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Photometrie photoelectrique globale de la lune
... In particular, measurements of the integral brightness of the Moon may be accessible and useful for this purpose. Unfortunately, there are only few integral observations of the Moon (Rougier, 1933;Nikonova, 1949;Lane and Irvine, 1973). We decided to analyze the integral observations by Lane and Irvine (1973) in several spectral bands and, after applying a new a posteriori procedure to increase their accuracy, to use these data to study the phase dependence of brightness and color index of the Moon. ...
... In addition to the observations of Lane and Irvine (1973), the earlier integral observations by Rougier (1933) and Nikonova (1949) are well known. It is worth noting that their phase curves contain many more points than those by Lane and Irvine but, unfortunately, cannot be used to study color variations, because they were made only in one photometric band (in the B filter by Rougier and in a wide photoelectric band by KOROKHIN et al. ...
... The analogous calculations were Note: α is the phase angle (negative values correspond to the period before the full moon), k L is the correction coefficient of intensities for libration, k EA is the coefficient converting the relative intensities to the relative equigonal albedo, and k MR/HL is the correction coefficient for changing the portions of maria and highlands. KOROKHIN et al. fulfilled for the data by Rougier (1933). Thus, the data by Rougier (1933) and Lane and Irvine (1973) can be easily reduced to zero libration using the data on the factor k L . ...
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
le
−ρα + m
2e
−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.
... ∼570 (Whitaker, 1969;Rougier, 1933) Jupiter Main ring ∼460 (Throop et al., 2004) Io ∼570 (McEwen et al., 1988) Europa ∼500 (Thompson and Lockwood, 1992) Ganymede ∼600 (Morrison et al., 1974;Millis and Thompson, 1975;Blanco and Catalano, 1974) Callisto ∼500 (Thompson and Lockwood, 1992) Saturn C ring 672 B ring ∼650 (Franklin and Cook, 1965) B ring (HST) 672 A ring 672 E ring ∼650 (Pang et al., 1983;Larson, 1984;Showalter et al., 1991) Enceladus 439 (Verbiscer et al., 2005) Rhea ∼500 (Domingue et al., 1995;Verbiscer and Veverka, 1989) Iapetus ∼600 (Franklin and Cook, 1974) Phoebe ∼650 (Bauer et al., 2006) Uranus Rings ∼500 (Karkoschka, 2001) Portia group ∼500 (Karkoschka, 2001) Ariel ∼600 (Buratti et al., 1992;Karkoschka, 2001) Titania ∼600 (Buratti et al., 1992;Karkoschka, 2001) Oberon ∼600 (Buratti et al., 1992;Karkoschka, 2001) Neptune Fraternité ∼500 (de Pater et al., 2005;Ferrari and Brahic, 1994) Egalité ∼500 (de Pater et al., 2005;Ferrari and Brahic, 1994) Nereid ∼570 (Schaefer and Tourtellotte, 2001) Triton ∼400 (Buratti et al., 1991) Table 3 Direct output parameters of morphological models using opposition phase curves and "ideal" opposition phase curves of Solar System objects. The unit of w is the degree and the unit of the slope I s is I/F.deg −1 (Ferrari and Brahic, 1994) Egalité 0,02 480 (Ferrari and Brahic, 1994) Nereid 0,21 ∼500 (Thomas et al., 1991) Triton 0,97 500 (Lee et al., 1992) appropriate to use the semi-major axis. ...
In this paper, we characterize the morphology of the disk-integrated phase functions of satellites and rings around the giant planets of our Solar System. We find that the shape of the phase function is accurately represented by a logarithmic model (Bobrov, 1970, in Surfaces and Interiors of Planets and Satellites, Academic, edited by A. Dollfus). For practical purposes, we also parametrize the phase curves by a linear-exponential model (Kaasalainen et al., 2001, Journal of Quantitative Spectroscopy and Radiative Transfer, 70, 529-543) and a simple linear-by-parts model (Lumme and Irvine, 1976, Astronomical Journal, 81, 865-893), which provides three morphological parameters : the amplitude A and the Half-Width at Half-Maximum (HWHM) of the opposition surge, and the slope S of the linear part of the phase function at larger phase angles. Our analysis demonstrates that all of these morphological parameters are correlated with the single scattering albedos of the surfaces. By taking more accurately into consideration the finite angular size of the Sun, we find that the Galilean, Saturnian, Uranian and Neptunian satellites have similar HWHMs (0.5 degrees), whereas they have a wide range of amplitudes A. The Moon has the largest HWHM (2 degrees). We interpret that as a consequence of the solar size bias, via the finite size of the Sun which varies dramatically from the Earth to Neptune. By applying a new method that attempts to morphologically deconvolve the phase function to the solar angular size, we find that icy and young surfaces, with active resurfacing, have the smallest values of A and HWHM, whereas dark objects (and perhaps older surfaces) such as the Moon, Nereid and Saturn C ring have the largest A and HWHM.
