., and Owings, D.: 1964, “Wavelength dependence of polarization. III. The lunar surface”. Astron. J. 69, 826–852.Google Scholar
Gu, Z.-H., Dummer, R. S., Maradudin, A. A., and McGurn, A. R.: 1989, “Experimental study of the opposition effect in the scattering of light from a randomly rough metal surface”. Appl. Opt. 28, 537–543.Google Scholar
Hage, J.: 1991, “The optics of porous particles and the nature of comets”. PhD–thesis, University of Leiden.Google Scholar
Hapke, B.: 1963, “A theoretical photometric function for the lunar surface”. J. Geophys. Res. 68, 4571–4586.Google Scholar
Hapke, B.: 1966, “An improved theoretical lunar photometric function”. Astron. J. 71, 333–339.Google Scholar
Hapke, B.: 1981, “Bidirectional reflectance spectroscopy: 1. Theory”. J. Geophys. Res. 86, 3039–3054.Google Scholar
Hapke, B.: 1982, “The Lumme–Bowell photometric parameters: reality or fantasy?” Bull. Amer. Astron. Soc. 14, 726.Google Scholar
Hapke, B.: 1984, “Bidirectional reflectance spectroscopy: 3. Correction for macroscopic roughness”. Icarus 59, 41–59.CrossRefGoogle Scholar
Hapke, B.: 1986, “Bidirectional reflectance spectroscopy: 4. The extinction coefficient and the opposition effect”. Icarus 67, 264–280.Google Scholar
Hapke, B.: 1990, “Coherent backscatter and the radar characteristics of outer planet satellites”. Icarus 88, 407–417.Google Scholar
Hapke, B., and van Horn, H.: 1963, “Photometric studies of complex surfaces, with applications to the moon”. J. Geophys. Res. 68, 4545–4570.CrossRefGoogle Scholar
Hapke, B., and Wells, E.: 1981, “Bidirectional reflectance spectroscopy: 2. Experiments and observations”. J. Geophys. Res. 86, 3055–3060.Google Scholar
Hapke, B., Nelson, R. M., and Smythe, W. D.: 1993, “The opposition effect of the Moon: the contribution of coherent backscatter”. Science 260, 509–511.Google Scholar
Harris, A. W., and Young, J. W.: 1988, “Two dark asteroids with very small opposition effects”. Lunar Planet. Sci. XIX 18, 447–448.Google Scholar
Harris, A. W., and Young, J. W.: 1989, “Asteroid lightcurve observations from 1979–1981”. Icarus 81, 314–364.Google Scholar
Harris, A. W., Young, J. W., Contreiras, L., Dockweiler, T., Belkora, L., Salo, H., Harris, W. D., Bowell, E., Poutanen, M., Binzel, R. P., Tholen, D. J., and Wang, S.: 1989, “Phase relations of high albedo asteroids: the unusual opposition brightening of 44 Nysa and 64 Angelina”. Icarus 81, 365–374.Google Scholar
Herschel, J.: 1847, “Results of astronomical observations made at the Cape of Good Hope”. 353–374 (London, 1847).Google Scholar
Hopfield, J. J.: 1966, “Mechanism of lunar polarization”. Science 151, 1380–1381.Google Scholar
Hämeen–Anttila, K. A., and Vaaraniemi, P.: 1975, “A theoretical photometric function of Saturn's rings”. Icarus 25, 470–478.Google Scholar
Irvine, W. M.: 1966, “The shadowing effect in diffuse reflection”. J. Geophys. Res. 71, 2931–2937.CrossRefGoogle Scholar
Irvine, W. M., Muinonen, K., and Lumme, K.: 1988, “Is the mutual shadowing explanation for the opposition effect of Saturn's rings still valid?” Bull. Amer. Astron. Soc. 20, 853.Google Scholar
Ishimaru, A.: 1990, “Experimental and theoretical studies on enhanced backscattering from scatterers and rough surfaces”. In Scattering in Volumes and Surfaces (Nieto–Vesperinas, M. and Dainty, J. C., Eds.), 1–15, North Holland.Google Scholar
