Shadow-hiding Opposition Effect Research Articles

Field Reflectance Measurements at Night of Beach and Desert Sands within a Particulate BRDF Model

The Bidirectional Reflectance Distribution Function (BRDF) of soils is frequently assumed to be Lambertian in remote sensing applications, even though many soils are observed to have a distinct backscatter. This is largely due to the difficulty of obtaining accurate in-situ BRDF of these materials over the entire hemisphere. The objective of the work presented here is to describe a new technique that combines the measurement of field BRDF data on desert and beach sands measured at night with a model that reproduces the backscatter except in a small region around zero phase angle. It is found that this combination produces parameterized BRDF of sufficient accuracy to allow its inclusion in a remote sensing materials database. The measurement technique was developed in the laboratory and transitioned to perform in-plane BRDF field measurements of sands at night. Field measurements were obtained using a portable light source and field spectrometer over the range of 0.4–2.4 micrometers. The spectrometer sensor optics and light source were mounted on a portable, manually operated goniometer allowing in-plane measurements to within 3 degrees of backscatter. Unlike daytime measurements, corrections for background were unnecessary, and BRDF was obtained by referencing to a Spectralon calibration standard. Analysis of the spectrometer field data used a variant of the Shadow Hiding Opposition Effect (SHOE) wherein a series expansion of Legendre Polynomials was substituted for the angularly dependent backscatter function. It is shown that when the out-of-plane scattering and the backscatter peak are small, this model provides an adequate description of the BRDF. The combination of the nocturnal in-situ measurements with an analysis using a model that can describe the backscatter produces parameterized BRDF for these sands of sufficient accuracy to allow inclusion in the NEFDS materials database. Measurement and analysis techniques are assessed, sample results for both the laboratory and field data are shown, and the extension to future soils measurements are discussed.

An alternative to Hapke’s macroscopic roughness correction

In this paper, we present an alternative to Hapke’s correction for the photometric effect of macroscopic roughness of planetary surfaces (Hapke, 1984). Our model includes the effects of both single-facet scattering and multi-facet scattering. The single-facet scattering model is derived directly from the definition of bidirectional reflectance of a rough surface. We model projected shadowing by adopting an approximation published elsewhere in the literature. Monte Carlo simulations of single-facet scattering demonstrate very good agreement with the single-facet scattering component of our model. Using 3D printed molds with known roughness statistics, we prepared rough mineral surfaces consisting of quartz and olivine in the laboratory. We recorded extensive measurements of the rough surface bidirectional reflectance over a wide range of illumination and view geometries at 1751 wavelength bands ranging from 500–2250 nm. By fitting the residual between the measured bidirectional reflectance and our single-facet scattering model, we developed an empirical approximation for multi-facet scattering. Our results show that the multi-facet scattering is proportional to the surface’s diffusive reflectance, RMS slope, and the cosine of the illumination angle. Furthermore, the multi-facet scattering is approximately Lambertian for phase angles less than 90° but becomes forward scattering at higher phase angles. Our empirical multi-facet scattering model incorporates all of these features. As a surface becomes more macroscopically rough, our data show that the overall reflectance distribution becomes progressively more backscattering in a way that is distinct from the shadow hiding opposition effect. We refer to this effect as the macroscopic roughness backscattering bias (MRBB), which affects the entire hemisphere rather than being localized to small phase angles. Our proposed model is more accurate than Hapke’s for phase angles less than 90°, and the accuracy of the two models is comparable at higher phase angles. However, researchers should be aware of an issue regarding the roughness parameter defined in Hapke’s model, namely the fact that “ϑ¯” is not actually equal to the mean slope angle of the surface for the probability density function used in the model. This is an issue which apparently has gone unnoticed in the literature, and has potentially caused the model to be applied incorrectly in past studies.

Low-phase spectral reflectance and equivalent “geometric albedo” of meteorites powders