... finally, by (16), we find the illuminance per unit angular length as a function of the phase and position angles ...
We expose and analyze the proposed models of the visual magnitude of the Moon for large phase angles (>150º). We devised a method to determine the luminance and illuminance per unit angular length of the lunar crescent as a function of position and phase angles.
... Helfenstein and Veverka (1987), adjusting (7) to the measurements of Rusell (1916), Rougier (1933), Shorthill et al. (1969), and Lane and Irvine (1972) obtained the value of the six average parameters for the Moon. The photometric data of the Moon are applicable up to the phase angle of 150º, that is to say, that we cannot assure that for higher phase angles, which are those that occur in the first visibility of the lunar crescent, Helvenstein and Veverka parameters are correct. ...
Schaefer (1991) determined the Danjon limit or minimum angle between the Sun and the Moon from which the Moon can be seen shortly after the conjunction. Schaefer's method uses Hapke's (1984) lunar photometric theory and considers a fixed value for the threshold illuminance. We show Schaefer's method and its shortcomings, and we expose a modified theory, where the threshold illuminance to see the lunar crescent depends on several factors, mainly atmospheric absorption. We consider that vision is a probabilistic phenomenon; that is, when we use the experimental data of Blackwell (1946), we cannot be sure whether or not the Moon will be seen. Finally, we conclude that «perhaps» Hapke's theory overestimates the shielding of the sun's rays by the irregularities of the lunar surface at large phase angles.
... For more than 25 years, the use of Hapke's photometric model (with successive variants) has been implemented on data acquired on numerous objects of the Solar System (e.g., Warell, 2004;Chevrel et al., 2006;Jehl et al., 2008;Hillier et al., 2011 for some examples). Until very recently, integrated telescopic phase curves such as the one of Rougier (1933) were still used in lunar photometry (e.g., Warell, 2004), but today, important advances are under way: (1) data from the Spectral Profiler onboard SELENE spacecraft (Haruyama et al., 2008) enable the determination of photometric properties of three different types of terrain of the lunar surface on a large spectral range (Yokota et al., 2011); (2) data from the Lunar Reconnaissance Orbiter Camera (LROC) onboard the Lunar Reconnaissance Orbiter spacecraft (Robinson et al., 2010) are used to map Hapke's parameters, and thus the physical surface properties of the Moon, with an ever increasing resolution (Sato et al., 2011); and (3) data from the Moon Mineralogy Mapper (M 3 ) (Pieters et al., 2009) are used to study the photometric properties of lunar mare and highlands with a spectral range from 0.4 to 3 lm (Hicks et al., 2011). This shows that photometry on planetary bodies dealt previously with global (integrated disc, highlands or mare), and not local (few km 2 ) studies. ...
... There should be noted the data of integral brightness of the Moon by Rougier (1933) as well as discrete photometry by Fedorets (1952) and Peacock (1968); however, these data have no absolute calibration. Janz et al. (1996) have obtained lunar geometrical albedo in ultraviolet (250-400 nm) from the ATLAS-3 mission data. ...