Ishimaru, A., and Tsang, L.: 1988, “Backscattering enhancement of random discrete scatterers of moderate sizes”. J. Opt. Soc. Am. A 5, 228–236.Google Scholar
Jakeman, E.: 1988, “Enhanced backscattering through a deep random phase screen”. J. Opt. Soc. Am. A 5, 1638–1648.Google Scholar
Johnson, P. E., Kemp, J. C., King, R., Parker, T. E., and Barbour, M. S.: 1980, “New results from optical polarimetry of Saturn's rings”. Nature 283, 146–149.Google Scholar
Kim, M.-J., Dainty, J. C., Friberg, A. T., and Sant, A. J.: 1990, “Experimental study of enhanced backscattering from one– and two–dimensional random rough surfaces”. J. Opt. Soc. Am. A 7, 569–577.CrossRefGoogle Scholar
Kolokolova, L. O.: 1990, “Dependence of polarization on optical and structural properties of the surfaces of atmosphereless bodies”. Icarus 84, 305–314.Google Scholar
Kolokolova, L. O., Mishchenko, M. I., and Wolff, M.: 1993, “On the negative polarization of light scattered by subwavelength regolithic grains”. Mon. Not. R. Astron. Soc. 260, 550–552.Google Scholar
Kravtsov, Y. A., and Saichev, A. I.: 1982, “Effects of double passage of waves in randomly in homogeneous media”. Sov. Phys. Usp. 25, 494–508.CrossRefGoogle Scholar
Kuga, Y., and Ishimaru, A.: 1984, “Retroreflectance from a dense distribution of spherical particles”. J. Opt. Soc. Am. A 1, 831–835.Google Scholar
Levasseur–Regourd, A. C., Dumont, R., and Renard, J. B.: 1990, “A comparison between polarimetric properties of cometary dust and interplanetary dust particles”. Icarus 86, 264–272.Google Scholar
Lindell, I. V., Sihvola, A. H., Muinonen, K. O., and Barber, P. W.: 1991, “Scattering by a small object close to an interface. I. Exact Image Theory formulation”. J. Opt. Soc. Am. A 8, 472–476.Google Scholar
Lumme, K.: 1971, “Interpretation of the light curves of some non–atmospheric bodies in the solar system”. Astrophys. Space Sci. 13, 219–230.Google Scholar
Lumme, K.: 1979, “A model for the polarization of atmosphereless bodies”. Bull. Amer. Astron. Soc. 11, 562.Google Scholar
Lumme, K., and Bowell, E.: 1981a, “Radiative transfer in the surfaces of atmosphereless bodies. I. Theory”. Astron. J. 86, 1694–1704.Google Scholar
Lumme, K., and Bowell, E.: 1981b, “Radiative transfer in the surfaces of atmosphereless bodies. II. Interpretation of phase curves”. Astron. J. 86, 1705–1721.Google Scholar
Lumme, K., and Bowell, E.: 1982, “A reply to Hapke's criticism of the Lumme–Bowell photometric theory”. Bull. Amer. Astron. Soc. 14, 726.Google Scholar
Lumme, K., and Bowell, E.: 1985, “Photometric properties of zodiacal light particles”. Icarus 62, 54–71.Google Scholar
Lumme, K., and Irvine, W. M.: 1982, “Radiative transfer in the surfaces of atmosphereless bodies. III. Interpretation of lunar photometry”. Astron. J. 87, 1076–1082.Google Scholar
Lumme, K., and Rahola, J.: 1994, “Light scattering by porous dust particles in the discrete–dipole approximation”. Ap. J., in press.Google Scholar
Lumme, K., Bowell, E., and Zellner, B.: 1980, “The negative polarization of light scattered from rough surfaces seems to be largely due to diffraction”. Bull. Amer. Astron. Soc. 12, 663.Google Scholar
Lumme, K., Peltoniemi, J. I., and Irvine, W. M.: 1990, “Diffuse reflection in stochastically bounded semi–infinite media”. Trans. Theory and Stat. Phys. 19(3–5), 317–332.Google Scholar
Lyot, B.: 1929, “Recherches sur la polarisation de la lumière des planètes et de quelques substances terrestres”. Ann. Obs. Paris 8(1), 1–161.Google Scholar
