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The phase dependence of brightness and color of the lunar surface: a study based on integral photometric data

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Abstract

A procedure of an a posteriori correction of the available data on the integral photometry of the Moon is described. This procedure reduces the regular errors of the integral phase curves caused by variations of the libration parameters; the effect due to libration can reach 4%. A method allowing the integral measurements of the Moon to be compared correctly with the photometric measurements of the lunar areas or laboratory samples imitating the lunar soil has been developed. To approximate the phase curves of integral albedo in the phase-angle range from 6° to 120°, we proposed a simple empirical formula A eq(α) = m l e −ρα + m 2 e −0.7α, where α is the phase angle, ρ is the factor of effective roughness, and m 1 + m 2 is the surface albedo at a zero phase angle. An empirical phase dependence of the slope of the lunar spectrum in the 360–1060 nm range has been obtained. The results may be used to test various theoretical models of the light scattering by the lunar surface and to calibrate the data of ground-based and space-borne spectrophotometric observations.

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References

  • Akimov, L.A., Antipova-Karataeva, I.I., and Shkuratov, Yu.G., Indicatrix Measurements of Lunar Samples from Landing Sites of Luna 24, Luna 16, and Luna 20, Lunar and Planet. Sci. Conf. 10th, 1979, pp. 9–11.

  • Akimov, L.A., Gol’dberg, E.P., Omarov, S.Z., et al., Optical Investigations of the Moon and Spectrophotometric Standards, Astron. Vestn., 1982, vol. 16, no. 3, pp. 153–158 [Sol. Syst. Res. (Engl. Transl.), vol. 16, no. 3, pp. 121–126].

    ADS  Google Scholar 

  • Akimov, L.A., Light Reflection by the Moon. I, Kinematika Fiz. Nebesnykh Tel, 1988a, vol. 4, no. 1, pp. 3–10.

    MathSciNet  ADS  Google Scholar 

  • Akimov, L.A., Light Reflection by the Moon. II, Kinematika Fiz. Nebesnykh Tel, 1988b, vol. 4, no. 2, pp. 10–16.

    ADS  Google Scholar 

  • Akimov, L.A., Velikodsky, Yu.I., and Korokhin, V.V., Dependence of the Brightness of Lunar Highlands on Photometric Latitude, Kinematika Fiz. Nebesnykh Tel, 1999, vol. 15, no. 4, pp. 304–309.

    Google Scholar 

  • Akimov, L.A., Velikodsky, Yu.I., and Korokhin, V.V., Dependence of Latitude Distribution of Brightness over the Lunar Disk on Albedo and Relief, Kinematika Fiz. Nebesnykh Tel, 2000, vol. 16, no. 2, pp. 181–187.

    ADS  Google Scholar 

  • Domingue, D. and Hapke, B., Fitting Theoretical Photometric Functions To Asteroid Phase Curves, Icarus, 1989, vol. 78, pp. 330–336.

    Article  ADS  Google Scholar 

  • Evsyukov, N.N., On Relation between Colorimetrical and Spectrometric Measurements of the Lunar Surface, Problemy Kosmicheskoi Fiziki (Problems of Space Physics), Kiev: Kiev. Univ., 1975, no. 10, pp. 89–95.

    Google Scholar 

  • Hapke, B., Theory of Reflectance and Emittance Spectroscopy, Cambridge: UP, 1993.

    Google Scholar 

  • Jaumann, R., Grobner, C., and Oehler, A., Color-Dependent Variations of the Photometric Phase Function: Implications on the Interpretation of Multispectral Data, Bull. Am. Astron. Soc., 1992, vol. 24, no. 3, p. 1021.

    ADS  Google Scholar 

  • Kieffer, H. and Stone, T., The Spectral Irradiance of the Moon, Astron. J., 2005, vol. 129, pp. 2887–2901.

    Article  ADS  Google Scholar 

  • Korokhin, V.V. and Akimov, L.A., Mapping the Phase Dependence of the Lunar Surface Brightness: Reduction of Observations to Standard Conditions, Mapping of Equigonal Albedo, Kinematika Fiz. Nebesnykh Tel, 1994, vol. 10, no. 2, pp. 3–10.

