A photometric investigation of the packing state of apollo 11 lunar regolith samples

The angular light scattering properties of an Apollo 11 lunar regolith ‘fines’ sample have been determined experimentally for both flat and undulating sample surface preparations. The light scattering curves, whose shapes are known to be a function of the porosity and slope distribution of the measured surface, have been compared with corresponding Earth-based lunar measurements. The comparison method involves the numerical fitting of theoretical photometric functions to both the astronomical and laboratory data.It is deduced that regolith material can, under favourable circumstances, maintain a very underdense structure (porosity of the surface layer greater than 90 per cent) in air, so that vacuum cold-welding is not essential in the formation of such a structure. Photometric scanning is shown to provide a rapid method of determining the effective porosity of regolith sample surfaces in the laboratory.     

Regolith thickness over the lunar nearside: Results from Earth-based 70-cm Arecibo radar observations

The inversion of regolith thickness over the nearside hemisphere of the Moon from newly acquired Earth-based 70-cm Arecibo radar data is investigated using a quantitative radar scattering model. The radar scattering model takes into account scattering from both the lunar surface and buried rocks in the lunar regolith, and three parameters are critically important in predicting the radar backscattering coefficient: the dielectric constant of the lunar regolith, the surface roughness, and the size and abundance of subsurface rocks. The measured dielectric properties of the Apollo regolith samples at 450 MHz are re-analyzed, and an improved relation among the complex dielectric constant, bulk density and regolith composition is obtained. The complex dielectric constant of the lunar regolith is estimated globally from this relation using the regolith composition derived from Lunar Prospector gamma-ray spectrometer data. To constrain the lunar surface roughness and abundance of subsurface rocks from radar data, nine regions are selected as calibration sites where the regolith thickness has been estimated using independent analysis techniques. For these sites, scattering from the lunar surface and buried rocks cannot be perfectly distinguished, and a tradeoff relationship exists between the size and abundance of buried rocks and surface roughness. Using these tradeoff relations as guidelines for globally representative parameters, the regolith thickness of four regions over the lunar nearside is inverted, and the inversion uncertainties caused by calibration errors of the radar data and model input parameters are analyzed. The regolith thickness of the maria is generally smaller than that of highlands, and older surfaces have thicker regolith thicknesses. Our approach cannot be applied to regions where the surface roughness is very high, such as with young rocky craters and regions in the highly rugged highlands.     

Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scattering

The effects of various types of topography on the shadow-hiding effect and multiple scattering in particulate surfaces are studied. Two bounding cases were examined: (1) the characteristic scale of the topography is much larger than the surface particle size, and (2) the characteristic scale of the topography is comparable to the surface particle size. A Monte Carlo ray-tracing method (i.e., geometric optics approximation) was used to simulate light scattering. The computer modeling shows that rocky topographies generated by randomly distributed stones over a flat surface reveal much steeper phase curves than surface with random topography generated from Gaussian statistics of heights and slopes. This is because rocks may have surface slopes greater than 90°. Consideration of rocky topography is important for interpreting rover observations. We show the roughness parameter in the Hapke model to be slightly underestimated for bright planetary surfaces, as the model neglects multiple scattering on large-scale topographies. The multiple scattering effect also explains the weak spectral dependences of the roughness parameter in Hapke's model found by some authors. Multiple scattering between different parts of a rough surface suppresses the effect of shadowing, thus the effects produced by increases in albedo on the photometric behavior of a surface can be compensated for with the proper decreases in surface roughness. This defines an effective (photometric) roughness for a surface. The interchangeability of albedo and roughness is shown to be possible with fairly high accuracy for large-scale random topography. For planetary surfaces that have a hierarchically arranged large-scale random topography, predictions made with the Hapke model can significantly differ from real values of roughness. Particulate media with surface borders complicated by Gaussian or clumpy random topographies with characteristic scale comparable to the particle size reveal different photometric behaviors in comparison with particulate surfaces that are flat or the scale of their topographies is much larger than the particle size.     