A 2-month series of quasi-simultaneous imaging photometric observations of the Moon and the Sun has been performed at Maidanak Observatory (Uzbekistan). New absolute values of lunar albedo have been obtained. Maps of lunar apparent albedo and equigonal albedo at phase angles 1.7–73° at wavelength 603 nm are presented. The standard deviation of our data from a best-fitted phase curve is 2%. The average ratio of the Clementine albedo to ours is 1.41. While the ratio of ROLO albedo to ours is 0.87, our data are in agreement with independent measurements of absolute albedo by Saiki et al. (Saiki, K., Saito, K., Okuno, H., Suzuki, A., Yamanoi, Y., Hirata N., Nakamura, R. [2008]. Earth Planets Space 60, 417–424) at a phase angle near 7°. A phase ratio imaging near opposition (1.6°/2.7°) shows almost the same ratio for maria and highlands, though bright craters (e.g., Tycho, Copernicus, Aristarchus) clearly reveal smaller slopes of phase function. This is an unexpected result, as the craters are bright and one could anticipate a manifestation of the coherent backscattering effect resulting in the opposition spike increasing at so small phase angles.Highlights► New determination of absolute apparent albedo of the Moon is carried out. ► Difference near 13% is found between ROLO and our albedo. ► Smaller slope of phase curve was found for bright craters at small phase angles.
... It is worth noting that the amplitude of the phase effect of color is small, and there are a limited number of spec trophotometric observations of the Moon fulfilled with a substantially high accuracy in a wide phase angle range, which can allow for this effect to be reli ably detected. For example, Korokhin et al. (2007) recalibrated the old data of integral spectrophotome try obtained by Rougier (1933) and by Lane and Irvine (1973), which allowed them to estimate the change of the spectral slope in the 360 to 1060 nm wavelength range for the whole near side of the Moon. These data confirm that the lunar surface reddens with an increasing phase angle. ...
From the ground-based colorimetry performed for two surface regions of the near side of the Moon, images of the phase ratio
of the color index C(600 nm/470 nm) have been built for the phase angles between 2° and 95°. It has been found that for phase angles smaller than
α ∼ 40°–50°, the color index of the highlands grows with the phase quicker than that of the mare regions. For larger phase
angles, α > 50°, a reverse situation is observed. The laboratory data on the spectrophotometry of the lunar samples confirm
the peculiarities found in the phase dependence of color. The influence of multiple scattering on the phase dependence of
the color of the mare and highland regions of the Moon are discussed.
... 12). As a consequence, disk-integrated brightness measurements of the Moon are only available for phase angles smaller than 145 @BULLET (Rougier, 1933). For the planet Mercury, the phase angle range accessible by ground-based observations can be extended using images of the Solar and Heliospheric Observatory (SOHO) spacecraft, which continuously observes an angular field of view of about 20 @BULLET diameter around the sun from solar orbit. ...
The remote sensing analysis of planetary surfaces is a field in which photopolarimetric techniques allow the estimation of
the average small-scale 3D properties of the examined surfaces (i.e. on millimeter or sub-millimeter scales) from large distances.
This work provides an overview of image-based photometric and polarimetric methods for the remote determination of small-scale
3D properties of planetary regolith surfaces. Specifically, the surface porosity governs the phase angle dependence of the
reflectance function of the surface material for near-zero phase angles, while the reflectance behavior at large phase angles
between around 90° and 180° allows to estimate the surface roughness on sub-millimeter and millimeter scales. For the lunar
regolith, a calibration of the phase angle dependence of the polarization behavior of the light reflected from the surface
based on returned lunar sample material provides a framework to determine the median regolith grain size based on measurements
of the polarization degree. In this work, the corresponding methodologies as well as their application to specific planetary
bodies are discussed. Where deemed favorable, new photometric and polarimetric measurements of prototypical areas of the lunar
surface are provided to exemplify the described approaches in an illustrative manner.
KeywordsReflectance–imaging photometry–imaging polarimetry–porosity–roughness–grain size
... To interpret the results, we use a semiempirical photometric model for regolith-like surfaces (Shkuratov and Ovcharenko 1998) and simulating laboratory measurements in two ranges of phase FIG. 1. The integral brightness phase functions of the Moon nearside at 0.45 µm according to Rougier (1933), Shorthill et al. (1969) ...
