Multispectral polarimetry as a tool to investigate texture and chemistry of lunar regolith particles

Icarus 187 (2007) 406–416 www.elsevier.com/locate/icarus

Multispectral polarimetry as a tool to investigate texture and chemistry of lunar regolith particles Yuriy Shkuratov a,∗ , Nikolay Opanasenko a , Evgenij Zubko a,b , Yevgen Grynko a,c , Viktor Korokhin a , Carlé Pieters d , Gorden Videen e,f , Urs Mall d , Alexander Opanasenko a a Astronomical Institute of V.N. Karazin Kharkov National University, 35 Sumskaya St., Kharkov 61022, Ukraine b Institute of Low Temperature Science, Hokkaido University, Kita-ku North 19 West 8, Sapporo 060-0819, Japan c Max-Planck Institute for Solar System Research, Max-Planck St. 2, 37191 Katlenburg-Lindau, Germany d Department of Geological Sciences, Brown University, Providence, RI 02912, USA e Space Science Institute, 4750 Walnut St., Suite 205, Boulder, CO 80301, USA f Astronomical Institute, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands

Received 31 May 2006; revised 15 October 2006 Available online 11 December 2006

Abstract We report results of telescope polarimetric imaging of the Moon with a CCD LineScan Camera at large phase angles, near 88◦ . This allows measurements of the polarization degree with an absolute accuracy better than 0.3% and detection of features with polarization contrast as small as 0.1%. The measurements are carried out in two spectral bands centered near 0.65 and 0.42 µm. We suggest characterizing the lunar regolith with the parameter (Pmax )a A, where Pmax , A, and a are the degree of maximum polarization, albedo, and the parameter describing the linear regression of the correlation Pmax –A. The parameter bears significant information on the particle characteristic size and packing density of the lunar regolith. We also suggest characterizing the lunar regolith with color-ratio images obtained with a polarization filter at large phase angles. We here consider the color-ratios C|| (0.65/0.42 µm) and C⊥ (0.65/0.42 µm). Using light scattering model calculations we show that the color-ratio images obtained with a polarization filter at large phase angles suggest a new tool to study the lunar surface. In particular, it turns out that the color-ratios C|| (0.65/0.42 µm) and C⊥ (0.65/0.42 µm) are sensitive to somewhat different thicknesses of the surfaces of regolith particles. We consider the applicability of the Hubble Space Telescope, the Very Large Telescope (ESO), and a spacecraft on a lunar polar orbit for polarimetric observations of the lunar surface. © 2006 Elsevier Inc. All rights reserved. Keywords: Polarimetry; Moon, surface; Regolith

1. 1. Introduction Light coming from the Sun is not polarized on the level of sensitivity 10−6 (Kemp et al., 1987). If the natural light is scattered by a planetary surface it can become polarized. For dielectric particulate surfaces like the lunar regolith, the polarization is linear (Lyot, 1929; Dollfus, 1962); the circular polarization of the Moon (the forth Stokes parameter) is extremely small and localized at the lunar poles, revealing different signs (e.g., * Corresponding author.

E-mail address: [email protected] (Y. Shkuratov). 0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.10.012

Shkuratov et al., 1984). When the surfaces have a very complicated structure the degree of linear polarization P is found to depend largely on the phase angle α, the plane of polarization being either normal to the plane of scattering (TE) or parallel to it (TM) (scattering plane includes incident and emergent rays); this regularity keeps with an accuracy of ±0.5◦ (Lyot, 1929), which implies that the third Stokes parameter of the lunar surface is also very small. In the first case (TE), the polarization is referred to as being positive; in the second case (TM), the polarization is negative. Thus the polarization of the scattered light can be defined as P = (I⊥ − I|| )/(I⊥ + I|| ), where I⊥ and I|| are the polarization components of intensity perpendicular (TE) and parallel (TM) to the scattering plane.

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Fig. 1. Two images of the Moon obtained with a small telescope in blue light at perpendicular (left) and parallel (right) orientations of the axis of analyzer relatively the scattering plane.