Ma, Y., Varadan, V. V., and Varadan, V. K.: 1988, “Scattered intensity of a wave propagating in a discrete random medium”. Appl. Opt. 27, 2469–2477.Google Scholar
MacKintosh, F. C., and John, S.: 1988, “Coherent backscattering of light in the presence of time–reversal–noninvariant and parity–nonconserving media”. Phys. Rev. B 37, 1884–1897.Google Scholar
Markov, A.: 1924, “Les particularités dans la réflexion de la lumière par la surface de la Lune”. Astron. Nachr. 221, 65–78.CrossRefGoogle Scholar
McCoyd, G. C.: 1967, “Polarization properties of a simple dielectric rough–surface model”. J. Opt. Soc. Am. 57, 1345–1350.CrossRefGoogle Scholar
McGurn, A. R.: 1990, “Enhanced retroreflectance effects in the reflection of light from randomly rough surfaces”. Surf. Sci. Rep. 10, 357–410.Google Scholar
McGurn, A. R., Maradudin, A. A., and Celli, V.: 1985, “Localization effects in the scattering of light from a randomly rough crating”. Phys. Rev. B 31, 4866–4871.Google Scholar
Michel, T., Maradudin, A. A., and Mendez, E. R.: 1989, “Enhanced backscattering of light from a non–Gaussian random metal surface”. J. Opt. Soc. Am. B 6, 2438–2446.Google Scholar
Mikhail, J. S.: 1970, “Colour variations with phase of selected regions of the lunar surface”. The Moon 2, 167–201.CrossRefGoogle Scholar
Mishchenko, M. I.: 1992, “Polarization characteristics of the coherent backscatter opposition effect”. Earth, Moon, Planets 58, 127–144.Google Scholar
Mishchenko, M. I.: 1993, “On the nature of the polarization opposition effect exhibited by Saturn's rings”. Ap. J. 411, 351–361.Google Scholar
Mishchenko, M. I., and Dlugach, J. M.: 1991, “The amplitude of the opposition effect due to weak localization of photons in discrete disordered media”. Astrophys. Space Sci. 189, 151–154.Google Scholar
Mishchenko, M. I., and Dlugach, J. M.: 1992, “Can weak localization of photons explain the opposition effect of Saturn's rings?” Mon. Not. Royal Astron. Soc. 254, 15p–18p.Google Scholar
Mishchenko, M. I., and Dlugach, J. M.: 1993, “Coherent backscatter and the opposition effect for E–type asteroids”. Planet. Space Sci. 41, 173–181.Google Scholar
Muinonen, K.: 1989a, “Scattering of light by crystals: a modified Kirchhoff approximation”. Appl. Opt. 28, 3044–3050.Google Scholar
Muinonen, K.: 1989b, “Electromagnetic scattering by two interacting dipoles”. In Proc. 1989 URSI Electromagnetic Theory Symp. (Stockholm, Sweden), 428–430.Google Scholar
Muinonen, K.: 1990, “Light scattering by inhomogeneous media: backward enhancement and reversal of polarization”. PhD–thesis, University of Helsinki.Google Scholar
Muinonen, K.: 1991, “Scattering of light by crystals: a full Kirchhoff approximation”. Optical Society of America, 1991 Annual Meeting, Technical Digest (San Jose, California, U.S.A.), 119.Google Scholar
Muinonen, K., and Lumme, K.: 1991, “Light scattering by solar system dust: the opposition effect and the reversal of linear polarization”. In IAU Colloquium 126, Origin and Evolution of Interplanetary Dust (Levasseur–Regourd, A.-C. and Hasekawa, H., Eds.), 159–162, Kluwer Academic Press.Google Scholar
Muinonen, K., Lumme, K., Peltoniemi, J. I., and Irvine, W. M.: 1989, “Light scattering by randomly oriented crystals”. Appl. Opt. 28, 3051–3060.Google Scholar
