Slope variations on the surface of Phobos

It has been suggested that slope fluctuations on the scale of pixel dimensions could be determined by statistical photoclinometry. A closer study of the surface of Phobos reveals variations in the scattering properties of single particles and micro-structures formed by the particles. In the present context, the photoclinometric method of brightness moments is extended to account for these variations by allowing statistical fluctuations in the phase function of the assumed Lommel-Seeliger scattering law. The mean slope on the investigated regions of Phobos has been found to vary from approximately 12 degrees on a 61m scale to approximately 7 degrees on a 216-272m scale. On the same scales, a value of the order of 2% has been obtained for the standard deviation of the scattering phase function. Hints of a fractal-like scale-invariance have been noticed in the covariance function of brightness.     

Photometry of rough planetary surfaces: The role of multiple scattering

Topographic features affect the scattering properties of planetary surfaces by casting shadows and altering the local incidence and emission angles. Measurements of this phenomenon were obtained on the Cornell goniometer for both high and low albedo surfaces. For the low albedo surface, the decrease in reflected radiation due to topography increases sharply with increasing phase angle, whereas for the high albedo sample the effects are approximately constant between phase angles of 30 and 70°. The observations are in good agreement with a theoretical model in the case of the dark surface. However, for the high albedo surface the model overestimates the effects by about a factor of 2, since it does not include the partial illumination of shadows by multiple scattering. For both high and low albedo surfaces, the effects of topography do not become significant until a phase angle of 30–40°.     

Comparison of USGS and DLR topographic models of Comet Borrelly and photometric applications

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.     

An interpretation of Pluto's light variation

A first albedo distribution of a zonal region of Pluto's surface is presented which is based on the analysis of the observed light variations. Light scattering on the planet's surface is described by LAMBERT 's law.     

Observing the martian surface albedo pattern: Comparing the AEOS and TES data sets

High spatial resolution images of Mars were acquired with the Advanced Electro-Optical System (AEOS) 3.63-meter telescope at the Maui Space Surveillance System (MSSS) during both the 2001 and 2003 Mars apparitions. Comparisons are made of the surface albedo patterns obtained from these AEOS images to the surface albedo maps constructed from the Mars Global Surveyor (MGS) Thermal Emission Spectrometer (TES) data taken during the same time periods. These comparisons demonstrate that the images provide albedo information in a limited area surrounding the sub-Earth point that is consistent with the TES-derived albedo field. Additionally, it is shown that by employing adaptive optics (AO), the typical ground-based observing season of Mars can be extended. This is the only known published AO data set of Mars with temporal coverage over an entire apparition. Changes in the surface albedo affect the local ground temperature, which impacts the depth of the planetary boundary layer (PBL) above the surface. Since it is the state of the PBL that controls surface/atmospheric interaction, albedo variations have the power to alter the amount of dust that is lifted. A one-dimensional radiative/convective version of the NASA Ames Mars General Circulation Model is used to demonstrate that the measured albedo variations can alter the daytime ground temperatures by as much as 5 K, which in turn alters the structure of the planetary boundary layer (PBL). Therefore, albedo changes are thermodynamically important, and the ability to characterize them, should orbital observations become unavailable, is a valuable capability.     

A laboratory study of the bidirectional reflectance from particulate samples

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.     

Emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo,II

For the evaluation of the effect of the non-uniform surface albedo on the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo is computed. This paper is the improved version of the previous paper (Takashima and Masuda, 1991). The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are (1) 0.25, 0.23, and 0.02, and (2) 0.75, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is calculated approximately by the contributions due to the multiple scattering in the atmosphere, and due to the diffusely or directly transmitted radiation through the atmosphere which is reflected by the surfaces once (4 interactive radiative modes between atmosphere and surface). Furthermore, to perform the hemispherical integration processing the radiative interaction, the transmission function based on the single scattering in the atmosphere is introduced and then the transmission function is averaged over the hemisphere with weighting function. The numerical simulation exhibits the extraordinary effect near the two half surface boundary of different albedoes. The effect decreases exponentially with the distance from the boundary. The effect depends on the atmospheric aerosol type, optical thickness, and surface albedo. The present version enables us to quantitatively discuss the radiative transfer trend near the boundary of two half surfaces. The upward radiance would simply be evaluated using the present scattering approximation method if the surface albedo is less than 0.3. The present method is thought of as a first step extending the one-dimensional radiative transfer model to two-dimensional using the doubling-adding method.     

Results of TV imaging of Phobos (Experiment VSK-Fregat)

From February to March 1989 the Phobos 2 spacecraft took 37 TV images of Phobos at a distance of 190-1100 km. These images complement Mariner-9 and Viking data by providing higher-resolution coverage of a large region West of the crater Stickney (40-160 degrees W) and by providing disk-resolved measurements of surface brightness at a greater range of wavelengths and additional phase angles. These images have supported updated mapping and characterization of large craters and grooves, and have provided additional observations of craters' and grooves' bright rims. Variations in surface visible/near-infrared color ratio of almost a factor of 2 have been recognized; these variations appear to be associated with the ejecta of specific large impact craters. Updated determinations of satellite mass and volume allow calculation of a more accurate value of bulk density, 1.90 +/- 0.1 g cm-3. This is significantly lower than the density of meteoritic analogs to Phobos' surface, suggesting a porous interior perhaps containing interstitial ice.     