The Moon was the first celestial body investigated using polarimetry. In 1811 D.F. Arago (Arago, 1842) using a polariscope found that lunar maria exhibit positive polarization at phase angles closed to 90◦ . This effect can be observed with a small telescope using a polarizer. For instance, in Fig. 1 one can see images of the western part of the lunar disk taken in blue light with a polarizer whose axis is oriented along the terminator (left image) and perpendicular to it (right one). Note that terminator line near the lunar photometric equator is perpendicular to the scattering plane. The images shown in Fig. 1 are acquired under strictly the same conditions. Thus the difference between these images is related strictly to polarization. The classic work of Lyot (1929) began systematic studies of the Moon using polarimetric methods in France. The important work of Barabashev (1926) played the same role in developing lunar polarimetry in the USSR. Polarimetric investigations of the Moon have a rather meager history in the USA (McCord et al., 1976), and are not being actively pursued at present. One reason is that there is an inverse correlation between albedo A and polarization degree P of light scattered by the lunar surface at large phase angles. This effect is often called Umov’s law (Umov, 1912). The correlation is approximately linear on a log–log scale: log P + a log A = b, where a and b are constants (e.g., Dollfus and Bowell, 1971). The correlation coefficient is up to 0.95. Because of this correlation, mapping polarization degree often is considered as noninformative for remote sensing of the lunar surface. The consequence is that polarimetry

of the lunar surface has never been carried out from spacecraft. Attempts to acquire further information from polarization have been undertaken by quantifying the deviation of the polarization from the regression line of the albedo correlation (Shkuratov, 1980; Shkuratov and Basilevsky, 1981; Shkuratov, 1981). To characterize the deviations, the parameter (Pmax )a A has been proposed. It has been shown that the parameter bears significant information on the characteristic size and microporosity of the lunar regolith (Shkuratov, 1981; Shkuratov and Basilevsky, 1981; Shkuratov and Opanasenko, 1992; Dollfus 1998, 1999). Analysis of the images of the distribution of (Pmax )a A shows the following (Shkuratov and Opanasenko, 1992): (1) rayed young craters including the Aristarchus crater have increased values of the parameter, perhaps because of the immature character of the regolith (coarse grains); and (2) regions characterized by decreased values of (Pmax )a A, e.g., Aristarchus Plateau and Marius Hills area, which are regions of volcanism that could be accompanied by ash deposits containing fine (dust) particles. These features are illustrated in Fig. 2 (Shkuratov and Opanasenko, 1992). Fig. 2a shows an image of the lunar albedo for the western portion of the lunar nearside. The image has been obtained at the wavelength 0.43 µm. The brightness trend from the lunar limb to the terminator has been compensated as described in Shkuratov and Opanasenko (1992). Fig. 2b shows the distribution of the degree of linear polarization that is very similar to an albedo negative of Fig. 2a

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Fig. 2. Earth-based telescope photopolarimetric images of the western part of the lunar nearside: (a) an albedo image after compensation of the brightness trend from limb to terminator, (b) an image of polarization degree, and (c) an image of deviation from Umov’s law, the parameter (Pmax )a A (Shkuratov and Opanasenko, 1992).

owing that there is an approximate inverse correlation between albedo and polarization degree. Fig. 2c is the image demonstrating the distribution of the parameter (Pmax )a A. Laboratory measurements of lunar samples and size-particle separates of terrestrial glasses have shown that the variations of this parameter are closely correlated with the particle size (Shkuratov and Opanasenko, 1992). Young craters are more clearly visible in Fig. 2c indicating their coarse regolith particles. In addition, potentially useful polarimetric parameters recently were studied by Korokhin and Velikodsky (2005). The distribution of the positions of Pmax , i.e., the phase angles αmax , was mapped at wavelengths λeff = 0.46 and 0.67 µm using polarimetric CCD observations of the eastern portion of the lunar disk. To map αmax , polarimetric images at 10 large phase angles were acquired. For each pixel a curve fitting the measured polarization phase dependence was used to determine αmax . An example of such αmax distribution at wavelength λeff = 0.46 µm is shown in Fig. 3. As can be seen, this parameter is strongly correlated with albedo. Smaller αmax corresponds to higher albedo. Distributions of the “color” ratios CPmax = Pmax (0.67 µm)/Pmax (0.46 µm) and Cαmax = αmax (0.67 µm)/αmax (0.46 µm) also have been mapped. Except for noise, no spatial variations were found for the ratio Cαmax . Two branches have been found on the “CPmax –albedo” correlation diagram (Korokhin and Velikodsky, 2005). This diagram is qualitatively the same as was found earlier by Opanasenko et al. (1988) using discrete spectropolarimetric observations: the ratio CPmax decreases with albedo for mare regions and the opposite effect is observed for highlands.