Generally, the reflectance of a particulate surface depends on the phase angle at which it is observed. This is true for laboratory measurements on powders of natural materials as well as remote observations of Solar System surfaces. Here, we measured the dependences of reflectance spectra with phase angles, of a suite of 72 meteorites in the 400–2600 nm range. The 10–30° phase angle range is investigated in order to study the contribution of Shadow Hiding Opposition Effect (SHOE) to the phase behavior. The behavior is then extrapolated to phase angle of 0° using a polynomial fit, in order to provide grounds for comparison across meteorite groups (enabling to remove the contribution of shadows to reflectance) as well as to provide “equivalent albedo” values that should be comparable to geometric albedo values derived for small bodies. We find a general behavior of increasing strength of the SHOE with lower reflectance values (whether between samples or for a given samples with absorption features). This trend provides a first order way to correct any reflectance spectra of meteorite powders measured under standard conditions (g = 30°) from the contribution of shadows. The g = 0° calculated reflectance and equivalent albedos are then compared to typical values of albedos for main-belt asteroids. This reveals that among carbonaceous chondrites only Tagish Lake group, CI, and CM chondrites have equivalent albedo compatible with C- and D-type asteroids. On the other hand equivalent albedo derived with CO, CR and CK chondrites are compatible with L- and K-type asteroids. The equivalent albedo derived for ordinary chondrites is related to petrographic types, with low-grade petrographic type (type 3.6 and less) being generally darker that higher petrographic types. This works provides a framework for further understanding of the asteroids meteorite linkage in particular when combining with colors and spectroscopy.

Opposition effect on S-type asteroid (25143) Itokawa

Aims.The opposition effect has been detected on solar system bodies such as asteroids and comets. Two mechanisms have been proposed to explain the effect: the shadow-hiding opposition effect (SHOE) and the coherent backscattering opposition effect (CBOE). The Hayabusa asteroid sample return mission provides a unique opportunity to investigate the opposition effect on disk-resolved images of the S-type asteroid (25413) Itokawa at very small phase anglesα.Methods.We made use of the data taken atα= 0.°04–2.°54 using the Asteroid Multi-band Imaging Camera (AMICA) on UT 2005 October 13. Comparing sets of two images taken at different phase angles, we derived the opposition slope parameter (SOE) that characterizes a linear increase in the reflectanceI∕Fper unit phase angle.Results.We found that (i)SOEis less dependent on the incidence and emission angles; (ii) the reflectance increases nonlinearly toward the opposition at small angles withα≲ 1.°4, showing a good correlation between meanI∕FandSOE; and (iii)SOEbecomes nearly constant atα≳ 1.°4 and shows no clear correlation betweenI∕FandSOE.Conclusions.From these results, we conjecture that CBOE is dominant atα≲ 1.°4, while SHOE is dominant atα≳ 1.°4.

Asteroid (21) Lutetia: Disk-resolved photometric analysis of Baetica region

(21) Lutetia has been visited by Rosetta mission on July 2010 and observed with a phase angle ranging from 0.15° to 156.8°. The Baetica region, located at the north pole has been extensively observed by OSIRIS cameras system. Baetica encompass a region called North Pole Crater Cluster (NPCC), shows a cluster of superposed craters which presents signs of variegation at the small phase angle images. For studying the location, we used 187 images distributed throughout 14 filter recorded by the NAC (Narrow Angle Camera) and WAC (Wide Angle Camera) of the OSIRIS system on-board Rosetta taken during the fly-by. Then, we photometrically modeled the region using Minnaert disk-function and Akimov phase function to obtain a resolved spectral slope map at phase angles of 5° and 20°. We observed a dichotomy between Gallicum and Danuvius-Sarnus Labes in the NPCC, but no significant phase reddening (-0.04±0.045%μm-1deg-1). In the next step, we applied the Hapke (Hapke, B. [2008]. Icarus 195, 918–926; Hapke, B. [2012]. Theory of Reflectance and Emittance Spectroscopy, second ed. Cambridge University Press) model for the NAC F82+F22 (649.2nm), WAC F13 (375nm) and WAC F17 (631.6nm) and we obtained normal albedo maps and Hapke parameter maps for NAC F82+F22. On Baetica, at 649.2nm, the geometric albedo is 0.205±0.005, the average single-scattering albedo is 0.181±0.005, the average asymmetric factor is -0.342±0.003, the average shadow-hiding opposition effect amplitude and width are 0.824±0.002 and 0.040±0.0007, the average roughness slope is 11.45°±3° and the average porosity is 0.85±0.002. We are unable to confirm the presence of coherent-backscattering mechanism. In the NPCC, the normal albedo variegation among the craters walls reach 8% brighter for Gallicum Labes and 2% fainter for Danuvius Labes. The Hapke parameter maps also show a dichotomy at the opposition effect coefficients, single-scattering albedo and asymmetric factor, that may be attributed to the maturation degree of the regolith or to compositonal variation. In addition, we compared the Hapke (Hapke, B. [2008]. Icarus 195, 918–926; Hapke, B. [2012]. Theory of Reflectance and Emittance Spectroscopy, second ed. Cambridge University Press) and Hapke (Hapke, B. [1993]. Theory of Reflectance and Emittance Spectroscopy) parameters with laboratory samples and other small Solar System bodies visited by space missions.

Resolved Hapke parameter maps of the Moon

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.

