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1.
The Hapke (Hapke, B. [1981]. J. Geophys. Res. 86, 3039-3054) photometric model and its modifications are widely used to characterize telescopic, spacecraft, and laboratory observations of the bidirectional reflectance of particulate surfaces. Following work and methods laid out in a companion paper (Helfenstein, P., Shepard, M.K. [2011]. Icarus, in press), we deconstruct the Hapke model and, separating all empirical and ad hoc parameters (opposition surge, particle phase function, surface roughness), combine them into a single parameter called the surface phase function, F(α). We illustrate how to extract this function from scattering data sets acquired with the Bloomsburg University Goniometer (BUG). We show how this method can be used to rapidly and accurately characterize bidirectional reflectance data sets from laboratory and spacecraft measurements, often giving better fits to the data. We examine samples with strong color contrasts in different wavelengths. This allows us to examine the exact same surface, changing only the albedo to investigate how the amplitude and the detailed shape of the surface phase function might systematically depend on wavelength and albedo. We also examine the changes in scattering behavior that result when samples are compacted and find the surface phase function and single scattering albedo to be significantly changed. We suggest that these observations support the hypothesis that much of the scattering behavior attributed to the single particle phase function is instead cause by the surface micro-structure.  相似文献   

2.
We present near-infrared spectrometer (NIS) observations (0.8 to 2.4 μm) of the S-type asteroid 433 Eros obtained by the NEAR Shoemaker spacecraft and report results of our Hapke photometric model analysis of data obtained at phase angles ranging from 1.2° to 111.0° and at spatial resolutions of 1.25×2.5 to 2.75×5.5 km/spectrum. Our Hapke model fits successfully to the NEAR spectroscopic data for systematic color variations that accompany changing viewing and illumination geometry. Model parameters imply a geometric albedo at 0.946 μm of 0.27±0.04, which corresponds to a geometric albedo at 0.550 μm of 0.25±0.05. We find that Eros exhibits phase reddening of up to 10% across the phase angle range of 0-100°. We observe a 10% increase in the 1-μm band depth at high phase angles. In contrast, we observe only a 5% increase in continuum slope from 1.486 to 2.363 μm and essentially no difference in the 2-μm band depth at higher phase angles. These contrasting phase effects imply that there are phase-dependent differences in the parametric measurements of 1- and 2-μm band areas, and in their ratio. The Hapke model fits suggest that Eros exhibits a weaker opposition surge than either 951 Gaspra or 243 Ida (the only other S-type asteroids for which we possess disk-resolved photometric observations). On average, we find that Eros at 0.946 μm has a higher geometric albedo and a higher single-scatter albedo than Gaspra or Ida at 0.56 μm; however, Eros's single-particle phase function asymmetry and average surface macroscopic roughness parameters are intermediate between Gaspra and Ida. Only two of the five Hapke model parameters exhibit a notable wavelength dependence: (1) The single-scatter albedo mimics the spectrum of Eros, and (2) there is a decrease in angular width of the opposition surge with increasing wavelength from 0.8 to 1.7 μm. Such opposition surge behavior is not adequately modeled with our shadow-hiding Hapke model, consistent with coherent backscattering phenomena near zero phase.  相似文献   

3.
Images of Mars in the visible to near-infrared acquired from 1996 to 2005 using the Hubble Space Telescope WFPC2 have been used to model the martian surface photometric function at 502, 673, 953, and 1042 nm. These data range in spatial resolution from 12 to 70 km/pixel at the sub-Earth point, and in phase angle coverage from 0.34° to 40.5°. The WFPC2 images have been calibrated to radiance factor or I/F and projected to a cylindrical map for coregistration and comparison to similarly mapped spacecraft data sets of albedo, topography, thermal inertia, composition, and geology. We modeled the observed I/F as a function of phase angle using Minnaert, Lambert, lunar-Lambert, and Hapke photometric functions for numerous regions of interest binned into albedo units defined by Viking and TES albedo maps, and thermal-inertia units defined by TES thermal-inertia maps. Visibly opaque water-ice clouds and data acquired under high dust opacity conditions were excluded from the analysis. Our modeling suggests that under average to low atmospheric dust opacity conditions and over this range of phase angles, the photometric properties of the martian surface at 502, 673, 953, and 1042 nm are best modeled by lunar-Lambert functions with parameters derived for three surface units defined by low, moderate, and high TES bolometric albedos.  相似文献   