Re-analysis of previous laboratory phase curves: 1. Variations of the opposition effect morphology with the textural properties,and an application to planetary surfaces

Typical variations in the opposition effect morphology of laboratory samples at optical wavelengths are investigated to probe the role of the textural properties of the surface (roughness, porosity and grain size). A previously published dataset of 34 laboratory phase curves is re-analyzed and fit with several morphological models. The retrieved morphological parameters that characterize the opposition surge, amplitude, width and slope (A, HWHM and S respectively) are correlated to the single scattering albedo, the roughness, the porosity and the grain size of the samples. To test the universality of the laboratory samples’ trends, we use previously published phase curves of planetary surfaces, including the Moon, satellites and rings of the giant planets. The morphological parameters of the surge (A and HWHM) for planetary surfaces are found to have a non-monotonic variation with the single scattering albedo, similar to that observed in asteroids (Belskaya, I.N., Shevchenko, V.G. [2000]. Icarus 147, 94–105), which is unexplained so far. The morphological parameters of the surge (A and HWHM) for laboratory samples seem to exhibit the same non-monotonic variation with single scattering albedo. While the non-monotonic variation with albedo was already observed by Nelson et al. (Nelson, R.M., Hapke, B.W., Smythe, W.D., Hale, A.S., Piatek, J.L. [2004]. Planetary regolith microstructure: An unexpected opposition effect result. In: Mackwell, S., Stansbery, E. (Eds.), Proc. Lunar Sci. Conf. 35, p. 1089), we report here the same variation for the angular width.     

Properties of the Hermean regolith: IV. Photometric parameters of Mercury and the Moon contrasted with Hapke modelling

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.     

Polarization of Light Scattered by Solar System Bodies and the Aggregate Model of Dust Particles

The present study considers the dependence of characteristics of light scattering by aggregate particles on the refractive index, size, and number of spherical particles composing the aggregate, as well as on the structure and porosity of the cluster. The parameters were varied in sufficiently wide ranges to let a coherent picture of the polarimetric properties of relatively small aggregate particles emerge (the size parameter of the aggregate is less than 10). It was shown that, in the framework of the aggregate model, the behavior of polarization phase curves observed for both comets and regolith surfaces can be explained. The modeling carried out confirms that the sizes of the cometary dust particles are larger than the wavelength. However, the grains forming the cometary dust particles or the regolith (or details of the particle surface) have a size less than 0.3–0.5 m. This agrees with estimates obtained by other methods. The determining role in the formation of the polarization phase curve is played by the structure of the external layer of the clusters. The appearance of the negative branch of polarization and its shape substantially depend on the effectiveness of the interference of multiply scattered waves and on the interaction in the near field at these phase angles. Interference and interaction in the near field in turn are determined by the sizes of elementary scatterers and the structure of the ensemble. If the number of constituent particles in the aggregate is larger than several tens, its role in the formation of the negative branch of polarization is minor, while the influence on the polarization maximum position is rather substantial. The polarimetric data alone cannot provide a unique estimate of the refractive index: the brightness measurements must be invoked as well. For a more complete quantitative interpretation of the observations, the scattering matrix of aggregates comparable in size to or larger than the wavelength must be calculated in the short- and long-wavelength ranges, which still encounters serious theoretical and technical difficulties. Moreover, in order to obtain unique results, it is obvious that the spectral range of observations must be extended and that other types of measurements, such as spectroscopic ones, must also be used.     