Spectral measurements and color-ratio imaging are effective tools to study chemical and mineral composition of the Moon (e.g., McCord et al., 1976, 1981; Pieters, 1978, 1986, 1993; Pieters et al., 2006; Lucey et al., 1998, 2000; Gillis et al., 2003; Shkuratov et al., 1999). This results partially from the fact that the illuminating/observing geometry plays a secondary role in the formation of the spectral and color-ratio data (McCord, 1969). This means that colorimetric data obtained at different phase angles can be compared to each other. In the first approximation, all spectral polarization effects especially manifesting themselves at large phase angles are ignored. We show, however, that spectral and color-ratio investigations demand more careful accounting for these effects. We also demonstrate that these effects may potentially provide additional important information on the lunar surface composition. In this paper we study (1) color-ratio images of the Moon obtained at a large phase angle near 90◦ for the parallel and perpendicular components of scattered light and (2) the parameter (Pmax )a A with higher spatial resolution than was obtained by Shkuratov and Opanasenko (1992). We examine the regular color-ratio C(0.65/0.42 µm) = A(0.65 µm)/A(0.42 µm) as well as the polarimetric color-ratios C|| (0.65/0.42 µm) = A|| (0.65 µm)/A|| (0.42 µm) and C⊥ (0.65/0.42 µm) = A⊥ (0.65 µm)/A⊥ (0.42 µm) for the albedo components corresponding to the parallel and perpendicular orientations of the polarization filter to the scattering plane. Regular colorratio images also can be found in many works, as they have been used to estimate the titanium distribution over the lu-

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ing a CCD LineScan Camera SONY ILX707. The western portion of the lunar disk is scanned with the 2048-pixel line in two wide spectral bands, λred = 0.65 µm and λblue = 0.42 µm. Several scans of the Moon are made at a phase angle near 88◦ that is rather close to the angle of maximal lunar polarization. We use a polarization filter oriented parallel and perpendicular to the scattering plane. Then we use a geometrical transformation of the scans and images to bring them to the same projection with zero libration, allowing images to be matched. To compensate for the brightness longitude and latitude trends at the phase angle, we apply the Akimov formula (Akimov, 1988), or the so-called disk function, to all images:    π α (cos β)α/(π−α) cos γ− , D(α, β, γ ) = (1) cos γ π −α 2 where α, β, and γ are the phase angle, photometric latitude and longitude, respectively. We note that this formula can be derived for light-scattering pre-fractal surfaces (Shkuratov et al., 2003). We calculate the albedo distribution that is the brightness at λ = 0.42 µm after compensation of the global longitude and latitude trends with formula (1). We find the polarization degree distribution P = (A⊥ − A|| )/A and A = (A⊥ + A|| ) at λ = 0.42 µm, the distribution of the parameter (Pmax )a A (λ = 0.42 µm), the regular color-ratios (0.65/0.42 µm), as well as the ratios C|| (0.65/0.42 µm) and C⊥ (0.65/0.42 µm). The images are presented in Figs. 4–9, respectively. Figs. 4–6 resemble those in Fig. 2. As anticipated, the new albedo and polarization degree images show a very close inverse correlation. The effect of terminator shadows is suppressed significantly in the polarimetric image, as it should be. The (Pmax )a A image differs from the albedo, polarization degree (as expected), and has some resemblance with the regular color-ratio C(0.65/0.42 µm) (see Fig. 7). For instance, in Figs. 6 and 7 one can see Aristarchus Plateau and the region of Marius Hills. Figs. 8 and 9, presenting C|| (0.65/0.42 µm) and C⊥ (0.65/ 0.42 µm), are the first attempt to map polarimetric colorimetry parameters of the Moon. These two maps are very different. This is demonstrated in Fig. 10, showing different correlations with albedo. Fig. 11 presents the correlation diagram C|| (0.65/0.42 µm)–C⊥ (0.65/0.42 µm) that reveals no correlation at all, although three overlapping clusters can be seen; the main two correspond to the mare/highland division. 3. Modeling and primary interpretation