An analysis of Clementine data obtained from a UVVIS camera and simulating laboratory photometric and polarimetric measurements is presented with the use of a new photometric three-parameter function combining the shadow-hiding and coherent backscatter mechanisms. The fit of calculated curves to the average brightness phase function of the Moon derived from Clementine data indicates that the coherent backscatter component is nonzero. The average amplitude of the opposition surge of the Moon in the range of phase angles 0°–1° is approximately 10%. The Clementine data also show a flattening of phase-dependent brightness at angles less than 0.25° that is caused by the angular size of the solar disk. The lunar brightness phase curves at small phase angles are nearly the same in different wavelengths even though at larger phase angles (5°–50°) the lunar surface becomes distinctly redder with increasing phase angle. According to the model, the lack of wavelength-dependent brightness variations at small phase angles can be due to quasifractal properties of the lunar surface. Results of related laboratory measurements suggest that: (1) besides the narrow coherent backscatter opposition spike there is a broad component which can contribute to phase angles up to 10° and (2) a component of coherent backscatter can be important even for low albedo surfaces. The latter testifies the opposition effect of the lunar surface to be substantially formed by the coherent backscatter mechanism.
... ∼570 (Whitaker, 1969;Rougier, 1933) Jupiter Main ring ∼460 (Throop et al., 2004) Io ∼570 (McEwen et al., 1988) Europa ∼500 (Thompson and Lockwood, 1992) Ganymede ∼600 (Morrison et al., 1974;Millis and Thompson, 1975;Blanco and Catalano, 1974) Callisto ∼500 (Thompson and Lockwood, 1992) Saturn C ring 672 B ring ∼650 (Franklin and Cook, 1965) B ring (HST) 672 A ring 672 E ring ∼650 (Pang et al., 1983;Larson, 1984;Showalter et al., 1991) Enceladus 439 (Verbiscer et al., 2005) Rhea ∼500 (Domingue et al., 1995;Verbiscer and Veverka, 1989) Iapetus ∼600 (Franklin and Cook, 1974) Phoebe ∼650 (Bauer et al., 2006) Uranus Rings ∼500 (Karkoschka, 2001) Portia group ∼500 (Karkoschka, 2001) Ariel ∼600 (Buratti et al., 1992;Karkoschka, 2001) Titania ∼600 (Buratti et al., 1992;Karkoschka, 2001) Oberon ∼600 (Buratti et al., 1992;Karkoschka, 2001) Neptune Fraternité ∼500 (de Pater et al., 2005;Ferrari and Brahic, 1994) Egalité ∼500 (de Pater et al., 2005;Ferrari and Brahic, 1994) Nereid ∼570 (Schaefer and Tourtellotte, 2001) Triton ∼400 (Buratti et al., 1991) Table 3 Direct output parameters of morphological models using opposition phase curves and "ideal" opposition phase curves of Solar System objects. The unit of w is the degree and the unit of the slope I s is I/F.deg −1 (Ferrari and Brahic, 1994) Egalité 0,02 480 (Ferrari and Brahic, 1994) Nereid 0,21 ∼500 (Thomas et al., 1991) Triton 0,97 500 (Lee et al., 1992) appropriate to use the semi-major axis. ...
In this paper, we characterize the morphology of the disk-integrated phase
functions of satellites and rings around the giant planets of our Solar System.
We find that the shape of the phase function is accurately represented by a
logarithmic model (Bobrov, 1970, in Surfaces and Interiors of Planets and
Satellites, Academic, edited by A. Dollfus). For practical purposes, we also
parametrize the phase curves by a linear-exponential model (Kaasalainen et al.,
2001, Journal of Quantitative Spectroscopy and Radiative Transfer, 70, 529-543)
and a simple linear-by-parts model (Lumme and Irvine, 1976, Astronomical
Journal, 81, 865-893), which provides three morphological parameters : the
amplitude A and the Half-Width at Half-Maximum (HWHM) of the opposition surge,
and the slope S of the linear part of the phase function at larger phase
angles. Our analysis demonstrates that all of these morphological parameters
are correlated with the single scattering albedos of the surfaces. By taking
more accurately into consideration the finite angular size of the Sun, we find
that the Galilean, Saturnian, Uranian and Neptunian satellites have similar
HWHMs (0.5 degrees), whereas they have a wide range of amplitudes A. The Moon
has the largest HWHM (2 degrees). We interpret that as a consequence of the
solar size bias, via the finite size of the Sun which varies dramatically from
the Earth to Neptune. By applying a new method that attempts to morphologically
deconvolve the phase function to the solar angular size, we find that icy and
young surfaces, with active resurfacing, have the smallest values of A and
HWHM, whereas dark objects (and perhaps older surfaces) such as the Moon,
Nereid and Saturn C ring have the largest A and HWHM.