Scattering properties of planetary regolith analogs

The physics of scattering of electromagnetic waves by media in which the particles are in contact, such as planetary regoliths, has been thought to be relatively well understood when the particles are larger than the wavelength. However, this is not true when the particles are comparable with or smaller than the wavelength. We have measured the scattering parameters of planetary regolith analogs consisting of suites of well-sorted abrasives whose particles ranged from larger to smaller than the wavelength. We measured the variation of reflectance as the phase angle varied from 0.05° to 140°. The following parameters of the media were then deduced: the single scattering albedo, single scattering phase function, transport mean free path, and scattering, absorption, and extinction coefficients. A scattering model based on the equation of radiative transfer was empirically able to describe quantitatively the variation of intensity with angle for each sample. Thus, such models can be used to characterize scattering from regoliths even when the particles are smaller than the wavelength. The scattering parameters were remarkably insensitive to particle size. These results are contrary to theoretical predictions, but are consistent with earlier measurements of alumina abrasives that were restricted to small phase angles. They imply that a basic assumption made by virtually all regolith scattering models, that the regolith particles are the fundamental scattering units of the medium, is incorrect. Our understanding of scattering by regoliths appears to be incomplete, even when the particles are larger than the wavelength.     

Prospects for Estimating the Properties of a Loose Surface from the Phase Profiles of Polarization and Intensity of the Scattered Light

It has been shown that the model of a scattering medium composed of clusters located in the far zones of each other allows some properties of regolith-like surfaces to be quantitatively estimated from the phase dependences of intensity and polarization measured in the backscattering domain. From the polarization profiles, the sizes of particles, the structure and porosity of the medium, and a portion of the surface area covered with a disperse material can be determined. At the same time, the intensity profiles of the scattered light weakly depend on the sizes and structure of particles; they are mainly controlled by the concentration of scatterers in the medium and the shadow-hiding contribution at small phase angles. Since the latter effect is beyond the considered model, a good agreement between the model and the measured intensity cannot be achieved. Nevertheless, if a portion of the surface that participates in coherent backscattering has been found from the phase profile of polarization, the present model makes it possible to determine the relative contribution of the shadow-hiding effect to the brightness surge measured at zero phase angle. This, in turn, may allow the roughness of the scattering surface to be estimated. The model contains no free parameters, but there is currently no possibility to verify it comprehensively by the data obtained in laboratory measurements of the samples with thoroughly controlled characteristics, because such measurements are rare for a wide range of the properties of particles in a medium, their packing density, and phase angles.

     

A Study of Saturn's Ring Phase Curves from HST Observations

Solar phase curves between 0.3° and 6.0° and color ratios at wavelengths λ=0.336 μm and λ=0.555 μm for Saturn's rings are presented using recent Hubble Space Telescope observations. We test the hypothesis that the phase reddening of the rings is less due to collective properties of the ring particles than to the individual properties of the ring particles. We use a modified Drossart model, the Hapke model, and the Shkuratov model to model reddening by either intraparticle shadow-hiding on fractal and normal surfaces, multiple scattering, or some combination. The modified Drossart model (including only shadowing) failed to reproduce the data. The Hapke model gives fair fits, except for the color ratios. A detailed study of the opposition effect suggests that coherent backscattering is the principal cause of the opposition surge at very small phase angles. The shape of the phase curve and color ratios of each main ring regions are accurately represented by the Shkuratov model, which includes both a shadow-hiding effect and coherent backscatter enhancement. Our analysis demonstrates that in terms of particle roughness, the C ring particles are comparable to the Moon, but the Cassini division and especially the A and B ring particles are significantly rougher, suggesting lumpy particles such as often seen in models. Another conspicuous difference between ring regions is in the effective size d of regolith grains (d∼λ for the C ring particles, d∼1-10 μm for the other rings).     

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

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 a(Pmax)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.     

