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We present reflectance and polarization phase curve measurements of highly reflective planetary regolith analogues having physical characteristics expected on atmosphereless solar system bodies (ASSBs) such as a eucritic asteroids or icy satellites. We used a goniometric photopolarimeter (GPP) of novel design to study thirteen well-sorted particle size fractions of aluminum oxide (Al2O3). The sample suite included particle sizes larger than, approximately equal to, and smaller than the wavelength of the incident monochromatic radiation (λ = 635 nm). The observed phase angle, α, was 0.056 o ∼95%). The incident radiation has a very high probability of being multiply scattered before being backscattered toward the incident direction or ultimately absorbed. The five smallest particle sizes exhibited extremely high void space (> ∼95%). The reflectance phase curves for all particle size fractions show a pronounced non-linear reflectance increase with decreasing phase angle at α∼ The polarization phase curves for particle size fractions with size parameter (particle radius/wavelength) r/λ ∼1 we detect no polarization. This polarization behavior is distinct from that observed in low albedo solar system objects such as the Moon and asteroids and for absorbing materials in the laboratory. We suggest this behavior arises because photons that are backscattered have a high probability of having interacted with two or more particles, thus giving rise to the CB process. These results may explain the unusual negative polarization behavior observed near small phase angles reported for several decades on highly reflective ASSBs such as the asteroids 44 Nysa, 64 Angelina and the Galilean satellites Io, Europa and Ganymede. Our results suggest these ASSB regoliths scatter electromagnetic radiation as if they were extremely fine grained with void space > ∼95%, and grain sizes of the order The GPP used in this study was modified from our previous design so that the sample is presented with light that is alternatingly polarized perpendicular to and parallel to the scattering plane. There are no analyzers before the detector. This optical arrangement, following the Helmholtz Reciprocity Principle (HRP), produces a physically identical result to the traditional laboratory reflectance polarization measurements in which the incident light is unpolarized and the analyzers are placed before the detector. The results are identical in samples measured by both methods. We believe that ours is the first experimental demonstration of the HRP for polarized light, first proposed by Helmholtz in 1856.

Theoretical modelling has suggested that the deposition of charged solar energetic particles in the lunar regolith can generate electric fields strong enough to cause millimeter-scale dielectric breakdown, and that these violent electric discharges are responsible for such space weathering effects as submicron iron particles, glass, low albedo and reddish color. It is shown that, when secondary electron emission and the particulate, porous, reentrant structure of the regolith are taken into account, electric fields sufficient to initiate breakdown are unlikely to occur there.

The visible (400–700 nm) and near-infrared (700–2800 nm) reflectance of the lunar regolith is dominantly controlled by variations in the abundance of plagioclase, iron-bearing silicate minerals, opaque minerals (e.g., ilmenite), and maturation products (e.g., agglutinate glass, radiation-produced rims on soil grains, and Fe-metal). The same materials control reflectance into the near-UV (250–400 nm) with varying degrees of importance. A key difference is that while ilmenite is spectrally neutral in the visible to near-infrared, it exhibits a diagnostic upturn in reflectance in the near-UV, at wavelengths shorter than about 450 nm. The Lunar Reconnaissance Orbiter Wide Angle Camera (WAC) filters were specifically designed to take advantage of this spectral feature to enable more accurate mapping of ilmenite within mare soils than previously possible. Using the reflectance measured at 321 and 415 nm during 62 months of repeated near-global WAC observations, first we found a linear correlation between the TiO2 contents of the lunar soil samples and the 321/415 nm ratio of each sample return site. We then used the coefficients from the linear regression and the near-global WAC multispectral mosaic to derive a new TiO2 map. The average TiO2 content is 3.9 wt% for the 17 major maria. The highest TiO2 values were found in Mare Tranquillitatis (∼12.6 wt%) and Oceanus Procellarum (∼11.6 wt%). Regions contaminated by highland ejecta, lunar swirls, and the low-TiO2 maria (e.g., Mare Frigoris, the northeastern units of Mare Imbrium) exhibit very low TiO2 values ( 2.6 Ga), whereas only medium to high TiO2 values (average = 6.8 wt%, minimum = 4.5 wt%) are found for younger mare units (