Fig. 3. A map of αmax of the eastern portion of the lunar disk in blue light. The values of αmax were determined with polarimetric image data obtained at 10 different phase angles (Korokhin and Velikodsky, 2005)

nar surface (e.g., McCord et al., 1976; Johnson et al., 1991; Shkuratov et al., 1999). 2. Data acquisition, processing, and results Polarimetric observations of the Moon are carried out with the Zeiss-600 telescope of the Simeiz Observatory (Crimea) us-

In spite of the availability of several quantitative techniques to predict chemical and mineral composition using regular colorimetry and spectrophotometry of the Moon (e.g., Lucey et al., 1998, 2000; Johnson et al., 1991; Shkuratov et al., 1999; Pieters et al., 2006), their capability is somewhat limited. There are many problems quantitatively interpreting multispectral data of the lunar surface obtained using remote sensing. A portion of these problems have been analyzed in detail for titanium mapping (Gillis et al., 2003). The interpretation basis of lunar polarimetric experimental data is much poorer. We suggest a qualitative consideration of the fine structure and composition features of the lunar regolith with the C|| (0.65/0.42 µm) and

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Fig. 4. A blue light reflectance image of the western portion of the lunar disk with compensated brightness trend from the limb to terminator.

Fig. 5. A polarization degree image in blue light. The same portion of the lunar disk as in Fig. 4 is shown.

C⊥ (0.65/0.42 µm) images using the geometric optics ray tracing and discrete dipole approximation (DDA) technique.

of reflection and refraction using the Fresnel formulas are applicable. One can apply a normal to each surface facet of any particle and calculate all necessary local angles. Hence, the procedure reduces to: (1) a sequence of reflections and refractions on facets that make up the particle and (2) light absorption within the particle. The complex refractive index of the particles is designated by m = n + ik, where n and k are the real and imaginary parts of m. We also assume that the value k can affect results only through absorption, described by exp(−4πlk/λ), where l is the characteristic distance that light of wavelength λ goes through the particle. We consider the following parameters: λ = 0.5 µm, n = 1.6, the diameter D of spheres that circumscribe the particle is 200 µm. Our calculations showed that for such an RGF particle, the distance l is approximately equal to 0.25D (Shkuratov and Grynko, 2005). We consider

3.1. Geometric optics approximation Our numerical simulations of light scattering by irregular particles in the geometric optics approximation are described in Grynko and Shkuratov (2003). A sample of a 3-D random field with Gaussian statistics is generated in the computer memory. Then we use a cutoff level below which points of the sample are designated as particulate. After such a procedure a 3-D medium consisting of Random-Gaussian-Field (RGF) particles with irregular shapes and different sizes is formed. The inset in Fig. 12 shows an example of such a particle. We present RGF particles with a succession of triangular facets for which the laws

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Fig. 6. An image of the polarimetric anomaly parameter (Pmax )a A in blue light. The same portion of the lunar disk is shown as in Fig. 4.

Fig. 7. An image of the standard color ratio C(0.65/0.42 µm). The same portion of the lunar disk is shown as in Fig. 4.

two cases: (1) negligible absorption, k = 10−5 and (2) “lunar” absorption, k = 5 × 10−4 . The Monte-Carlo ray-tracing technique we use is based on our previous work (Grynko and Shkuratov, 2003). A particle is placed at the origin of a coordinate system and is illuminated with a beam of parallel rays of unpolarized light, typically 107 . The interaction of a ray with the particle surface results in two new rays, transmitted and reflected. We randomly choose one of these, treating intensities as the corresponding probabilities. Similarly, the probability of absorption is calculated for a given ray pathlength l. These tracing steps are repeated until the ray emerges from the particle. Finally we calculate the scattering matrix Fik for a given trajectory. To average the result over all possible orientations, the particle is rotated around different axes at random angles. We here study phase dependencies of the following radiation components: I||external , I⊥external (i.e.,