A test of Hapke’s model by means of Monte Carlo ray-tracing

One of the most applied solution of the radiative transfer equation for a particulate medium is the so called Hapke’s model. It is widely used to describe the photometric output of the surfaces of atmosphereless bodies of the Solar System and to interpret remote sensing data. In this paper we use a Monte Carlo routine which simulates ray-tracing in particulate media to test three formulations of the Hapke’s model: IMSA (Isotropic Multiple Scattering Approximation), AMSA (Anisotropic Multiple Scattering Approximation) and an updated version of the model described in Hapke (Hapke, B. [2008]. Icarus 195, 918–926) (from now on H2008). While IMSA and AMSA assume a continuos medium, H2008 accounts for the discreteness of a particulate medium (regolith) and introduces a dependence of the photometric output on the filling factor. Using Monte Carlo ray-tracing we have simulated photometric output of media with different porosities and scattering behaviors (isotropic, back-scattering and forward-scattering). The Shadow Hiding Opposition Effect (SHOE) has been investigated as well. What emerges from this analysis is that H2008 is the most appropriate model to describe the photometric output of particulate media with arbitrary porosities, far from the opposition effect regime, and it is also able to characterize anisotropic scattering, unless the medium exhibits a strongly forward-scattering behavior. On the contrary, IMSA and AMSA models are effective only for sparse materials with a filling factor of the order of 0.01. Surprisingly the former provides a better description also in the anisotropic scattering case.

Disk-resolved photometry of Asteroid (2867) Steins

We present a new method to perform disk-resolved photometry in order to investigate the intrinsic photometric properties of the surface of small Solar System bodies. We adopt the standard approach where a shape model is combined with a photometric formalism – in practise the Hapke formalism – to remove the effects of topography and recover the photometric (Hapke) parameters of either the global surface or, in its most elaborated form, the spatial variations of these parameters across the surface. Our method operates in the space of the facets representing the three-dimensional shape of the body, whereas all past analysis have always been performed in the space of the image pixels although they are not intrinsic to the surface of the body. This has the advantage of automatically tracking the same local surface element on a series of images. We first apply our method to images of the nucleus of Comet 9P/Tempel 1 obtained by the High-Resolution Imager (HRI) instrument on board the Deep Impact spacecraft and our derived Hapke parameters are in good agreement with those published by Li et al. (Li, J.-Y. et al. [2007]. Icarus 187, 41–55) within their respective uncertainties. We confirm the presence of an extended region of higher roughness in the southern hemisphere of the nucleus and the higher albedo of the ice-rich regions identified by Sunshine et al. (Sunshine, J.M. et al. [2006]. Science 311, 1453–1455) near the equator. The photometric properties of Asteroid (2867) Steins are then studied from multi-spectral images obtained with the OSIRIS Wide Angle Camera (WAC) on board the Rosetta spacecraft during its flyby on 5 September 2008. Our analysis indicates that the surface is highly porous (∼84%) and that it exhibits both a shadow-hiding opposition effect (SHOE) and probably, a coherent-backscatter opposition effect (CBOE). The single scattering albedo is the highest (SSA=0.57) ever observed among small bodies visited by spacecrafts. Our modelled roughness parameter is indicative of a high microscale roughness. The surface of Steins may in fact exhibit a fractal surface with high roughness present on a large range of scales, from micrometers to centimeters. The geometric and Bond albedos are calculated with the Hapke parameters yielding Ap=0.39±0.02 and AB=0.24±0.01. This high albedo is consistent with an iron-poor surface composition similar to aubrite meteorites which are suspected to originate from the E-type asteroids. We find no photometric variations on the surface at the (limited) spatial resolution of the WAC images.

Theory of reflectance and emittance spectroscopy

Theory of reflectance and emittance spectroscopy

Photometry of meteorites

We have measured the bi-directional reflectance phase function on selected meteorite samples (1 howardite, 1 eucrite, 1 diogenite, Orgeuil (CI), Tagish Lake (CC), Allende (CV), Lunar meteorite (MAC 88105), Forest Vale (H4)) covering part of the geochemical and petrologic diversity expected for asteroid surfaces. Samples were measured as powders, for which we achieved reflectance measurements from phase angles down to 3°, and up to 150°, at five different wavelengths covering the VIS–NIR spectral region. The data were fitted by the photometric model of Hapke (Hapke, B. [1993]. Theory of reflectance and emittance spectroscopy. Cambridge University Press, Cambridge). The physical sense of the retrieved Hapke’s parameters seems unclear but they permit to interpolate the data to any observation geometry. Strong opposition effects were observed for all samples. The absolute intensity of this effect appears moderately variable among our sample suite, and is not correlated with the average sample reflectance. We interpret this observation as Shadow-Hiding Opposition Effect (SHOE). In the case of samples presenting intense absorption bands (the Fe crystal field band at 1μm of HED and the ordinary chondrite), we observe significant dependence of band depth to phase angle, up to 70°, even for moderate variation of phase angle. In addition, a general trend of spectral reddening with phase angle is observed. This reddening, linear with phase angle, is present in all meteorites studied. This behavior is not predicted by classical radiative theories. We propose that small-scale roughness (of the order of or below the wavelength) may induce such a behavior.