A Negative Branch of Polarization for Comets and Atmosphereless Celestial Bodies and the Light Scattering by Aggregate Particles

Optical observations of comets and atmosphereless celestial bodies show that a change of sign of the linear polarization of scattered light from negative to positive at phase angles less than 20° is typical of the cometary coma, as well as of the regolith of Mercury, the Moon, planetary satellites, and asteroids. To explain a negative branch of polarization, this research suggests a unified approach to the treatment of cometary-dust particles and regolith grains as aggregate forms. A composite structure of aggregate particles resulting in the interaction of composing structural elements (monomers) in the light-scattering process is responsible for the negative polarization at small phase angles, if the monomer sizes are comparable to the wavelength. The characteristics of single scattering of light calculated for aggregates of this kind turned out to be close to the properties observed for cometary dust. Unlike the cometary coma, the regolith is an optically semi-infinite medium, where the interaction between particles is significant. To find the reflectance characteristics of regolith, the radiative-transfer equation should be solved for a regolith layer. In this case, the interaction between scatterers can be modeled to a certain extent by representing the regolith grains as aggregate structures consisting of several or many elements. Although real regolith grains are much larger than the particles considered here, laboratory measurements have shown that it is precisely the surface irregularities comparable to the wavelength that cause a negative branch of polarization. The main observed features of the phase and spectral dependence of the linear polarization of light scattered from comets and atmosphereless celestial bodies, which are due to the difference of the elementary scatterers in composition, size, and structure, can be successfully explained using the aggregate model of particles.     

Implications for asteroidal regolith properties from comparisons with the lunar phase relation and theoretical considerations

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 SMART-1 AMIE experiment: implication to the lunar opposition effect

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.     

Light Scattering by Dust Under Microgravity Conditions

Most of our knowledge on heterogeneous media in the Universe comes from the light they scatter. This light is mainly linearly polarized, and the polarization phase curves contain information about the properties of the scattering dust. In the solar system, the dust seems to be made of irregular aggregates with a size greater than a few microns and a fractal structure. Many constraints appear in the scattering computations, due to the trickiness of the mathematical calculations, and to our ignorance of the precise structure of the dust. This leads to the necessity to perform light scattering measurements on characteristic aggregates, built under low velocity ballistic collisions. Microgravity is a sensible way to achieve such measurements on a cloud of levitating and aggregating dust particles. A first step has been the PROGRA² experiment, which operates during parabolic flights on an aircraft. The instrument is a polar nephelometer measuring successively the light scattered by a dust sample at various angles; it is fully operational, and will provide a data base of polarization phase curves. A second step is the CODAG-SR experiment, which uses the duration of a rocket flight to build up dust aggregates. The instrument measures simultaneously the light scattered at numerous phase angles; it is now space qualified, and should provide in a near future a monitoring of the intensity and polarization phase curves while the aggregation processes are taking place. This revised version was published online in July 2006 with corrections to the Cover Date.     

Deep Space 1 photometry of the nucleus of Comet 19P/Borrelly

The NASA-JPL Deep Space 1 Mission (DS1) encountered the short-period Jupiter-family Comet 19P/Borrelly on September 22, 2001, about 8 days after perihelion. DS1's payload contained a remote-sensing package called MICAS (Miniature Integrated Camera Spectrometer) that included a 1024 square CCD and a near IR spectrometer with ∼12 nm resolution. Prior to its closest approach of 2171 km, the remote-sensing package on the spacecraft obtained 25 CCD images of the comet and 45 near-IR spectra (L. Soderblom et al., 2002, Science 296, 1087-1091). These images provided the first close-up view of a comet's nucleus sufficiently unobscured to perform quantitative photometric studies. At closest approach, corresponding to a resolution of 47 meters per pixel, the intensity of the coma was less than 1% of that of the nucleus. An unprecedented range of high solar phase angles (52-89 degrees), viewing geometries that are in general attainable only when a comet is active, enabled the first quantitative and disk resolved modeling of surface photometric physical parameters, including the single particle phase function and macroscopic roughness. The disk-integrated geometric albedo of Borrelly's nucleus is 0.029±0.006, comparable to the dark hemisphere of Iapetus, the lowest albedo C-type asteroids, and the uranian rings. The Bond albedo, 0.009±0.002, is lower than that of any Solar System object measured. Such a low value may enhance the heating of the nucleus and sublimation of volatiles, which in turn causes the albedo to decrease even further. A map of normal reflectance of Borrelly shows variations far greater than those seen on asteroids. The two main terrain types, smooth and mottled, exhibit mean normal reflectances of 0.03 and 0.022. The physical photometric parameters of Borrelly's nucleus are typical of other small dark bodies, particularly asteroids, except preliminary modeling results indicate its regolith may be substantially fluffier. The nucleus exhibits significant variations in macroscopic roughness, with the oldest, darkest terrain being slightly smoother. This result suggests the infilling of low-lying areas with dust and particles that have not been able to leave the comet. The surface of the comet is backscattering, but there are significant variations in the single particle phase function. One region exhibits a flat particle phase function between solar phase angles of 50° and 75° (like cometary dust and unlike planetary surfaces), suggesting that its regolith is controlled by native dust rather than by meteoritic bombardment.     