singly reflected light by particle facets) and I||internal , I⊥internal (i.e., refracted light multiply reflected within the particle). Our calculations with the Fresnel formulae show that in the range of phase angle 70◦ –140◦ , the component I||external is negligibly small. Fig. 12 shows phase angle curves for the other components. As one may see for small particle absorption, the components I||internal and I⊥internal dominate the scattered radiation. However, for the “lunar” case (k = 5 × 10−4 ) the component I⊥external is higher than I||internal and I⊥internal . We also note that I||internal ≈ I⊥internal 3.2. Model of discrete dipole approximation We analyzed the same problem for small particles using the discrete dipole approximation (DDA) originally developed by

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Fig. 8. An image of the color ratio C|| (0.65/0.42 µm). The same portion of the lunar disk is shown as in Fig. 4.

Purcell and Pennypacker (1973). In this case, the monochromic electromagnetic plane wave is incident on the arbitrary particle with volume V . In this case the scattered field Es (r) can be expressed as   E(r) = Einc (r) + graddiv + k 2        exp(ik|r − r |)  1 ε r − 1 E r × (2) dr , 4π |r − r | V

where r is the radius-vector of the observer; r is the radiusvector of a point inside V ; Einc (r) is the incident field at the point of observation; E(r ) is the field inside the volume; ε(r ) is the permittivity of the particle substance; and k = ω/c is the wave-number. The main idea of DDA method consists in replacing the dielectric continuum medium by a finite set of

Fig. 9. An image of the color ratio C⊥ (0.65/0.42 µm). The same portion of the lunar disk is shown as in Fig. 4.

small discrete scatterers (dipoles). This allows one to transform the integral equation (2) into a system of linear algebraic equations (Draine and Flatau, 1994) that can be solved iteratively. We compute the amplitudes of the scattered fields far from a model particle for two different incident polarization states. The Mueller matrix is calculated based on the base of these amplitudes (Zubko et al., 2003). The method of generating irregular particles (see the inset in Fig. 13) also is described by Zubko et al. (2003). Results of calculations are averaged over a large number of random model particle samples, usually about 100. We made calculations for silica model particles, n = 1.5 with k = 0 and k = 0.02, with the size parameter x = 2πr/λ = 12, where r and λ are the gyration radius of the particle and wavelength, respectively. Two cases

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(a)

Fig. 11. A Correlation diagram for color ratios C|| (0.65/0.42 µm) and C⊥ (0.65/0.42 µm).

tions from more-or-less smooth facets (or the outer shell) of the particle and with contributions from the internally scattered radiation. The parallel polarization component is formed almost exclusively by internal scattering and depends strongly on particle absorption. Thus, in the first case, the scattered radiation bears information on the external as well as internal features of the particle; whereas, in the second case, information on the interior of the particle (its absorbing properties) can be obtained. (b)

(c) Fig. 10. A correlation diagram for albedo and color ratios: (a) regular C(0.65/0.42 µm), (b) C|| (0.65/0.42 µm), and C⊥ (0.65/0.42 µm).

are calculated: (1) homogeneously filled particles and (2) hollow shells whose thickness is 1 dipole. As shown in Fig. 13, the phase angle behavior of the components is qualitatively the same as in the geometric optics modeling: (1) I||shell is relatively small and (2) I⊥shell is the dominant contributor to the scattered radiation when the absorption is increased. This suggests that at large phase angles the perpendicular polarization component of the scattered light from the lunar regolith particles is produced mainly from quasi-Fresnel reflec-