The porosity of the upper centimeter or so of the lunar regolith strongly affects several properties that are commonly studied remotely. Hence, it is important to determine its value. We have reanalyzed the data of Ohtake et al. (Ohtake et al. [2010]. Space Sci. Rev., 154, 57–77), who used spacecraft and laboratory reflectance measurements of the Moon by Kaguya Multiband Imager instruments and an Apollo sample to infer a lunar regolith porosity of 74–87%. Our analysis was augmented by using Lunar Reconnaissance Orbiter Wide and Narrow Angle Camera images. We confirm the Ohtake et al. (Ohtake et al. [2010]. Space Sci. Rev., 154, 57–77) estimate and refine it to 83 ± 3%. However, depending on the validity of key assumptions, this value could be a lower limit, so that the actual porosity could be somewhat higher. Even though the magnetic resonance index of the sample indicates that it is mature, it is appears to be optically less mature than a standard photometric site near the sample collection site.

The opposition effect is the sharp, narrow surge observed in the reflectance of a scattering medium near zero phase angle. Numerous observations and experiments have shown that the primary cause of the phenomenon in particulate media is coherent backscattering, in which wavelets traveling in opposite directions along chains of scatterers interfere constructively and generate the peak. A broader opposition surge caused by shadow hiding and preferential escape is also present, but is entangled with the incoherent continuum reflectance on which the coherent peak is superposed, making it difficult to identify and isolate. Theoretical models of media of independent scatterers predict that the angular width and shape of the coherent backscatter peak depend on the wavelength, porosity and particle size. It was hoped that remote measurements of the opposition effect would give information on the latter two quantities in planetary regoliths. However, observations and laboratory studies of media of large particles in contact with one another find little dependence on any of these quantities. Instead, these studies imply that the opposition effect in regolith-like media comes from reflection by short chains only a few scatterers long located on the surfaces of the particles of the medium, and that the lengths of these chains are proportional to the wavelength. Since the angular width of the peak is controlled by the ratio of the wavelength to the mean scattering chain length, the width is independent of wavelength. Because the wavelets never enter a particle, low albedo media can exhibit a strong coherent backscatter peak. Opposition effect peaks less than a degree wide on solar system bodies can imply an immature regolith; peaks several degrees wide imply a mature regolith.

A critical typographical error and the value of a parameter in the new Lunar Reconnaissance Orbiter Wide Angle Camera TiO2 algorithm are corrected.

We derived spatially resolved near-global Hapke photometric parameter maps of the Moon from 21 months of Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) multispectral observations using a novel “tile-by-tile method” (1° latitude by 1° longitude bins). The derived six parameters (w,b,c,BS0,hS, andθp) for each tile were used to normalize the observed reflectance (standard angles i = g = 60°, e = 0° instead of the traditional angles i = g = 30°, e = 0°) within each tile, resulting in accurate normalization optimized for the local photometric response. Each pixel in the seven-color near-global mosaic (70°S to 70°N and 0°E to 360°E) was computed by the median of normalized reflectance from large numbers of repeated observations (UV: ∼50 and visible: ∼126 on average). The derived mosaic exhibits no significant artifacts with latitude or along the tile boundaries, demonstrating the quality of the normalization procedure. The derived Hapke parameter maps reveal regional photometric response variations across the lunar surface. The b, c (Henyey-Greenstein double-lobed phase function parameters) maps demonstrate decreased backscattering in the maria relative to the highlands (except 321 nm band), probably due to the higher content of both SMFe (submicron iron) and ilmenite in the interiors of back scattering agglutinates in the maria. The hS (angular width of shadow hiding opposition effect) map exhibits relatively lower values in the maria than the highlands and slightly higher values for immature highland crater ejecta, possibly related to the variation in a grain size distribution of regolith.

We investigate the effects of space weathering at ultraviolet wavelengths using a near-global seven-band (321–689 nm) mosaic from the Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC). We confirm that for moderate- to high-iron compositions (≳ 5 wt % FeO), the steeply positive UV slope at wavelengths