Lunar photometric properties at wavelengths 0.5–1.6 μm acquired by SELENE Spectral Profiler and their dependency on local albedo and latitudinal zones

The lunar photometric function, which describes the dependency of the observed radiance on the observation geometry, is used for photometric correction of lunar visible/near-infrared data. A precise photometric correction parameter set is crucial for many applications including mineral identification and reflectance map mosaics. We present, for the first time, spectrally continuous photometric correction parameters for both sides of the Moon for wavelengths in the range 0.5–1.6 μm and solar phase angles between 5° and 85°, derived from Kaguya (SELENE) Spectral Profiler (SP) data. Since the measured radiance also depends on the surface albedo, we developed a statistical method for selecting areas with relatively uniform albedos from a nearly 7000-orbit SP data set. Using the selected data set, we obtained empirical photometric correction parameter sets for three albedo groups (high, medium, and low). We did this because the photometric function depends on the albedo, especially at phase angles below about 20° for which the shadow hiding opposition effect is appreciable. We determined the parameters in 160 bands and discovered a small variation in the opposition effect due to the albedo variation of mafic mineral absorption. The consistency of the photometric correction was checked by comparing observations made at different times of the same area on the lunar surface. Variations in the spectra obtained were lower than 2%, except for the large phase angle data in mare. Lastly, we developed a correction method for low solar elevation data, which is required for high latitude regions. By investigating low solar elevation data, we introduced an additional correction method. We used the new photometric correction to generate a 1° mesh global lunar reflectance map cube in a wavelength range of 0.5–1.6 μm. Surprisingly, these maps reveal that high latitude (≳75°) regions in both the north and south have much lower spectral continuum slopes (color ratio r 1547.7nm/ r 752.8nm ≲ 1.8) than the low and medium latitude regions, which implies lower degrees of space weathering.

Testing the Hapke photometric model: Improved inversion and the porosity correction

In conjunction with a companion paper (Shepard, M.K., Helfenstein, P. [2011]. Icarus, submitted for publication), we derive, test, and apply a detailed approach for visualizing the phase angle dependence of light scattering in particulate soils from both whole-disk and disk-resolved observations. To reduce the number of model parameters and provide stronger constraints on model fits, we combine Hapke’s (Hapke, B. [2008]. Icarus 195, 918–926) recent correction for effects of porosity with his (Hapke, B. [1986]. Icarus 67, 264–280) model of the shadow hiding opposition effect. We further develop our method as a tool for least-squares fitting of Hapke’s model to photometric data. Finally, we present an improved method for estimating uncertainties in retrieved values of Hapke model parameters. We perform a preliminary test of the model on spectrogoniometric measurements from three selected laboratory samples from Shepard and Helfenstein (Shepard, M.K., Helfenstein, P. [2007]. J. Geophys. Res. 112 (E03001), 17). Our preliminary suite of test samples is too small and selective to permit the drawing of general conclusions. However, our results suggest that Hapke’s porosity correction improves the fidelity of fits to samples composed of low- and moderate-albedo particles and may allow for more reliable retrieval of porosity estimates in these materials. However, we find preliminary evidence that in high-albedo surfaces, the effects of porosity may be difficult to detect.

Europa's opposition surge in the near-infrared: interpreting disk-integrated observations by Cassini VIMS