3.3. Application to the lunar regolith The results described above shows that the polarization degree at large phase angles is partially formed by single (quasi-Fresnel) scattering. Thus the C⊥ (0.65/0.42 µm) image acquired at large phase angles provides information on the composition of superficial shells of regolith grains. These shells usually contain a surplus of nanophase metallic iron (npFe0 ) that is an indicator of the maturity of the lunar regolith, the parameter Is /FeO (Morris, 1978). Agglutinate particles of the mature lunar regolith include the npFe0 in the surface shells as well as in their volume; whereas, particles of the immature lunar regolith contain npFe0 only in superficial zones (Morris, 1978). This means that the parameter C⊥ (0.65/0.42 µm) should not be as sensitive to the mature effects as the C|| (0.65/0.42 µm). This is why we almost do not see bright young craters in Fig. 9 (except for the crater Aristarchus). In contrast, the image in Fig. 8 presents information about deeper layers of the regolith grains and the parameter C|| (0.65/0.42 µm) should be more sensitive to the npFe0 in bulk. This results in the observability of young craters and ray systems in Fig. 8. Due to high absorption of the lunar regolith particles the C⊥ (0.65/0.42 µm) image looks almost like the regular color ratio C(0.65/0.42 µm) one (cf. Figs. 7 and 9). We conclude that the perpendicular polarization component, which is primarily the result of quasi-Fresnel scattering at large phase angles, is the basis for the commonly used color-index distribution on the lunar surface. The color-ratio image corresponding to the parallel albedo component (Fig. 8) is primarily

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(a)

Fig. 13. Phase curves of the polarimetric components of a particle shown in the inset at x = 12 and m = 1.5 + 0i (upper panel) and m = 1.5 + 0.02i (lower panel). In both panels the bold solid, thin solid, bold dashed, and thin dashed lines present the perpendicular component of the solid particle and that of shell, the parallel component of the solid particle and that of shell, respectively.

4.1. HST and VLT observations

(b) Fig. 12. Phase curves of the polarimetric components of a particle model shown in the inset at m = 1.6 + 10−5 i (upper panel) and m = 1.6 + 5 × 10−4 i (lower panel).

formed by internal multiple scattering that depends strongly on absorbing properties of regolith particles. As one can see, the ray systems of large craters, like craters Kepler and Aristarchus, clearly show up on this image. To make this interpretation quantitative and, hence, more attractive, wide polarimetric studies of lunar regolith samples are necessary. Unfortunately, this is beyond scope of this paper.

4. Polarimetry with HST, VLT, and from lunar orbit

Joint analyses of C|| (0.65/0.42 µm) and C⊥ (0.65/0.42 µm) images may potentially suggest information on systematic inhomogeneities of regolith particles. This interpretation provides an attractive opportunity to study the Moon. These can be observations from the Hubble Space Telescope (HST) and the ESO Very Large Telescope (VLT) or from lunar orbit via spacecraft. We present below a sketch of these possibilities.

The HST Advanced Camera for Surveys (ACS) in short wavelengths may provide images of approximately 50 km × 50 km areas with a spatial resolution near 50 m/pixel in the lunar disc center that is better than the resolution of Clementine images. In the spectral range 220–380 nm the lunar surface has very low albedo of only a few percent. Due to the low albedo one may expect the maximum degree of polarization of the lunar surface to be as high as 30–40%. This can be measured with the HST ACS camera that allows detection of features with polarization degree contrast as small as 0.2%, as reported for polarimetric imaging observations of Mars during the 2003 opposition (Shkuratov et al., 2005). These observations can provide the highest spatial resolution of polarimetric data ever achieved from Earth. The observations should be carried out at phase angles from the range 80◦ – 115◦ . Each observation series should consist of 3 sets of images taken with different wide-band spectral filters (F250W, F330W, F435W). Each filter set will contain 3 images taken with 3 wide-spectral-band polarization filters (POL0UV, POL60UV, and POL120UV). Unfortunately, in its current state, the HST has only 2 gyros working; thus further imaging of the Moon can be problematic. Similar polarimetric studies of the Moon at phase angles from the range 80–115◦ can be carried out with the ESO Very Large Telescope (VLT) at the Paranal Observatory (Atacama, Chile). This could be, for instance, the 8.2-m reflecting telescope (Yepun) equipped with the NAOS-CONICA adaptive op-