High-resolution images of the Surveyor, Luna, and Apollo landing sites obtained by the Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) show regions around the landers where reflectivity of the surface was modified. We interpret the change in reflectance properties of these regions mainly as disturbance of the regolith by rocket exhaust during descent of the spacecraft and we refer to these areas herein as “blast zones” (BZs). The BZs consist of an area of lower reflectance (LR-BZ) compared to the surroundings that extends up to a few meters out from the landers, as well as a broader halo of higher reflectance (HR-BZ) that extends tens to hundreds of meters away from the landers. When approximated as an ellipse, the average Apollo BZ area is ∼29,000 m2 (∼175 ± 60 m by 200 ± 27 m) which is 10× larger than the average Luna BZ, and over 100× larger than the average Surveyor BZ. The LR-BZs are most evident at the Apollo sites, especially where astronaut activity disturbed the soil, leading to a 15–30% (relative to background undisturbed areas) reduction in reflectance at ∼30° phase angle. The LR-BZs at the Surveyor and Luna sites are less evident and are unresolvable with NAC images. The average reflectance in the HR-BZs as determined for 30° phase angle is 3–12% higher than in the undisturbed surrounding areas; this magnitude is the same, within uncertainty, for all sites, indicating a common process or combination of processes causing differences in reflectance properties of the regolith. Phase-ratio images and photometric data collected over a range of illumination geometries show that a greater separation in reflectance occurs between the HR-BZs and undisturbed areas at phase angles between 0° and 70° and indicates that the HR-BZs are less backscattering than undisturbed areas. The LR-BZs are affected by macroscopic disruption of the surface and astronaut activity (at the Apollo sites). For the HR-BZ areas, reflectance has likely been affected by scouring from particles entrained by exhaust gases with low-angle trajectories. Regolith particle interactions with surface soil within HR-BZs may destroy fine-scale surface structure (e.g., “fairy-castle”) and decrease macroscopic roughness, contributing to a decrease in backscattering character within the HR-BZs and an increase in backscattering character within the LR-BZs. Redistribution of fine particles from the LR-BZ to the HR-BZ may have also contributed to the changed reflectance. Photometric modeling is consistent with one or a combination of these processes.

International audience; We report infrared spectrophotometric variability on the surface of Saturn's moon Titan detected in images returned by the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini Saturn Orbiter. The changes were observed at 7°S, 138°W and occurred between October 27, 2005 and January 15, 2006. After that date the surface was unchanged until the most recent observation, March 18, 2006. We previously reported spectrophotometric variability at another location (26°S, 78°W). Cassini Synthetic Aperture RADAR (SAR) images find that the surface morphology at both locations is consistent with surface flows possibly resulting from cryovolcanic activity (Wall et al., companion paper, this issue). The VIMS-reported time variability and SAR morphology results suggest that Titan currently exhibits intermittent surface changes consistent with present ongoing surface processes. We suggest that these processes involve material from Titan's interior being extruded or effused and deposited on the surface, as might be expected from cryovolcanism.

The measured volume-average single particle angular scattering functions of a large number of types of particle of interest for planetary regoliths in the visible-near-IR wavelength region can be represented to a reasonable approximation by two-parameter, double Henyey–Greenstein functions. When the two parameters of this function are plotted against one another they are found to be inversely correlated and lie within a restricted zone shaped like a hockey stick within the parameter space. The centroid of the zone is a curve that can be represented by a simple empirical equation. The wide variety of types of particles used to construct the plot implies that this equation may represent most of the particles found in regoliths. This means that when modeling the bidirectional reflectance of a regolith it may be possible to reduce the number of parameters necessary to specify the reflectance, and also to characterize the entire single particle phase function from observations at phase angles less than 90°. Even if the hockey stick relation has a finite width, rather than being a line, it restricts the parameter space that must be searched when fitting data. The curve should also be useful for forward modeling particle phase functions.

Predictions of two widely-used regolith reflectance models, a numerically exact computer code and an approximate analytic equation, based on the equation of radiative transfer were tested against the measured reflectance of a medium of close-packed spheres, whose properties supposedly can be well-characterized. Surprisingly, the approximate analytic model was a better match to the experimental data than the numerically exact computer solution. Other approximate regolith models were tested briefly with similar results. Discrepancies between the two models and between models and experiment can be explained if the phase functions and albedos of the spheres are not the same as when the particles are isolated. Differences include the absence of the Fraunhoffer diffraction peak, which is an intrinsic assumption of the approximate analytical model but not the exact numerical model, and increased scattering in the mid-range of phase angles, which the approximate analytic model fortuitously describes more accurately than the exact numerical model. These changes may be caused by the close proximity of surrounding particles. If they are taken into account, models based on the radiative transfer equation appear able to quantitatively predict the reflectances of regoliths and other particulate media. Interparticle perturbations are also predicted to cause a coherent backscatter opposition effect in the backward direction that was observed, but its angular width was found to be much larger than predicted by theories for sparsely-packed media.

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.