Muinonen, K., Lumme, K., Zhukov, B., Peltoniemi, J. I., Kaasalainen, M. and Irvine, W. M.: 1990, “Statistical photoclinometric methods for the analysis of surface topography”. Space Research Institute, Academy of Sciences, USSR, Preprint 1631, 1–16.Google Scholar
Muinonen, K. O., Sihvola, A. H., Lindell, I. V., and Lumme, K. A.: 1991, “Scattering by a small object close to an interface. II. Study of backscattering”. J. Opt. Soc. Am. A 8, 477–482.Google Scholar
Muinonen, K., Peltoniemi, J. I., and Lumme, K.: 1992, “Is the negative linear polarization of solar system dust caused by shadowing or coherent backscattering?” In Workshop on Polarization III, Light Scattered by Irregular Dust Grains, with Emphasis on Cometary and Interplanetary Dust (Paris, France), 4pp.Google Scholar
Müller, G.: 1893, “Helligkeitsbestimmungen der grossen Planeten und einiger Asteroiden”. Publ. Astrophys. Obs. Potsdam Nr. 30, 8, 193–389.Google Scholar
Newton, I.: 1952, Opticks, Dover. (Based on the Fourth Edition, London, 1730.) Google Scholar
Nieto–Vesperinas, M., and Dainty, J. C., Eds. : 1990, Scattering in Volumes and Surfaces, North–Holland.Google Scholar
O'Donnell, K. A., and Mendez, E. R.: 1987, “Experimental study of scattering from characterized random surfaces”. J. Opt. Soc. Am. A 4, 1194–1205.CrossRefGoogle Scholar
Oetking, P.: 1966, “Photometric studies of diffusely reflecting surfaces with applications to the brightness of the moon”. J. Geophys. Res. 71, 2505–2513.Google Scholar
Ozrin, V. D.: 1992a, “Exact solution for coherent backscattering from a semi-infinite random medium of anisotropic scatterers”. Phys. Lett. A 162, 341–345.Google Scholar
Ozrin, V. D.: 1992b, “Exact solution for coherent backscattering of polarized light from a random medium of Rayleigh scatterers”. Waves Random Med. 2, 141–164.Google Scholar
Öhman, Y.: 1955, “A tentative explanation of the negative polarization in diffuse reflection”. Stockholm Obs. Ann. 18, 8, 1–10.Google Scholar
Pellicori, S. F.: 1971, “Polarizing properties of pulverized materials with special reference to the lunar surface”. Appl. Opt. 10, 270–285.Google Scholar
Peltoniemi, J. I.: 1993, “Light scattering in planetary regoliths and cloudy atmospheres”. PhD–thesis, University of Helsinki.Google Scholar
Peltoniemi, J. I., and Lumme, K.: 1992, “Light scattering by closely packed particulate media”. J. Opt. Soc. Am. A 9, 1320–1326.Google Scholar
Peltoniemi, J. I., Lumme, K., Muinonen, K., and Irvine, W. M.: 1989, “Scattering of light by stochastically rough particles”. Appl. Opt. 28, 4088–4095.Google Scholar
Peters, K. J.: 1992, “Coherent–backscatter effect: a vector formulation accounting for polarization and absorption effects and small or large scatterers”. Phys. Rev. B 46, 801–812.Google Scholar
Piironen, J., and Muinonen, K.: 1993, “Backscattering of light by snow: laboratory experiments”. IAU Symposium 160: Asteroids, Comets, Meteors 1993 (Belgirate, Italy), 248.Google Scholar
Purcell, E. M., and Pennypacker, C. R.: 1973, “Scattering and absorption of light by nonspherical dielectric grains”. Ap. J. 186, 705–714.Google Scholar
Rougier, A.: 1933, “Photométrie photoélectrique globale de la Lune”. Ann. Obs. Strasbourg 2, 205–339.Google Scholar
Russell, H. N.: 1916a, “The stellar magnitudes of the sun, moon, and planets”. Ap. J. 43, 103–129.CrossRefGoogle Scholar
Russell, H. N.: 1916b, “On the albedo of the planets and their satellites”. Ap. J. 43, 173–196.Google Scholar