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tics camera allows imaging reflectance polarimetry of the Moon with a spatial resolution about of 130 m at wavelengths from the range 1.0–2.4 µm. Lunar polarization degree at this range is rather low (a few percents). However the camera can provide high polarimetric accuracy, allowing measurements of the parameter (Pmax )a A and polarimetric color ratios with unprecedented optical resolution compared to HST observations. The choice of sites under study should avoid terminator regions where topography influence may prevent image processing and analyzing. For the eastern portion of the lunar disk, prospective areas are the landing sites of Luna 16, Luna 20, Luna 24, and Apollo 17. For the western portion, these could be regions of Reiner-γ formation, Marius Hills, and Plateau Aristarchus. 4.2. Orbital observations Interesting observations in shortwave spectral ranges with a high spatial resolution of images could be provided using a spacecraft imaging polarimeter from a lunar polar orbit. The main problem of such polarimetry is observations at large phase angles when surface topography can affect results significantly. Looking at a rough surface along its normal at grazing illumination we see shadows and brightness variations related to local slopes of the topography. To avoid this problem one needs to look at the surface with deflection from the normal. Then the shadows are hidden by surface roughness, and the influence of local slopes also decreases. In this case, however, the perspective distortion of images occurs. It is necessary to compromise between this distortion and the decreasing influence of the surface topography. The optimal balance is achieved at a deflection angle near 40◦ –50◦ . This may provide large phase angles in the range 90◦ –120◦ . The orbit parameters are also important for this experiment. There is a difference between low and high orbits for polarimetric observations. A high orbit is more appropriate for polarimetric imaging of the Moon than low one, since it allows one to look at regions that are close to the lunar horizon where the influence of the local topography is smaller (see Fig. 14). The orbit with a spacecraft altitude of 1000–2000 km seems to be optimal. This requires a large enough camera focus to obtain high resolution images of the lunar surface. Note that for such an experiment it is hardly possible to acquire global coverage of the lunar surface at the same large phase angle. Studies of selected areas are practical. Regions near the lunar pole are most appropriate for large phase-angle observations. A polarimeter for lunar spacecraft observations can be made as a multispectral camera. Depending on spacecraft working modes the optical axis of the polarimeter should be oriented with the mentioned deflection toward the Sun. 5. Conclusions In this paper we provide results of CCD polarimetric imaging observations of the Moon at a large phase angle 88◦ . Such measurements give valuable information concerning variations of regolith particle size using the parameter (Pmax )a A. This

Fig. 14. A scheme showing the difference between low- and high-orbit observations of the Moon from a lunar polar spacecraft.

was confirmed with laboratory polarimetric measurements of different powders including size particle separates of the lunar regolith (Shkuratov and Opanasenko, 1992). Color-ratio images obtained with a polarization filter suggest a new effective tool to study the lunar surface, since the C|| (0.65/0.42 µm) and C⊥ (0.65/0.42 µm) images are sensitive to different thicknesses of the regolith grain surfaces. Calculations of light scattering carried out for large (geometric optics approximation) and small (DDA method) particles confirm such an interpretation. This approach is especially applicable for lunar observation using spacecrafts, in particular, with the Hubble Space Telescope Advanced Camera for Surveys. The ESO VLT 8.2-m reflecting telescope (Yepun) equipped with the NAOS-CONICA adaptive optics camera at the Paranal Observatory allows imaging polarimetry of the Moon with a spatial resolution about of 130 m at wavelengths from the range 1.0– 2.4 µm. For quantitative development of this technique it is necessary to carry out spectral polarimetric studies of lunar samples and to proceed with light scattering computer modeling for particulate media. Acknowledgments The study was supported by CRDF Grant UKP2-2614KH-04. The authors are grateful to P. Lucey and B. Hapke for thoughtful reviews. References Akimov, L.A., 1988. Reflection of light by the Moon. 1. Kinemat. Fiz. Nebesnykh Tel. 4, 3–10. In Russian. Arago, D.F., 1842. Sur les vulcane dans la Lune. Annuere de Longitudes, Paris. 526 pp. Barabashev, N., 1926. Polarimetrische Beobachtungen an der Mondoberfläche und am Gesteinen. Astron. Nachr. 229, 14–26. Dollfus, A., 1962. The polarization of moonlight. Chapter 5. In: Kopal, Z. (Ed.), Physics and Astronomy of the Moon. Academic Press, New York/London, pp. 131–159.

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