4.
J Warell 《Icarus》2004,167(2):271-286
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.  相似文献   

5.
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.  相似文献   

6.
In March 2001, the Hayabusa spacecraft target, Asteroid 25143 Itokawa, made its final close approach to Earth prior to the spacecraft's launch. We carried out an extensive observing campaign from January to September 2001 to better characterize this near-Earth asteroid. Global physical properties of the surface of Itokawa were characterized by analyzing its photometric properties and behavior. Results included here capitalize on analysis of broadband photometric observations taken with a number of telescopes, instruments, and observers. We employed a Hapke model to estimate the surface roughness, single particle scattering albedo, single particle scattering characteristics, phase integral, and geometric and bond albedo. We find that this asteroid has a higher geometric albedo than average main belt S-class asteroids; this is consistent with results from other observers. The broadband colors of Itokawa further support evidence that this is an atypical S-class asteroid. Broadband colors show spectral characteristics more typically found on large-diameter main-belt asteroids believed to be space-weathered, suggesting the surface of this small diameter, near-Earth asteroid could likewise be space-weathered.  相似文献   

7.
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.  相似文献   

8.
A photometric analysis of the S-type Asteroid 25143 Itokawa is performed over multiple wavelengths ranging from 0.85 to 2.10 μm based on disk-resolved reflectance spectra obtained with the Hayabusa near-infrared spectrometer (NIRS). We derive the global photometric properties of Itokawa in terms of Hapke's photometric model. We find that Itokawa has a single-scatter albedo that is 35-40% less than that of Asteroid 433 Eros. Itokawa also has a single-particle phase function that is more strongly back-scattering than that of Eros. Despite its hummocky surface strewn with large boulders, Itokawa exhibits an opposition effect. However, the total amplitude of the opposition surge for Itokawa was estimated to be less than unity while Eros and other S-type asteroids have been found to have model values exceeding unity. The wavelength dependence of the opposition surge width reveals that coherent backscatter contributes to the opposition effect on Itokawa's surface. The photometric roughness of Itokawa is well constrained to a value of 26° ± 1° which is similar to Eros, suggesting that photometric roughness models the smallest surface roughness scale for which shadows exist.  相似文献   

9.
We have constructed an experiment to perform bidirectional reflectance distribution function (BRDF) measurements of laboratory samples, and have used the experiment to characterize a sample of JSC-1 lunar regolith simulant. Characterizations relied on in-plane BRDF measurements in visible and near-infrared (NIR) bandpasses. The optical properties of the simulant sample were found to be similar to those observed for bright, lunar highland regions. Reflectance models (Hapke 1981. Bidirectional reflectance spectroscopy 1. Theory. J. Geophys. Res. 86(B4), 3,039−3,054; 1984. Bidirectional reflectance spectroscopy 3. Correction for macroscopic roughness. Icarus 59, 41−59; 1986. Bidirectional reflectance spectroscopy 4. The extinction coefficient and the opposition effect. Icarus 67, 264−280; 2002. Bidirectional reflectance spectroscopy 5. The coherent backscatter opposition effect and anisotropic scattering. Icarus 157, 523−534) made excellent fits to fixed incidence angle, variable emission angle data sets. However, the models were not found to extrapolate well to fixed, near-zero phase angle data at varying incidence angles, and no solutions were found that provided simultaneous, high quality fits to the two types of data sets. Except for the single-scattering albedo, the best-fit parameters of the fixed incidence angle data were statistically the same in the visible and NIR. Correlations between the reflectance model parameters were systematically examined, and strong correlations were found between single-scattering albedo and the two two-stream Henyey-Greenstein scattering parameters and, to a lesser extent, the small-scale mean surface roughness.  相似文献   

10.
The quantitative measurement of surface roughness of planetary surfaces at all scales provides insights into geological processes. A characterization of roughness variations at the scale of a few tens of meters is proposed that complements the analysis of local topographic data of the martian surface at kilometer scale, as achieved from the Mars Orbiter Laser Altimeter (MOLA) data, and at the subcentimeter scale using photometric properties derived from multi-angular observations. Relying on a Gabor filtering process, an algorithm developed in the context of image classification for the purpose of texture analysis has been adapted to handle data from the High Resolution Stereo Camera (HRSC). The derivation of roughness within a wavelength range of tens of meters, combined with analyses at even longer wavelengths, gives an original view of the martian surface. The potential of this approach is evaluated for different examples for which the geological processes are identified and the geological units are mapped and characterized in terms of roughness.  相似文献   