... At elongation 150°( phase 0.94), hence 30°from full, the brightness of the Moon equals that of the solar corona, while the sky radiance during totality roughly approximates twilight conditions for a solar depression angle of about 5°-7°(or 6°AE 1°). Using the brightness data of the Moon [53] as a function of elongation and the radiance of the twilight sky as a function of solar depression and the Moon's position in the sky [11,12], we determined, for values of lunar elongation other than 150°, the solar depression angle at which the Moon/sky radiance ratio equals that of the Moon at elongation 150°(phase 0.94) and solar depression angle 6°. For instance, for the Moon in first quarter, where its radiance is a factor of 5 less than at elongation 150°, this happens when the solar depression is 7:6° (Fig. 8), which occurs in the mid-latitudes about 45 min after sunset. ...
The visibility of stars, planets, diffraction coronas, halos, and rainbows during the partial and total phases of a solar eclipse is studied. The limiting magnitude during various stages of the partial phase is presented. The sky radiance during totality with respect to noneclipse conditions is revisited and found to be typically 1 / 4000 . The corresponding limiting magnitude is + 3.5 . At totality, the signal-to-background ratio of diffraction coronas, halos, and rainbows has dropped by a factor of 250. It is found that diffraction coronas around the totally eclipsed Sun may nevertheless occur. Analyses of lunar halo observations during twilight indicate that bright halo displays may also persist during totality. Rainbows during totality seem impossible.
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.
Summarising the striking advances of the last two decades, this reliable introduction to modern astronomical polarimetry provides a comprehensive review of state-of-the-art techniques, models and research methods. Focusing on optical and near-infrared wavelengths, each detailed, up-to-date chapter addresses a different facet of recent innovations, including new instrumentation, techniques and theories; new methods based on laboratory studies, enabling the modelling of polarimetric characteristics for a wide variety of astronomical objects; emerging fields of polarimetric exploration, including proto-planetary and debris discs, icy satellites, transneptunian objects, exoplanets, and the search for extraterrestrial life; and unique results produced by space telescopes, and polarimeters aboard exploratory spacecraft. With contributions from an international team of accomplished researchers, this is an ideal resource for astronomers and researchers working in astrophysics, earth sciences, and remote sensing keen to learn more about this valuable diagnostic tool. The book is dedicated to the memory of renowned polarimetrist Tom Gehrels.
Remote-sensing techniques are widely implemented today for the exploration of planetary surfaces, called regoliths, such as the Moon's, Mercury's, Mars' or asteroids'. Photometry is a technique based on the observation of a surface under various angles which gives information on the physical surface properties: particles' diffusion mode (forward-scattering or backscattering), grain size, surface roughness, compaction state... This PhD is centred on volcanic materials and amorphous phases (or glasses), because of their significance in processes leading to the formation and evolution of regoliths: volcanism, cratering, interaction with space environment. Using Hapke's photometric model, whose parameters, once inverted, lead to the physical surface properties, this subject is explored under two approaches: in laboratory, and from orbital data. Multiangular experimental measurements, carried out with IRAP's spectro-imaging device, allowed the photometric characterization of different natural granular volcanic materials with various compositions, grain sizes, and contents of glass and monocrystals: basalts, volcanic sand, pyroclastics, olivine, and glass from the controlled melt of basalt. According to their compositions, shapes, and textures, an evolution of the samples photometric behaviour with grain size has been noticed. Materials which are rich in fresh glass and/or monocrystals display a specific behaviour seldom observed so far, which enable their distinction from glass-free materials or with more mature glass. Mixtures of basalt and basaltic glass showed also the strong and highly non linear optical influence of fresh glass. A photometric study of the lunar crater Lavoisier from orbital data showed the applicability of techniques implemented in laboratory on geological units, and photometric characteristics inherent to the pyroclastic deposits on the crater floor have been determined. Another pyroclastic deposit located at Lavoisier F displays a photometric behaviour distinct from crater Lavoisier's pyroclastic deposits, showing a textural, granulometric or compositional variety between these units. All the results obtained for these craters make sense in the light of laboratory experiments.