A new look at photometry of the Moon

We use ROLO photometry (Kieffer, H.H., Stone, T.C. [2005]. Astron. J. 129, 2887-2901) to characterize the before and after full Moon radiance variation for a typical highlands site and a typical mare site. Focusing on the phase angle range 45° < α < 50°, we test two different physical models, macroscopic roughness and multiple scattering between regolith particles, for their ability to quantitatively reproduce the measured radiance difference. Our method for estimating the rms slope angle is unique and model-independent in the sense that the measured radiance factor I/F at small incidence angles (high Sun) is used as an estimate of I/F for zero roughness regolith. The roughness is determined from the change in I/F at larger incidence angles. We determine the roughness for 23 wavelengths from 350 to 939 nm. There is no significant wavelength dependence. The average rms slope angle is 22.2° ± 1.3° for the mare site and 34.1° ± 2.6° for the highland site. These large slopes, which are similar to previous “photometric roughness” estimates, require that sub-mm scale “micro-topography” dominates roughness measurements based on photometry, consistent with the conclusions of Helfenstein and Shepard (Helfenstein, P., Shepard, M.K. [1999]. Icarus 141, 107-131). We then tested an alternative and very different model for the before and after full Moon I/F variation: multiple scattering within a flat layer of realistic regolith particles. This model consists of a log normal size distribution of spheres that match the measured distribution of particles in a typical mature lunar soil 72141,1 (McKay, D.S., Fruland, R.M., Heiken, G.H. [1974]. Proc. Lunar Sci. Conf. 5, Geochim. Cosmochim. Acta 1 (5), 887-906). The model particles have a complex index of refraction 1.65-0.003i, where 1.65 is typical of impact-generated lunar glasses. Of the four model parameters, three were fixed at values determined from Apollo lunar soils: the mean radius and width of the log normal size distribution and the real part of the refraction index. We used FORTRAN programs from Mishchenko et al. (Mishchenko, M.I., Dlugach, J.M., Yanovitskij, E.G., Zakharova, N.T. [1999]. J. Quant. Spectrosc. Radiat. Trans. 63, 409-432; Mishchenko, M.I., Travis, L.D., Lacis, A.A. [2002]. Scattering, Absorption and Emission of Light by Small Particles. Cambridge Univ. Press, New York. <http://www.giss.nasa.gov/staff/mmishchenko/books.html>) to calculate the scattering matrix and solve the radiative transfer equation for I/F. The mean single scattering albedo is ω = 0.808, the asymmetry parameter is 〈cos Θ〉 = 0.77 and the phase function is very strongly peaked in both the forward and backward scattering directions. The fit to the observations for the highland site is excellent and multiply scattered photons contribute ?80% of I/F. We conclude that either model, roughness or multiple scattering, can match the observations, but that the strongly anisotropic phase functions of realistic particles require rigorous calculation of many orders of scattering or spurious photometric roughness estimates are guaranteed. Our multiple scattering calculation is the first to combine: (1) a regolith model matched to the measured particle size distribution and index of refraction of the lunar soil, (2) a rigorous calculation of the particle phase function and solution of the radiative transfer equation, and (3) application to lunar photometry with absolute radiance calibration.     