The highest resolution images of Comet 19P/Borrelly show many dark features which, upon casual inspection, appear to be low albedo markings, but which may also be shadows or other photometric variations caused by a depression in the local topography. In order to distinguish between these two possible interpretations we conducted a photometric analysis of three of the most prominent of these features using six of the highest quality images from the September 22, 2001 Deep Space 1 (DS1) flyby. We find that: 1. The radiance in the darkest parts of each feature increases as phase angle decreases, similarly to the radiance behavior of the higher albedo surrounding terrain. The dark features could be either fully illuminated low albedo spots or, alternatively, they could be depressions. No part of any of the three regions was in full shadow. 2. One of the regions has a radiance profile consistent with a rimmed depression, the second, with a simple depression with no rim, and the third with a low albedo spot. 3. The regolith particles are backscattering and carbon black is one of the few candidate regolith materials that might explain this low albedo. We conclude that Borrelly's surface is geologically complex to the limit of resolution of the images with a combination complex topography, pits, troughs, peaks and ridges, and some very dark albedo markings, perhaps a factor of two to three darker than the average 3–4% albedo of the surrounding terrains. Our technique utilizing measured radiance profiles through the dark regions is able to discriminate between rimmed depressions, rimless depressions and simple albedo changes not associated with topography.

We measured the reflectance change with phase angle (0.05° 0.543 μm . We searched for changes with respect to wavelength in size of the half-width at half-maximum (HWHM) of the phase curve for each particle size. These changes in HWHM are predicted theoretically and observed experimentally in scattering measurements of widely spaced spherical particles in suspension. We find that at both wavelengths the materials exhibit opposition brightness surges of ∼30% at 0.05° relative to the brightness at 5°. At both wavelengths, and for all particle sizes, the slope of the phase curve and the circular polarization ratio both increase with decreasing phase angle, consistent with the opposition surge being due to the coherent backscattering opposition effect (CBOE). Theoretical models of CBOE predict that the HWHM of the phase curve will vary with λ, as λ/2πL, where L is the transport mean free path in the medium. Our samples were observed at two different wavelengths, therefore theory predicts that HWHM would be smaller by about 15% at 0.543 μm compared to 0.633 μm . We do not observe this. There may be several possible explanations. One possibility is that the particles, while well sorted, nevertheless have a variance about a mean size and therefore the change in HWHM is not as sharp as might be expected were all the particles exactly of the same size. Another possible explanation is that our particles are more closely packed and less spherical than those studied in the experimental observations of particles in suspension and hence, while our experiment more closely approximates a planetary regolith, it produces a different result from similar measurements of widely spaced spherical particles in suspension. Our result may explain the unsuccessful Clementine search for CBOE in the lunar regolith which found only a very small wavelength dependence of the phase curve of the same lunar regions when observed at different wavelengths, a result not consistent with theoretical models of CBOE. One explanation may be that the particle size variation in the lunar soil is greater than it was in our samples. Furthermore, our samples, which are better sorted than the lunar regolith, are less well sorted than the theoretical models. This suggests that measuring the change in phase curve HWHM with λ may not be a good test for CBOE in a planetary regolith unless the measurements include a large range of wavelength.

Modeling thermal energy transfer in planetary regoliths involves treating four processes: visible radiative transfer, thermal radiative transfer, conductive transfer, and heat storage. We explicitly treat these processes while considering time-dependent problems, and we apply this model to the regoliths of the Moon and Mercury. Fitting the model to observational data allows us to constrain the radiative resistivity and thermal inertia parameters of these regoliths and hence constrain their conductivities, thermal extinction coefficients, and average grain sizes. It is also found that water ice would be stable in the polar subsurfaces of both bodies, even in areas which receive sunlight during the day.