How a planetary regolith transfers and radiates thermal energy is
dependent on its composition and physical makeup. In this study a fully
time dependent model of thermal energy transport in planetary regoliths
which explicitly includes radiative transfer, conduction, and heat
storage, is presented and applied to the regoliths of the Moon, Mercury
and Io. In applying this study to the Moon, temperature versus depth
curves for equatorial and polar latitudes have been determined using the
derived values of the thermal inertia and radiative resistivity. It is
shown that at high latitudes, the lunar subsurface may be sufficiently
cold to harbor water ice over geologic time even in areas illuminated by
sunlight, a result consistent with recent observation (i.e. Feldman et
al., 1998). It is also shown that moderate near-surface positive
temperature gradients are likely to exist. For Mercury values of thermal
inertia and the radiative resistivity are determined which are
consistent with observations and lunar results appropriately scaled for
Mercury's increased surface gravity. Temperature versus depth curves
were also generated for equatorial and polar latitudes, as well as both
longitudinal poles. Mercury's polar subsurface was also determined to be
cold enough to harbor water ice over geologic time in sunlit regions.
This result agrees with observation (Butler et al., 1993; Harmon et al.,
1994). For Io likely surface temperatures for the high albedo
SO2 frost covered regions of the planet were determined in an
effort to resolve the conflict in the literature between previous
models, which predicted high surface temperatures (Simonelli and
Veverka, 1988; Matson and Nash, 1983), and observation, which implied
low surface temperatures (Sinton and Kaminski, 1988; Veeder et al.,
1994). It is determined that when radiative transfer is properly taken
into account, surface temperatures of Io's SO2 frost fields
are most likely low, resolving the conflict.
Images of the lunar nearside obtained by telescopes of Maidanak Observatory (Uzbekistan) and Simeiz Observatory (Crimea, Ukraine) equipped with Canon CMOS cameras and Sony CCD LineScan camera were used to study photometric properties of the lunar nearside in several spectral bands. A wide range of lunar phase angles was covered, and the method of phase ratios to assess the steepness of the phase function at different phase angles is applied. We found several areas with photometric anomalies in the south-west portion of the lunar disk that we refer to as Oceanus Procellarum anomalies. The areas being unique on the lunar nearside do not obey the inverse correlation between albedo and phase-curve slope, demonstrating high phase-curve slopes at intermediate albedo. Low-Sun images acquired with Lunar Orbiter IV and Apollo-16 cameras do not reveal anomalous topography of the regions, at least for scales larger than several tens of meters. The areas also do not have any thermal inertia, radar (70 and 3.8 cm), magnetic, or chemical/mineral peculiarities. On the other hand they exhibit a polarimetric signature that we interpret to be due to the presence of a porous regolith upper layer consisting of dust particles. The anomalies may be interpreted as regions of very fresh shallow regolith disturbances caused by impacts of meteoroid swarms consisting of rather small impactors. This origin is similar to one of the hypotheses for the origin of lunar swirls like the Reiner-γ formation. The photometric difference between the shallow and pervasive (Reiner-γ class) swirls is that the latter appear to have a significant amount of immature soils in the upper surface layers.
Scattering by a small object located close to an interface is analyzed according to the exact-image theory formulation. The scatterer is assumed to be small compared with wavelength, permitting the electric-dipole approximation, and to have a scalar polarizability. After the derivation of the dipole moment, investigations concentrate on far-field scattering. Backscattering enhancement and reversal of linear polarization are confirmed through statistical averaging over scatterer height and system orientation.
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.