Near-infrared observations of Europa's disk-integrated opposition surge by Cassini VIMS, first published in Fig. 4 of Brown et al. (2003, Icarus, 164, 461), have now been modeled with the commonly used Hapke photometric function. The VIMS data set emphasizes observations at 16 solar phase angles from 0.4° to 0.6°—the first time the < 1 ° phase “heart” of Europa's opposition surge has been observed this well in the near-IR. This data set also provides a unique opportunity to examine how the surge is affected by changes in wavelength and albedo: at VIMS wavelengths of 0.91, 1.73, and 2.25 μm, the geometric albedo of Europa is 0.81, 0.33, and 0.18, respectively. Despite this factor-of-four albedo range, however, the slope of Europa's phase curve at < 1 ° phase is similar at all three wavelengths (to within the error bars) and this common slope is similar to the phase coefficient seen in visible-light observations of Europa. The two components of the opposition surge—involving different models of the physical cause of the surge—are the Shadow Hiding Opposition Effect (SHOE) and the Coherent Backscatter Opposition Effect (CBOE). Because of sparse VIMS phase coverage, it is not possible to constrain all the surge parameters at once in a Hapke function that has both SHOE and CBOE; accordingly, we performed separate Hapke fits for SHOE-only and CBOE-only surges. At 2.25 μm, where VIMS data are somewhat noisy, both types of surges can mimic the slope of the VIMS phase curve at < 1 ° phase. At 0.91 and 1.73 μm, however—where VIMS data are “cleaner”—CBOE does a noticeably poorer job than SHOE of matching the VIMS phase coefficient at < 1 ° phase; in particular, the best CBOE fit insists on having a steeper phase-curve slope than the data. This discrepancy suggests that Europa's near-IR opposition surge cannot be explained by CBOE alone and must have a significant SHOE component, even at wavelengths where Europa is bright.

The Opposition Effect and the Quasi-fractal Structure of Regolith: I. Theory

We present a new heuristic model combining the coherent-backscatter and shadow-hiding opposition effects. The model considers the aggregate structure of regolith in a realistic way and accounts for the fractal architecture of planetary surfaces both on microscopic particulate and macroscopic, texturally faceted size scales. It describes how the shadow-hiding opposition effect is manifested in a fractally arranged surface, the important contribution of incoherent, multiply scattered light among small scatterers within a surface composed of aggregate grains and its amplification by backscatter interference. We provide a general theoretical model as well as a preliminary, simple analytical approximation that is suitable for investigating the opposition behavior of planet, satellite, and asteroid surfaces. The analytical approximation utilizes only four model parameters; ω 0, the average, single-scattering albedo of elemental scatterers that are the building blocks of aggregates, h, Hapke's (1986, Icarus 67, 264–280) angular-width parameter for the shadow-hiding opposition effect, L, the diffusion scale length of light through the regolith, and q, a structural parameter that characterizes the relative size and complexity of aggregate particles. Our model explains the simultaneous occurrence of the coherent-backscatter enhancement and shadow-hiding in moderate to low albedo soils in addition to the dominance of coherent-backscatter in bright soils. It predicts that coherent backscatter and shadow-hiding can occur at a variety of size scales within the regolith. Individual regolith particles can exhibit their own opposition effects which are convolved with the contribution that arises from their packing within the planetarysurface. The size domains over which coherent-backscatter and shadow-hiding, respectively, each have their most pronounced effect is strongly controlled by the albedo of internal scatterers and the number of hierarchical generations of aggregates required to characterize the particulate-scale behavior of the regolith surface.

The Lunar Opposition Effect: A Test of Alternative Models

We test the hypotheses that the lunar opposition effect is due to shadow-hiding, coherent backscatter, or some combination of the two phenomena. Hapke's photometric model is extended to include975726description of the coherent backscatter opposition effect. The model was fit simultaneously toV-filter (λ = 0.55 μm) whole-disk photometry of the Moon over many phase angles (2° ≤ α ≤ 143°) and to disk-resolved observations of the lunar surface over a broad range of incidence, emission, and phase angles. The shape of the Moon's opposition surge is accurately represented by the combination of a narrow coherent-backscatter peak whose effect is most strongly defined at α < 2° and a very broad shadow-hiding peak, best defined over α < 20°. The relative angular widths of the shadow-hiding and coherent backscatter contributions can be used to estimate the grain sizes most important for scattering at small phase angles. Scatterers with sizes comparable to the wavelength of light are required for coherent backscattering and are present in the smallest size fraction of lunar soil, but are predicted only for a model in which coherent backscatter causes the narrow component and shadow-hiding the wide one. The amplitude of the shadow-hiding opposition effect measures grain transparency and our solution implies that the lunar regolith particles responsible for the shadow-hiding contribution behave like opaque grains, consistent with complex structure of lunar regolith particles at much larger scales than those which control the coherent backscatter contribution. Most other airless planetary surfaces exhibit opposition surges whose broad components also appear to be caused by shadow-hiding. We propose that the submicron sized grains that control coherent backscatter do not contribute to the shadow-hiding opposition surge because the minute shadows cast by these grains are illuminated by their own forward-scattered light. We suggest that coherent backscatter cannot be responsible for the broad component of the Moon's opposition surge because such forward scattered light would illuminate all particle shadows and thereby eliminate the shadow-hiding contribution.