We measured the change in reflectance and in circular polarization ratio with respect to phase angle of a suite of well-sorted, highly reflective, aluminum oxide powders for the purpose of understanding the contribution of the coherent backscattering phenomenon to the reflectance phase curves of planetary regoliths. The goniometric photopolarimeter that we used measured reflectance and circular polarization ratio over the range of phase angles from 0.05° to 5° where it has been suggested that coherent backscattering becomes important. The particle size of the samples varied from 0.1 to 30 μm. The wavelength of the illuminating radiation from a HeNe laser was 0.633 μm. We find that the reflectance at 0.05° is weakly dependent on particle size. We measured to good approximation the half-width half-maximum (HWHM) of the phase curves, and we find that there is only a weak qualitative agreement between our experimental results and the theoretical estimates of the HWHM for particles of comparable index of refraction and packing density as predicted by M. Mishchenko (1992, Astrophys. Space Sci. 194 , 327–333). For particle sizes that are close to the wavelength of the illuminating radiation we find that Mishchenko's model overestimates the HWHM of the phase curve by an order of magnitude. For particle sizes that are much larger or much smaller than the wavelength of the incident radiation the theoretical model underestimates the HWHM of the phase curve by more than an order of magnitude for the smallest particle sizes and factors of several for the large particle sizes. This disagreement between our experimental data and the predictions from theoretical modeling is not unexpected given the assumptions made in the theoretical models that the particles scatter light like isolated, perfect uniform spheres and that the variation in particle size distribution used by Mishchenko was remarkably small, smaller than that of the well-sieved particle sizes used in our experiment. For all samples the circular polarization ratio increased with decreasing phase angle consistent with the hypothesis that the coherent backscattering process is the principal contributor to the reflectance phase curve near 0° for highly reflective, multiply scattering, particulate media. We confirm our previously reported significant opposition surges for powders with sizes 50 times larger and 6 times smaller than the wavelength of the incident light (R. Nelson et al. 1998, Proc. Lurar Planet. Sci. Conf. 29th , Abstract 1146). This suggests that for cases where the wavelength of the incident radiation is much larger than the candidate regolith particle size, the photons behave as if they were interacting with ensembles of particles of size comparable to the wavelength of the incident radiation. For cases where the particle size is much larger than the wavelength of the incident light, the photons appear to be interacting primarily with wavelength-sized cracks, surface asperities, or other irregularities in the regolith particles rather than with the particle as a whole. This work, using sorted powders as planetary surface regolith analogues, has applicability for remote sensing studies of highly reflective planetary regoliths such as might be expected to be found on many the icy satellites of the outer Solar System. Many of these bodies exhibit sharp opposition surges that are most likely due to coherent backscattering.

— Using new techniques to examine the products of space weathering of lunar soils, we demonstrate that nanophase reduced iron (npFe0) is produced on the surface of grains by a combination of vapor deposition and irradiation effects. The optical properties of soils (both measured and modeled) are shown to be highly dependent on the cumulative amount of npFe0, which varies with different starting materials and the energetics of different parts of the solar system. The measured properties of intermediate albedo asteroids, the abundant S-type asteroids in particular, are shown to directly mimic the effects predicted for small amounts of npFe0 on grains of an ordinary chondrite regolith. This measurement and characterization of space weathering products seems to remove a final obstacle hindering a link between the abundant ordinary chondrite meteorites and common asteroids.

The nature of diffraction and scattering by particles in planetary regoliths is discussed. It is pointed out that the Percus–Yevick approximation to the particle radial distribution function is not valid for a regolith, so that structure factor models based on it are incorrect. A simple analytic expression, valid for general shape and size distributions, for the decrease in scattering cross section caused by the proximity of other particles is derived. It is shown that the classical diffraction pattern of an isolated particle does not exist in a regolith, and that the diffracted light is indistinguishable from the incident irradiance. Hence, to an excellent approximation diffracted light may be treated as unscattered. It is shown that back scattering particles are common in nature and that this conclusion is consistent with the theoretical models published in the paper by Mishchenko and Macke (JQSRT, 1997, 57, 767). It is demonstrated that when exact solutions of the radiative transfer equation are used to analyze observational data sets with a small range of phase angles they retrieve particle asymmetry parameters that are erroneously negative, but that if the range is sufficiently large, approximate reflectance models retrieve correctly positive asymmetries. Hence, assertions that approximate models retrieve erroneously negative asymmetries are false. However, most laboratory and planetary observations are poorly suited to constrain the particle scattering properties in the forward direction, so that many planetary regoliths may have particle phase functions with forward scattering lobes, in addition to back scattering ones. It is pointed out that the radiative transfer equation has inherent deficiencies that make it intrinsically incapable of calculating exact descriptions of scattering by a close-packed regolith of large particles and also that the accuracies of typical absolute reflectance measurements are not high. For both reasons it is pointless to be overly concerned with the relative accuracies of exact and approximate regolith scattering models based on the equation of radiative transfer.