Polarization of Light Scattered by Surfaces with Complex Microstructure at Phase Angles 0.1°–3.5°

We present laboratory measurements of the phase dependences of linear polarization for surfaces with a complex microstructure in the range of phase angles 0.1°–3.5° A sample of freshly fallen snow (with particle sizes of about 50 × 500 m) exhibits a nearly zero polarization. Surfaces with submicron structure show a narrow branch of negative polarization at small phase angles, irrespective of whether the surface is powderlike or solid with microcrystalline structure. This polarization is similar to that exhibited by Jupiter's satellites. The negative polarization branch becomes deeper with decreasing porosity of light dielectric surfaces. At the phase angles between 0.5° and 3.0°, the polarization for quartz powder with 10-m particles is almost constant. The polarization for light dielectric surfaces depends on the geometry of illumination and observation. An inclination of the surface in the scattering plane produces a parallel shift of the negative polarization branch toward large values of the polarization modulus. The same inclination in a perpendicular direction produces the same shift toward positive degrees of polarization.     

Modeling of opposition effects with ensembles of clusters: Interplay of various scattering mechanisms

Although the opposition phenomena observed in brightness and polarization for various astronomical objects and laboratory samples have been under intense study for many years, their explanation is still far from being complete. The shadow hiding and coherent backscattering effects are mentioned most frequently in this connection. In the present work we first discuss how other coherent scattering mechanisms, in particular interference and interaction between scatterers in the near field, influence brightness and polarization of complex ensembles of particles at small phase angles. Then we demonstrate the contribution of the different mechanisms to the scattering process in a model regolith described as an ensemble of wavelength-sized clusters as constituents. While the clusters are always densely packed, the porosity of the ensemble itself, i.e., the average distances between the clusters within the ensemble, is allowed to vary. The modeling confirms that the phase dependence of intensity and polarization of light scattered by complex structures in the backscattering domain is mainly caused by the interplay of (1) the constructive interference of waves traveling through the particle ensemble along similar paths but in opposite directions and (2) the near-field effect caused by the inhomogeneity of waves in the immediate vicinity of constituent particles. The first mechanism works more effectively in sparse ensembles, while the second one manifests itself in more compact structures of wavelength-sized scatterers at distances comparable to the wavelength. It is difficult to distinguish quantitatively their contributions in models of simple structures and even more in measurements. A number of observations, especially of moderate and low albedo objects, can, however, be explained only by invoking the near-field effect.     

The effect of particle size and porosity on spectral contrast in the mid-infrared

Contrary to previous work, we find that the decreasing intensity of fundamental molecular vibration bands with decreasing particle size is due primarily to increasing porosity of the finer particle size ranges, rather than to particle size per se. This implies that laser reflectance measurements from orbiting spacecraft should avoid loss of spectral contrast for fine particulate surfaces, because such measurements near zero phase angle will benefit from the opposition effect.     

Polarimetry of the E-type asteroid 64 Angelina

Results of polarimetric observations of a high-albedo asteroid 64 Angelina obtained in the phase-angle range from 0.8° to 24.3° are presented. The observations were carried out in the period from September 28 to October 9, 2008, and on November 15, 2011, and September 18, 2012, with the 1.25-m and 2.6-m telescopes of the Crimean Astrophysical Observatory equipped with a five-color double-beam photopolarimeter and a single-channel photometer-polarimeter, respectively. Our observations confirm the polarimetric opposition effect in asteroid 64 Angelina at small phase angles and well agree with the other observations. The obtained results are discussed in terms of the currently available models of the light scattering by regolith surfaces.