    Google Scholar 

  • Korokhin, V.V. and Akimov, L.A., Zoning of the Lunar Surface by the Parameters of the Brightness-Phase Relation, Astron. Vestn., 1997, vol. 31, no. 2, pp. 143–152 [Sol. Syst. Res. (Engl. Transl.), vol. 31, no. 2, pp. 430].

    Google Scholar 

  • Korokhin, V.V., Beletskii, S.A., Velikodsky, Yu.I., et al., The Experience of Application of CCD-Photodetectors at the Astronomical Observatory of the Kharkiv National University, Kinematika Fiz. Nebesnykh Tel, 2000, vol. 16, no. 1, pp. 80–86.

    ADS  Google Scholar 

  • Korokhin, V.V. and Velikodsky, Yu.I., Parameters of the Positive Polarization Maximum of the Moon: Mapping, Astron. Vestn., 2005, vol. 39, no. 1, pp. 51–60 [Sol. Syst. Res. (Engl. Transl.), vol. 39, no. 1, pp. 45–53].

    Google Scholar 

  • Lane, A.P. and Irvine, W.M., Monochromatic Phase Curves and Albedos for the Lunar Disk, Astron. J., 1973, vol. 78, no. 3, pp. 267–277.

    Article  ADS  Google Scholar 

  • Nikonova, E.K., Photoelectrical Determination of Magnitudes of the Sun and Moon, Izv. Krym. Astrofiz. Obs., 1949, vol. 4, pp. 114–143.

    Google Scholar 

  • Rougier, G., Photometric Photoelectrique Globale de la Lune, Ann. Obs. Strasbourg, 1933, vol. 2, pp. 1–339.

    Google Scholar 

  • Shevchenko, V.V., The Lunar Photometric Constant in the System of True Full Moon, Sun and Planetary System, Dordrecht: Reidel, 1982, pp. 263–264.

    Google Scholar 

  • Shkuratov, Yu.G., Model of the Opposition Effect in the Brightness of Airless Cosmic Bodies, Astron. Zh., 1983, vol. 60, no. 5, pp. 105–108 [Sov. Astron. (Engl. Transl.), vol. 27, no. 5, p. 581].

    Google Scholar 

  • Shkuratov, Yu.G., Fractoids and Photometry of Solid Surfaces of Celestial Bodies, Astron. Vestn., 1995, vol. 29, no. 6, pp. 483–496.

    Google Scholar 

  • Shkuratov, Yu.G., Melkumova, L.Ya., Opanasenko, N.V., and Stankevich, D.G., Phase Dependence of the Color Indices of Solid Surfaces of Celestial Bodies, Astron. Vestn., 1996, vol. 30, no. 1, pp. 82–91 [Sol. Syst. Res. (Engl. Transl.), vol. 30, no. 1, pp. 76–79].

    Google Scholar 

  • Shkuratov, Yu., Kreslavsky, M., Ovcharenko, A., et al., Opposition Effect from Clementine Data and Mechanisms of Backscatter, Icarus, 1999, vol. 141, pp. 132–155.

    Article  ADS  Google Scholar 

  • Shkuratov, Yu.G., Stankevich, D.G., Petrov, D.V., et al., Interpreting Photometry of Regolith-Like Surfaces with Different Topographies: Shadowing and Multiple Scatter, Icarus, 2005, vol. 173, pp. 3–15.

    Article  ADS  Google Scholar 

  • Velikodsky, Yu.I., The Influence of Albedo and Relief on the Law of Brightness Distribution over the Lunar Disk, Cand. Sci. (Phys.-Math.) Dissertation, Kharkov: Astronomical Institute of Kharkov University, 2002.

    Google Scholar 

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Original Russian Text © V.V. Korokhin, Yu.I. Velikodsky, Yu.G. Shkuratov, U. Mall, 2007, published in Astronomicheskii Vestnik, 2007, Vol. 41, No. 1, pp. 24–32.

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Korokhin, V.V., Velikodsky, Y.I., Shkuratov, Y.G. et al. The phase dependence of brightness and color of the lunar surface: a study based on integral photometric data. Sol Syst Res 41, 19–27 (2007). https://doi.org/10.1134/S0038094607010029

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  • DOI: https://doi.org/10.1134/S0038094607010029

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