The electromagnetic scattering properties of Solar System regoliths are commonly interpreted using the lunar regolith as a prototype. Hence, a thorough understanding of the reflectance of lunar soil is essential to remote sensing planetary studies. We have measured the linearly and circularly polarized reflectances of samples of lunar soil in order to better understand the nature of the lunar opposition effect. Several independent observations show that the zero-phase peak is caused by both shadow hiding and coherent backscatter in roughly equal amounts. Any radiative transfer model for planetary regoliths must take this dual nature into account. The transport mean free path for photons in the lunar regolith is about 1 μm, which is much smaller than the mean particle size.

We present angular scattering measurements of a suite of particulate materials of varying particle sizes and albedos over phase angles of 1 Eight samples were each presented with both senses of linearly and circularly polarized light and the reflectance and the circular polarization ratio as a function of phase angle was measured. The reflectances of the samples varied from 3 to 99%. The circular polarization ratio was observed to increase in all the samples as the phase angle of the observation decreased near 0° phase angle. The traditional explanation of the opposition surge, the shadow hiding model, predicts that the circular polarization ratio should decrease as the phase angle of the observation decreases. The more reflective materials exhibit stronger opposition surge amplitudes than the less reflective ones. We find a non-linear relationship between the slope of the opposition curve measured at 2° and the single scattering albedo of the sample which is the opposite of what is predicted by the shadow hiding model for the opposition effect. Our results are consistent with predictions of theoretical models of coherent backscattering from spherical particles and strongly suggest that coherent backscattering is the major contributor to the opposition effect. They provide an explanation of the opposition surges reported in highly reflective particulate media, and also the high albedo icy satellites of outer Solar System, both of which cannot be explained by the shadow hiding model.

We observed slected mutual occultations of Jupiter's satellites in 1990-1991 and we used the occultation profiles to constrain the areal distribution of selected spectrally active compounds on Io's surface.

Two different mechanisms, shadow-hiding and coherent backscatter, can cause a hot spot, or opposition effect, in the bidirectional reflectance of vegetation and soils. Because the two mechanisms sample different properties, it is important to know which one is primarily responsible in a given medium. This question can be answered by measuring the bidirectional reflectance in circularly polarized light. If the results of the limited experiments reported here can be extrapolated to a wider range of materials, it appears that the primary cause of the hot spot in most vegetation canopies and in moist, clumpy soils is shadow-hiding. However, in vegetation with large numbers of wavelength-sized structures, such as mosses, and in dry, fine-grained soils, the hot spot is dominated by coherent backscatter.

Several problems of interest in planetary infrared remote sensing are investigated using a new radiative-conductive model of energy transfer in regoliths: the solid-state greenhouse effect, thermal beaming, and reststrahlen spectra. The results of the analysis are as follows: (1) The solid-state greenhouse effect is self-limiting to a rise of a few tens of degrees in bodies of the outer solar system. (2) Non-Lambertian directional emissivity can account for only about 20% of the observed thermal beaming factor. The remainder must have another cause, presumably surface roughness effects. (3) The maximum in a reststrahlen emissivity spectrum does not occur exactly at the Christiansen wavelength where, by definition, the real part of the refractive index equals one, but rather at the first transition minimum in reflectance associated with the transition from particle scattering being dominated by volume scattering to that dominated by strong surface scattering. The transparency feature is at the second transition minimum and does not require the presence of a second band at longer wavelength for its occurance. Subsurface temperature gradients have only a small effect on emissivity bands.

The thermal regime in planetary regoliths involves three processes: propagation of visible radiation, propagation of thermal radiation, and thermal conduction. The equations of radiative transfer and heat conduction are formulated for particulate media composed of anisotropically scattering particles. Although the equations are time dependent, only steady state problems are considered in this paper. Using the two-stream approximation, solutions are obtained for two cases: a layer of powder heated from below and an infinitely thick regolith illuminated by visible radiation. Radiative conductivity, subsurface temperature gradients, and the solid state greenhouse effect all appear intrinsically in the solutions without ad hoc additions. Although the equations are nonlinear, approximate analytic solutions that are accurate to a few percent are obtained. Analytic expressions are given for the temperature distribution, the optical and thermal radiance distributions, the hemispherical albedo, the hemispherical emissivity, and the directional emissivity. Additional applications of the new model to three problems of interest in planetary regoliths are presented by Hapke.