This survey is a general overview of modern optical studies of the Moon and their diagnostic meaning. It includes three united parts: phase photometry, spectrophotometry, and polarimetry. The first one is devoted to the progress in the photometry of the Moon, which includes absolute albedo determination to refine the albedo scale (e.g., to connect lunar observations and the data of lunar sample measurements) and mapping the parameters of a lunar photometric function (e.g., the phase-angle ratios method) with the aim of making qualitative estimates of regolith structure variations. This part also includes observations of the lunar opposition effect as well as photogrammetry and photoclinometry techniques. In particular, available data show that because of the low albedo of the lunar surface, the coherent backscattering enhancement hardly influences the lunar opposition spike, with the exception of the brightest lunar areas measured in the NIR. The second part is devoted to chemical/mineral mapping of the Moon's surface using spectrophotometric measurements. This section also includes analyses related to the detection of water ice or hydroxyl, prognoses of maturity, and helium-3 abundance mapping. In particular, we examine the relationship between superficial OH/H2O compounds spectrally detected recently and bulk “water ice” found earlier by the Lunar Prospector GRS and LRO LEND, assuming that the compounds are delivered to cold traps (permanently shadowed regions) with electrostatically levitated dust saturated by solar wind hydrogen. Significant problems arise with the determination of TiO2 content, as the correlation between this parameter and the color ratio C(750/415nm) is very non-linear and not universal for different composition types of the lunar surface; a promising way to resolve this problem is to use color ratios in the UV spectral range. The third part is devoted to mapping of polarization parameters of the lunar surface, which enable estimates of the average size of regolith particles and their optical inhomogeneity. This includes considerations of the Umov effect and results of spectropolarimetry, negative polarization imagery, and measurements of other polarimetric parameters, including the third Stokes parameter. Although these three research divisions have not been developed equally and the numbers of proper references are very different, we try to keep a balance between them, depicting a uniform picture. It should be emphasized that many results presented in this review can be applied to other atmosphereless celestial bodies as well.
Long experience of ground-based and cosmic studies of the Moon has shown that space-weathering processes play a key role in the formation of the surface layers of atmosphereless bodies. Undoubtedly, the surface of Mercury, which is subjected to the same processes, is covered by a mantle of shattered rocks—the regolith. The structure of the reflecting layer determines the photometric and polarization characteristics of the surface of a planetary body. Despite the general similarity of the integral optical properties of the surfaces of Mercury and the Moon, specific characteristics of the media of these celestial bodies manifest themselves as certain differences in the details of the measured parameters. Moreover, the similarity to the Moon permits in-depth interpretation of the results of remote observations of Mercury, such as integral polarimetry and integral spectropolarimetry. The data obtained suggest that the general structure of the surface layer of the Mercurian regolith is very similar to the structure of the lunar soil, although it is somewhat smoother and probably has a greater amount of the fine-grained fraction. The soil maturity matches the content of about 80% of the secondary particles. At the same time, the exposure age of the soil, which has the same degree of maturity, is less than the age of the soil formed under lunar conditions.
The phase relations of several asteroids. Mercury, and the Moon display the same basic characteristics, but differ slightly in detail. An improved treatment of the photometric function for open-work particulate layers shows that for phase angles greater than about 7°, the shape of the curves is diagnostic of the presence of such layers, and that both the shape and slope of the curves is dependent primarily upon the bulk density of these layers. This treatment also strongly indicates that the “opposition effect” is not due to shadow hiding in a regolith of very low bulk density. Other data support the idea that this effect is unrelated to shadow-hiding phenomena, and that it may thus be a diffraction/scattering effect with or without internal reflection phenomena also.
The lunar surface reveals a sharp opposition effect, which is to be explained by the shadowing and coherent backscattering mechanisms. Generalizing the radiative transfer theory via Monte Carlo methods, we are carrying out studies of backscattering in regolith-like scattering media. We have also started systematic laboratory measurements of structural simulators of lunar regolith. The SMART-1 AMIE and D-CIXS/XSM experiments provide us a unique opportunity for a simultaneous multiwavelength study of the lunar regolith close to opposition, since the SMART-1 spacecraft will pass over several different types of lunar surface at zero phase angles. Results of our theoretical and laboratory investigations can be used as a basis to interpret the SMART-1 AMIE and D-CIXS/XSM experiments. In particular, it seems to be possible to estimate regional variations of regolith particle volume fraction and their size. A short review of observational, experimental and theoretical works is also presented here.