11.
Stereo analysis of images obtained during the 2001 flyby of Comet Borrelly by NASA's Deep Space 1 (DS1) probe allows us to quantify the shape and photometric behavior of the nucleus. The shape is complex, with planar facets corresponding to the dark, mottled regions of the surface whereas the bright, smooth regions are convexly curved. The photometric as well as textural differences between these regions can be explained in terms of topography (roughness) at and below the image resolution, without invoking significant variations in single-particle properties; the material on Borrelly's surface could be quite uniform. A statistical comparison of the digital elevation models (DEMs) produced from the three highest-resolution images independently at the USGS and DLR shows that their difference standard deviation is 120 m, consistent with a matching error of 0.20 pixel (similar to reported matching accuracies for many other stereo datasets). The DEMs also show some systematic differences attributable to manual versus automatic matching. Disk-resolved photometric modeling of the nucleus using the DEM shows that bright, smooth terrains on Borrelly are similar in roughness (Hapke roughness θ=20°) to C-type asteroid Mathilde but slightly brighter and more backscattering (single-scattering albedo w=0.056, Henyey-Greenstein phase parameter g=−0.32). The dark, mottled terrain is photometrically consistent with the same particles but with roughnesses as large as 60°. Intrinsically darker material is inconsistent with the phase behavior of these regions. Many local radiance variations are clearly related to topography, and others are consistent with a topographic explanation; one need not invoke albedo variations greater than a few tens of percent to explain the appearance of Borrelly.  相似文献   

12.
The disk-resolved flyby images of the nucleus of Comet 81P/Wild 2 collected by Stardust are used to perform a detailed study of the photometric properties of this cometary nucleus. A disk-integrated phase function from phase angle 11° to about 100° is measured and modeled. A phase slope of 0.0513 ± 0.0002 mag/deg is found, with a V-band absolute magnitude of 16.29 ± 0.02. Hapke’s photometric model yields a single-scattering albedo of 0.034, an asymmetry factor of phase function −0.53, a geometric albedo 0.059, and a V-band absolute magnitude of 16.03 ± 0.07. Disk-resolved photometric modeling from both the Hapke model and the Minnaert model results in 11% model RMS, indicating small photometric variations. The roughness parameter is modeled to be 27 ± 5° from limb-darkening profile. The modeled single-scattering albedo and asymmetry factor of the phase function are 0.038 ± 0.004 and −0.52 ± 0.04, respectively, consistent with those from disk-integrated phase function. The bulk photometric properties of the nucleus of Wild 2 are comparable with those of other cometary nuclei. The photometric variations on the surface of the nucleus of Wild 2 are at a level of or smaller than 15%, much smaller than those on the nucleus of Comet 19P/Borrelly and comparable or smaller than those on the nucleus of Comet 9P/Tempel 1. The similar photometric parameters of the nuclei of Wild 2, Tempel 1, and the non-source areas of fan jets on Borrelly may reflect the typical photometric properties of the weakly active surfaces on cometary nuclei.  相似文献   

13.
Dawn spacecraft orbited Vesta for more than one year and collected a huge volume of multispectral, high-resolution data in the visible wavelengths with the Framing Camera. We present a detailed disk-integrated and disk-resolved photometric analysis using the Framing Camera images with the Minnaert model and the Hapke model, and report our results about the global photometric properties of Vesta. The photometric properties of Vesta show weak or no dependence on wavelengths, except for the albedo. At 554 nm, the global average geometric albedo of Vesta is 0.38 ± 0.04, and the Bond albedo range is 0.20 ± 0.02. The bolometric Bond albedo is 0.18 ± 0.01. The phase function of Vesta is similar to those of S-type asteroids. Vesta’s surface shows a single-peaked albedo distribution with a full-width-half-max ∼17% relative to the global average. This width is much smaller than the full range of albedos (from ∼0.55× to >2× global average) in localized bright and dark areas of a few tens of km in sizes, and is probably a consequence of significant regolith mixing on the global scale. Rheasilvia basin is ∼10% brighter than the global average. The phase reddening of Vesta measured from Dawn Framing Camera images is comparable or slightly stronger than that of Eros as measured by the Near Earth Asteroid Rendezvous mission, but weaker than previous measurements based on ground-based observations of Vesta and laboratory measurements of HED meteorites. The photometric behaviors of Vesta are best described by the Hapke model and the Akimov disk-function, when compared with the Minnaert model, Lommel–Seeliger model, and Lommel–Seeliger–Lambertian model. The traditional approach for photometric correction is validated for Vesta for >99% of its surface where reflectance is within ±30% of global average.  相似文献   