In a recent paper Mishchenko asserts that soil particles are strongly forward scattering, whereas particles on the surfaces of objects in the solar system have been inferred to be back scattering. Mishchenko suggests that this apparent discrepancy is an artifact caused by using an approximate light scattering model to analyse the data, and that planetary regolith particles are actually strong forward scatterers. The purpose of the present paper is to point out the errors in Mishchenko's paper and to show from both theoretical arguments and experimental data that inhomogencous composite particles which are large compared to the wavelength of visible light, such as rock fragments and agglutinates, can be strongly back scattering and are the fundamental scatterers in media composed of them. Such particles appear to be abundant in planetary regoliths and can account for the back scattering character of the surfaces of many bodies in the solar system. If the range of phase angles covered by a data set is insufficient, serious errors in retrieving the particle scattering properties can result whether an exact or approximate scattering model is used. However, if the data set includes both large and small phase angles, approximate regolith scattering models can correctly retrieve the sign of the particle scattering asymmetry.

The intensity and polarization of light scattered by a variety of types of artificial partices large compared to the wavelength were measured as a function of phase angle. Shape, surface roughness, absorption coefficient, and internal scattering coefficient were varied systematically and their effects studied. Scattering by clear, smooth-surfaced spheres is in quantitative agreement with the predictions of the geometrical optics (ray theory) approximation to physical optics (Mie theory). The phase functions of almost all of the particles measured have both forward and backward scattering lobes. A two-parameter, double Henyey-Greenstein function generally provides reasonably good descriptions of the data, while keeping the number of free parameters to the minimum necessary. On a double Henyey- Greenstein parameter plot all of the particles fall into an L-shaped area of restricted size in which the location is characteristic of the particle type. Formalisms based on the equivalent slab model are also given for estimating the scattering efficiency of a large, irregular particle. For most dielectric particles the transmitted, forward scattered light is partially negatively polarized. It is this component that is respopnsible for the well-known maximum in the polarization curves of planetary regoliths at phase angles around 100 deg. For phase angles between about 30 deg and 70 deg the internally scattered light is found to be randomly polarized in the particles studied here, so that the only contribution to the second component of the Stokes vector is by Fresnel reflection from the particle surface. If this empirical result is general, measurement of the second Stokes vector of the light scattered from a regolith at these angles may provide a method of remotely measuring the mean refractive index.

[1] The Lunar Reconnaissance Orbiter wide-angle camera measured the bidirectional reflectances of two areas on the Moon at seven wavelengths between 321 and 689 nm and at phase angles between 0° and 120°. It is not possible to account for the phase curves unless both coherent backscatter and shadow hiding contribute to the opposition effect. For the analyzed highlands area, coherent backscatter contributes nearly 40% in the UV, increasing to over 60% in the red. This conclusion is supported by laboratory measurements of the circular polarization ratios of Apollo regolith samples, which also indicate that the Moon's opposition effect contains a large component of coherent backscatter. The angular width of the lunar opposition effect is almost independent of wavelength, contrary to theories of the coherent backscatter which, for the Moon, predict that the width should be proportional to the square of the wavelength. When added to the large body of other experimental evidence, this lack of wavelength dependence reinforces the argument that our current understanding of the coherent backscatter opposition effect is incomplete or perhaps incorrect. It is shown that phase reddening is caused by the increased contribution of interparticle multiple scattering as the wavelength and albedo increase. Hence, multiple scattering cannot be neglected in lunar photometric analyses. A simplified semiempirical bidirectional reflectance function is proposed for the Moon that contains four free parameters and that is mathematically simple and straightforward to invert. This function should be valid everywhere on the Moon for phase angles less than about 120°, except at large viewing and incidence angles close to the limb, terminator, and poles.

Introduction The basic expression for the bidirectional reflectance of a semi-infinite medium of isotropically scattering particles was derived in Chapter 8 and is given by equation (8.48). This expression was further refined to include an approximate correction for anisotropic scatterers (8.60) and considerations of the effects of porosity (8.70) and the opposition effect in Chapter 9 (9.47). Variants in different geometries were discussed in Chapter 10. In this chapter we will derive expressions that involve integration of the bidirectional reflectance over one or both hemispheres. The remote sensing of bodies of the solar system has its own nomenclature because of the special problems of astronomical observation. Expressions for quantities commonly encountered in planetary spectrophotometry will be derived. Only media for which the porosity factor K = 1 will be treated. Approximate expressions when K > 1 may be readily obtained by substituting one of the linear approximations (8.54 or 8.55) for the H function in the integrand. Integrated reflectances Biconical reflectances If the source and detector do not occupy negligibly small solid angles as seen from the surface, appropriate expressions for the reflectances may be found by numerically integrating one of the above equations over the angular distribution of the radiance from the source and the angular distribution of the response of the detector. In general, such reflectances will be biconical. However, because they would be specific to each particular system, it would not be particularly useful to discuss biconical reflectances in detail.