An anomalous increase in surface brightness of the Moon in an area of over 60,000 km2 around and north of the crater Kepler was observed to occur twice on the night of November 1–2, 1963, on eight photographs secured with the 24-inch refractor of the Observatoire du Pic-du-Midi between 22.35–22.42 U.T. on November 1st, and00.20–00.35 U.T. on November 2nd, on Kodak 1-F plates exposed through an interference filter of45A˚ half-width centered on 6725A˚. Control photographs taken through an interference filter of 95A˚ half-width centered on 5450A˚ failed to show any such effect. The enhancement in the red was not only observed to recur twice during the same night, but plates taken between00.20–00.35 U.T. on November 2nd disclosed that the degree of enhancement (resulting nearly in a temporary doubling of surface brightness) increased appreciably within 15 minutes of observation.This observed enhancement is interpreted to be the result of luminescence of the respective parts of lunar surface excited by solar activity. Two Class-1 flares were indeed observed to occur on an identical place of an otherwise calm Sun earlier that day at the Sacramento Peak and McMath-Hulbert Observatories at 13.58 and again at 15.55 U.T. The time interval between these flares suggests that the recurrence of the observed brightening of the Moon may have been due to surface luminescence stimulated by them after a transit time close to 8.5 hours—of sufficient duration to rule out solar X-rays or UV light as the exciting source, and to direct attention to corpuscular radiation. If so, this transit time would correspond to a particle velocity of 5000 km/sec, and the energy flux to a density of the order of103 particles/cm3.
A comparison of the photometric properties of Mercury and the Moon is performed, based on their integral phase curves and disk-resolved image data of Mercury obtained with the Swedish Vacuum Solar Telescope. Proper absolute calibration of integral V-band magnitude observations reveals that the near-side of the Moon is 10–15% brighter than average Mercury, and 0–5% brighter for the “bolometric” wavelength range 400–1000 nm. As shown, this is supported by recent estimates of their geometric albedos. Hapke photometric parameters of their surfaces are derived from identical approaches, allowing a contrasting study between their surface properties to be performed. Compared to the average near-side Moon, Mercury has a slightly lower single-scattering albedo, an opposition surge with smaller width and of marginally smaller amplitude, and a somewhat smoother surface with similar porosity. The width of the lobes of the single-particle scattering function are smaller for Mercury, and the backward scattering anisotropy is stronger. In terms of the double Henyey–Greenstein b–c parameter plot, the scattering properties of an average particle on Mercury is closer to the properties of lunar maria than highlands, indicating a higher density of internal scatterers than that of lunar particles. The photometric roughness of Mercury is well constrained by the recent study of Mallama et al. (2002, Icarus 155, 253–264) to a value of about 8°, suggesting that the surfaces sampled by the highest phase angle observations (Borealis, Susei, and Sobkou Planitia) are lunar mare-like in their textural properties. However, Mariner 10 disk brightness profiles obtained at intermediate phase angles indicate a surface roughness of about twice this value. The photometric parameters of the Moon are more difficult to constrain due to limited phase angle coverage, but the best Hapke fits are provided by rather small surface roughnesses. Better-calibrated, multiple-wavelength observations of the integral and disk-resolved brightnesses of both bodies, and obtained at higher phase angle values in the case of the Moon, are urgently needed to arrive at a more consistent picture of the contrasting light scattering properties of their surfaces.
The way an asteroid or other atmosphereless solar system body varies in brightness in response to changing illumination and viewing geometry depends in a very complicated way on the physical and optical properties of its surface and on its overall shape. This paper summarizes the formulation and application of recent photometric models by Hapke (1981, 1984, 1986) and by Lumme and Bowell (1981). In both models, the brightness of a rough and porous surface is parameterized in terms of the optical properties of individual particles, by shadowing between particles, and by the way in which light is scattered among collections of particles. Both models succeed in their goal of fitting the observed photometric behavior of a wide variety of bodies, but neither has led to a very complete understanding of the properties of asteroid regoliths, primarily because, in most cases, the parameters in the present models cannot be adequately constrained by observations of integral brightness alone over a restricted range of phase angles.
Narrowband and UBV photoelectric phase curves of the entire lunar disk and surface photometry of some craters have been interpreted using a newly developed generalized radiative transfer theory for planetary regoliths. The data are well fitted by the theory, yielding information on both macroscopic and microscopic lunar properties. Derived values for the integrated disk geometric albedo are considerably higher than quoted previously, because of the present inclusion of an accurately determined opposition effect. The mean surface roughness, defined as the ratio of the height to the radius of a typical irregularity, is found to be 0.9 + or - 0.1, or somewhat less than the mean value of 1.2 obtained for the asteroids. From the phase curves, wavelength-dependent values of the single scattering albedo and the Henyey-Greenstein asymmetry factor for the average surface particle are derived.
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