Scaltriti, F., and Zappalà, V.: 1980, “The similarity of the opposition effect among asteroids”. Astron. Astrophys. 83, 249–251.Google Scholar
Seeliger, H. von: 1887, “Zur Theorie der Beleuchtung der grossen Planeten, insbesondere des Saturn”. Abh. Bayer. Akad. Wiss. Math. Naturwiss., Kl. 16, 405–516.Google Scholar
Shkuratov, Yu. G.: 1982, “A model for the negative polarization of light scattered by cosmic bodies deprived of atmospheres”. Astron. Zh. 59, 817–822.Google Scholar
Shkuratov, Yu. G.: 1988a, “Shadow component of phase brightness function of atmosphereless cosmic bodies”. Kin. Phys. Neb. Tel 4, 60–66.Google Scholar
Shkuratov, Yu. G.: 1988b, “Diffractional model of the brightness surge of complex structure surfaces”. Kin. Phys. Neb. Tel 4, 33–39.Google Scholar
Shkuratov, Yu. G.: 1989, “New mechanism of the negative polarization of light scattered by atmosphereless cosmic bodies”. Astron. Vestnik 23, 176–180.Google Scholar
Shkuratov, Yu. G., and Akimov, L. A.: 1987, “Laboratory studies of negative polarization of light scattered by complex structure surfaces. Some sequences for atmosphereless cosmic bodies. I”. Kin. Phys. Neb. Tel 3, 22–27.Google Scholar
Shkuratov, Yu. G., and Muinonen, K.: 1991, “Interpreting asteroid photometry and polarimetry using a model of shadowing and coherent backscattering”. In Asteroids, Comets, Meteors 1991 (Harris, A. W. and Bowell, E., Eds.), 549–552, Lunar and Planetary Institute.Google Scholar
Shkuratov, Yu. G., and Opanasenko, N. V.: 1992, “Polarimetric and photometric properties of the Moon: Telescope Observation and Laboratory Simulation. 2. The positive polarization”. Icarus 99, 468–484.Google Scholar
Shkuratov, Yu. G., Akimov, L. A., Stankevich, N. P., Melkumova, L. Ya., Latynina, I. I., and Bogdanova, T. B.: 1987, “Laboratory studies of negative polarization of light scattered by complex structure surfaces. Some sequences for atmosphereless cosmic bodies. II”. Kin. Phys. Neb. Tel 3, 32–37.Google Scholar
Shkuratov, Yu. G., Melkumova, L. Ya., and Badyukov, D. D.: 1988a, “Laboratory studies of negative polarization of light scattered by complex structure surfaces. Some sequences for atmosphereless cosmic bodies. III”. Kin. Phys. Neb. Tel 4, 11–18.Google Scholar
Shkuratov, Yu. G., Opanasenko, N. V., and Melkumova, L. Ya.: 1988b, “The model of negative polarization of light scattered by opaque rough surfaces”. Preprint No 366, IRE AN USSR, Kharkov, 1–26.Google Scholar
Shkuratov, Yu. G., Opanasenko, N. V., and Melkumova, L. Ya.: 1989, “Interference surge of backscattering and negative polarization of light reflected by complex structure”. Preprint No 361, IRE AN USSR, Kharkov, 1–26.Google Scholar
Shkuratov, Yu. G., Opanasenko, N. V., and Kreslavsky, M. A.: 1992, “Polarimetric and photometric properties of the Moon: Telescope Observations and Laboratory Simulations. 1. The negative polarization”. Icarus 95, 283–299.Google Scholar
Shkuratov, Yu. G., Muinonen, K., Bowell, E., Lumme, K., Peltoniemi, J. I., Kreslavsky, M. A., Stankevich, D. G., Tishkovetz, V. P., Opanasenko, N. V., and Melkumova, L. Y.: 1994, “A critical review of theoretical models for the negative polarization of light scattered by atmosphereless solar system bodies”. Submitted to Earth, Moon, and Planets. Google Scholar
Soto–Crespo, J. M., and Nieto–Vesperinas, M.: 1989, “Electromagnetic scattering from very rough random surfaces and deep reflection gratings”. J. Opt. Soc. Am. A 6, 367–384.Google Scholar