Introduction The scattering of electromagnetic radiation by perfect, uniform, spherical particles was described in Chapter 5. However, such particles are rarely found in nature. Most pulverized materials, including planetary regoliths, volcanic ash, laboratory samples, and industrial substances, have particles that are irregular in shape, have rough surfaces, and are not uniform in either structure or composition. Even the liquid droplets in clouds are not perfectly spherical, and they contain inclusions of submicroscopic particles around which the liquid has condensed, so that they are not perfectly uniform. At the present state of our computational and analytical capabilities it is possible to find exact solutions of scattering by such particles only by the expenditure of considerable computer time and memory (to say nothing of the effort of writing detailed programs), so that approximate models remain extremely useful. The objective of any model of single-particle scattering is to relate the microscopic properties of the particle (its structure and complex refractive index) to the macroscopic properties (the scattering and extinction efficiencies and the phase function) that, in principle, can be measured by an appropriate scattering experiment. This chapter describes a variety of models that have been proposed to describe the scattering of light by irregular particles. This is not an exhaustive survey; rather, it is a commentary on those models that are most often encountered in remote-sensing applications or that offer some particular insight into the problem. The organization of this chapter is as follows. First, the quantities defined in Chapter 5 for spherical particles are extended to particles that are nonspherical in shape.

Introduction The opposition effect is a sharp surge observed in the reflected brightness of a particulate medium around zero phase angle. Its name derives from the fact that the phase angle is zero for solar-system objects at astronomical opposition when the Sun, the Earth, and the object are aligned. Depending on the material the angular width of the peak can range from about 1° to more than 20°. It has many names including the heiligenschein (literally “ holy glow ”), hot spot, bright shadow and backscatter peak . We have already encountered the opposition effect peak in Figures 8.12 and 8.18. and it is further illustrated in Figures 9.1–9.3. It should not be confused with the glory in the phase function of a sphere (Chapter 5), which is also often called the heiligenschein. The opposition effect is a nearly ubiquitous property of particulate media, including vegetation (Hapke et al ., 1996), laboratory powders (Hapke andVan Horn, 1963; Oetking, 1966; Egan and Hilgeman, 1976; Montgomery and Kohl, 1980; Nelson et al ., 1998, 2000), and regoliths of the Moon (Gehrels et al ., 1964; Whitaker, 1969; Wildey, 1978; Buratti et al ., 1996), Mars (Thorpe, 1978), asteroids (Gehrels et al ., 1964; Bowell and Lumme, 1979; Belskaya and Shevchenko, 2000), satellites of the outer planets (Brown and Cruikshank, 1983; Domingue et al ., 1991), and the rings of Saturn (French et al ., 2007). On a clear day you can see it as a glow around the shadow of your head when your shadow falls on grass or soil.

Reflectance and emittance spectroscopy are increasingly important tools in remote sensing and have been employed in most recent planetary spacecraft missions. They are primarily used to measure properties of disordered materials, especially in the interpretation of remote observations of the surfaces of the Earth and other terrestrial planets. This book gives a quantitative treatment of the physics of the interaction of electromagnetic radiation with particulate media, such as powders and soils. Subjects covered include electromagnetic wave propagation, single particle scattering, diffuse reflectance, thermal emittance and polarisation. This new edition has been updated to include a quantitative treatment of the effects of porosity, a detailed discussion of the coherent backscatter opposition effect, a quantitative treatment of simultaneous transport of energy within the medium by conduction and radiation, and lists of relevant databases and software. This is an essential reference for research scientists, engineers and advanced students of planetary remote sensing.

The photometric textures of Europa geologic units possessing the same small mean photometric slope angle as found by Dominique et al. (1991) are presently examined on the basis of Hapke's (1981) photometric model. With only one exception, the particles composing the surfaces of most of the units exhibit similar scattering properties. Attention is given to the single-particle scattering functions of the two bright plains regions examined; these are noted to be no less different from each other than both are from the other units. An aging process that affects the albedos and single-particle phase functions is hypothesized for Europa.