14.
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15.
The Short Wavelength Channel of the Planetary Fourier Spectrometer (PFS) covers the 8333-1750 cm−1 (1.2-5.7 μm) spectral range, that is well suited to study the reflectance properties of the martian soil. These properties vary with time due to the dust dynamics in the martian environment. Wind can blow off dust exposing soil and fresh rocks and can support grain mobility inducing local dust settling. We have analyzed PFS data from January 2004 to April 2005. A detailed photometric study of the radiance acquired from the planet has been performed in order to compare correctly measurements obtained at different viewing geometries and to produce a mosaic image of the planet. The results show good agreement with data from the Thermal Emission Spectrometer (on-board NASA Mars Global Surveyor orbiter), although some variations are observed. Some albedo changes could be due to small to medium scale dust storms. A very accurate estimation of the limb-darkening parameter has been computed from the analyzed data. The obtained values are compared with a surface roughness and a thermal inertia map in order to assess the relation between the limb-darkening parameter and the physical properties of surface.  相似文献   

16.
We observed Phoebe for 13 nights over a period of 55 days before, during, and after the 2005 Saturn opposition with the New Mexico State University (NMSU) 1-m telescope at Apache Point Observatory (APO) in Sunspot, NM and characterized the width and magnitude of Phoebe’s opposition surge in BVRI filters. Our observations cover a phase angle range of 4.87° to 0.0509°. We use a Hapke reflectance model incorporating shadow hiding and coherent backscatter to investigate the wavelength dependence of Phoebe’s opposition surge. We find a significant opposition surge magnitude of 55-58% between phase angles of 5° and 0°. We find the strongest opposition surge for phase angles less than 2° in the I-band. The coherent backscatter angular width is on the order of 0.50°. We find Phoebe’s albedo to be spectrally flat within our error limits, with a B-band albedo of 0.0855 ± 0.0031, a V-band albedo of 0.0856 ± 0.0023, an R-band albedo of 0.0843 ± 0.0020, and an I-band albedo of 0.0839 ± 0.0023. We compare Phoebe’s albedo, color, and opposition surge magnitudes and slopes with those of other outer solar system bodies and find similarities to Centaurs, Nereid, Puck, and Comets 19P/Borrelly, 9P/Tempel 1, and 81P/Wild 2. We find that this comparison supports the idea that Phoebe originated in the Kuiper Belt. We also discuss the caveats of using results from a Hapke reflectance model to derive specific surface particle properties.  相似文献   

17.
We present the results of photometric observations of trans-neptunian object 20000 Varuna, which were obtained during 7 nights in November 2004-February 2005. The analysis of new and available photometric observations of Varuna reveals a pronounced opposition surge at phase angles less than 0.1 deg with amplitude of 0.2 mag relatively to the extrapolation of the linear part of magnitude-phase dependence to zero phase angle. The opposition surge of Varuna is markedly different from that of dark asteroids while quite typical for moderate albedo Solar System bodies. We find an indication of variations of the scattering properties over Varuna's surface that could result in an increase of the lightcurve amplitude toward zero phase angle. It is shown that a similar phase effect can be responsible for lightcurve changes found for TNO 19308 (1996 TO66) in 1997-1999.  相似文献   

18.
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.  相似文献   

19.
Remote-sensing observations of Gale Crater and Melas Chasma are synthesized to better understand the present surface layer in these two scientifically interesting regions. Data sets analyzed include geologic maps, Mars Orbiter Laser Altimeter (MOLA) elevation, Thermal Emission Spectrometer (TES) albedo, TES thermal inertia, MOLA residual pulse width, TES rock abundance, and Viking and Mars Orbiter Camera images. Using these data sets, we constrain the properties of and processes acting on the present surface and create self-consistent models for the surface layer. Surface properties within Gale Crater are variable and complex, and interpreting the surface layer is not straightforward. Observations indicate that aeolian processes have shaped some of the intracrater surface, but other areas do not comply with this model and have counterintuitive surface characteristics. In contrast, aeolian activity appears to have played a large role in shaping the present-day physical structure of all surfaces in Melas Chasma and is reflected in the remote-sensing data sets. Here we summarize our analysis and discuss the surface attributes as determined from these data sets.  相似文献   

20.
In deriving the physical properties of asteroids from their photometric data, the scattering law plays an important role, although the shape variations of asteroids result in the main variations in lightcurves. By following the physical behaviors of light reflections, Hapke et al. deduced complex functions to represent the scattering process, however, it is very hard to accurately simulate the surface scattering law in reality. For simplicity, other numerical scattering models are presented for efficiently calculating the physical properties of asteroids, such as the Lommel-Seeliger(LS) model. In this article,these two models are compared numerically. It is found that in some numerical applications the LS model in simple form with four parameters can be exploited to replace the Hapke model in complex form with five parameters. Furthermore, the generated synthetic lightcurves by the Cellinoid shape model also show that the LS model can perform as well as the Hapke model in the inversion process. Finally, by applying the Principal Component Analysis(PCA) technique to the parameters of the LS model, we present an efficient method to classify C and S type asteroids, instead of the conventional method using the parameters of the Hapke model.  相似文献   

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