Soto–Grespo, J. M., Nieto–Vesperinas, M., and Friberg, A. T.: 1990, “Scattering from slightly rough random surfaces: a detailed study on the validity of the small perturbation method”. J. Opt. Soc. Am. A 7, 1185–1201.Google Scholar
Steigman, G. A.: 1978, “A polarimetric model for a dust–covered planetary surface”. Mon. Not. R. Astr. Soc. 185, 877–888.CrossRefGoogle Scholar
Tapster, P. R., Weeks, A. R., and Jakeman, E.: 1989, “Observation of backscattering enhancement through atmospheric phase screens”. J. Opt. Soc. Am. A 6, 517–522.Google Scholar
Thompson, D. T., and Lockwood, G. W.: 1992, “Photoelectric photometry of Europa and Callisto”. J. Geophys. Res. 97, 14761–14772.Google Scholar
Trowbridge, T. S.: 1978, “Retroreflection from rough surfaces”. J. Opt. Soc. Am. 68, 1225–1242.Google Scholar
Trowbridge, T. S.: 1984, “Rough–surface retroreflection by focusing and shadowing below a randomly undulating interface”. J. Opt. Soc. Am. A 1, 1019–1027.Google Scholar
Tsang, L. and Ishimaru, A.: 1984, “Backscattering enhancement of random discrete scatterers”. J. Opt. Soc. Am. A 1, 836–839.Google Scholar
Tsang, L., and Ishimaru, A.: 1985, “Theory of backscattering enhancement of random discrete isotropic scatterers based on the summation of all ladder and cyclical terms”. J. Opt. Soc. Am. A 2, 1331–1338.Google Scholar
van Albada, M. P., and Lagendijk, A.: 1985, “Observation of weak localization of light in a random medium”. Phys. Rev. Lett. 55, 2692–2695.Google Scholar
van de Hulst, H. C.: 1957, Light Scattering by Small Particles, Wiley.Google Scholar
van Diggelen, J.: 1964, “The radiance of lunar objects near opposition”. Planet. Space Sci. 13, 271–279.Google Scholar
van Tiggelen, B. A.: 1992, “Multiple scattering and localization of light”. PhD–thesis, University of Amsterdam.Google Scholar
Varadan, V. K., Vringi, V. N., Varadan, V. V., and Ishimaru, A.: 1983, “Multiple scattering theory for waves in discrete random media and comparison with experiments”. Radio Sci. 18, 321–327.Google Scholar
Varadan, V. V., Varadan, V. K., Ma, Y., and Steele, W. A.: 1987, “Effects of non–spherical statistics on EM wave propagation in discrete random media”. Radio Sci. 22, 491.Google Scholar
Watson, K. M.: 1969, “Multiple scattering of electromagnetic waves in an underdense plasma”. J. Math. Phys. 10, 688–702.Google Scholar
Whitaker, E. A.: 1979, “Implications for asteroidal regolith properties from comparisons with the lunar phase relation and theoretical considerations”. Icarus 40, 406–417.Google Scholar
Wolf, P.-E., and Maret, G.: 1985, “Weak localization and coherent backscattering of photons in disordered media”. Phys. Rev. Lett. 55, 2696–2699.Google Scholar
Wolff, M.: 1975, “Polarization of light reflected from rough planetary surface”. Appl. Opt. 14, 1395–1405.Google Scholar
Zellner, B., and Gradie, J.: 1976, “Minor planets and related objects. XX. Polarimetric evidence for the albedos and compositions of 94 asteroids”. Astron. J. 81, 262–280.Google Scholar
Zellner, B., Gehrels, T., and Gradie, J.: 1974, “Minor planets and related objects. XVI. Polarimetric diameters”. Astron. J. 79, 1100–1110.Google Scholar
Zellner, B., Lebertre, T., and Day, K.: 1977, “Laboratory polarimetry of dark carbon-bearing silicates and the asteroid albedo scale”. Proc. 8th Lunar Sci. Conf., Preprint Nr. 770006, 1–8.Google Scholar