Are the circular, dark features on Comet Borrelly's surface albedo variations or pits?

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.     

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

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

Titan's 5 micrometers spectral window: carbon monoxide and the albedo of the surface

We have measured the spectrum of Titan near 5 micrometers and have found it to be dominated by absorption from the carbon monoxide 1-0 vibration-rotation band. The position of the band edge allows us to constrain the abundance of CO in the atmosphere and/or the location of the reflecting layer in the atmosphere. In the most likely case, 5 micrometers radiation is reflected from the surface and the mole fraction of CO in the atmosphere is qCO=10(+10/-5) ppm, significantly lower than previous estimates for tropospheric CO. The albedo of the reflecting layer is approximately 0.07(+0.02/-0.01) in the 5 micrometers continuum outside the CO band. The 5 micrometers albedo is consistent with a surface of mixed ice and silicates similar to the icy Galilean satellites. Organic solids formed in simulated Titan conditions can also produce similar albedos at 5 micrometers.     

Removal of topographic effects from lunar images using Kaguya (LALT) and Earth-based observations

Lunar images acquired at non-zero phase angles show brightness variations caused by both albedo heterogeneities and local topographic slopes of the surface. To distinguish between these two factors, altimetry measurements or photoclinometry data can be used. The distinction is especially important for imagery of phase-function parameters of the Moon. The imagery is a new tool that can be used to study structural anomalies of the lunar surface. To illustrate the removal of the topographic effects from photometric images, we used Earth-based telescopic observations, altimetry measurements carried out with the Kaguya (JAXA) LALT instrument, and a new photoclinometry technique that includes analysis of several images of the same scenes acquired at different phase angles. Using this technique we have mapped the longitudinal component of lunar topography slopes (the component measured along the lines of constant latitude). We have found good correlations when comparing our map with the corresponding data from Kaguya altimetry. The removal of the topographic surface properties allows for the study of the phase-function parameters of the lunar surface, not only for flat mare regions, but for highlands as well.     

Electrical properties of Titan's surface from Cassini RADAR scatterometer measurements

We report regional-scale low-resolution backscatter images of Titan's surface acquired by the Cassini RADAR scatterometer at a wavelength of 2.18-cm. We find that the average angular dependence of the backscatter from large regions and from specific surface features is consistent with a model composed of a quasi-specular Hagfors term plus a diffuse cosine component. A Gaussian quasi-specular term also fits the data, but less well than the Hagfors term. We derive values for the mean dielectric constant and root-mean-square (rms) slope of the surface from the quasi-specular term, which we ascribe to scattering from the surface interface only. The diffuse term accommodates contributions from volume scattering, multiple scattering, or wavelength-scale near-surface structure. The Hagfors model results imply a surface with regional mean dielectric constants between 1.9 and 3.6 and regional surface roughness that varies between 5.3° and 13.4° in rms-slope. Dielectric constants between 2 and 3 are expected for a surface composed of solid simple hydrocarbons, water ice, or a mixture of both. Smaller dielectric constants, between 1.6 and 1.9, are consistent with liquid hydrocarbons, while larger dielectric constants, near 4.5, may indicate the presence of water-ammonia ice [Lorenz, R.D., 1998. Icarus 136, 344-348] or organic heteropolymers [Thompson, W.R., Squyres, S.W., 1990. Icarus 86, 336-354]. We present backscatter images corrected for angular effects using the model residuals, which show strong features that correspond roughly to those in 0.94-μm ISS images. We model the localized backscatter from specific features to estimate dielectric constant and rms slope when the angular coverage is within the quasi-specular part of the backscatter curve. Only two apparent surface features are scanned with angular coverage sufficient for accurate modeling. Data from the bright albedo feature Quivira suggests a dielectric constant near 2.8 and rms slope near 10.1°. The dark albedo feature Shangri-La is best fit by a Hagfors model with a dielectric constant close to 2.4 and an rms slope near 9.5°. From the modeled backscatter curves, we find the average radar albedo in the same linear (SL) polarization to be near 0.34. We constrain the total-power albedo in order to compare the measurements with available groundbased radar results, which are typically obtained in both senses of circular polarization. We estimate an upper limit of 0.4 on the total-power albedo, a value that is significantly higher than the 0.21 total albedo value measured at 13 cm [Campbell, D., Black, G., Carter, L., Ostro, S., 2003. Science 302, 431-434]. This is consistent with a surface that has more small-scale structure and is thus more reflective at 2-cm than 13-cm. We compare results across overlapping observations and observe that the reduction and analysis are repeatable and consistent. We also confirm the strong correlations between radar and near-infrared images.     

Voyager disk resolved photometry of the Saturnian satellites

Photometric analysis of Voyager images of the medium-sized icy satellites of Saturn shows that their surfaces exhibit a wide range of scattering properties. At low phase angles, Rhea and Dione closely follow lunar behavior with almost no limb darkening. Mimas, Tethys, and especially Enceladus shiw significant limb darkening at low phase angles, which suggests multiple scattering is important for their surfaces. A simple photometric function of the form I/F = f(α)Aμ₀/(μ + μ₀) + (1 ? A)μ₀ has been fit to the observations. For normal reflectances <0.6, we find lunar-like scattering properties (A = 1). No satellite's surface can be described by Lambert's Law (A = 0). Dione exhibits the widest albedo variations (about 50%). A longitudinal dark stripe which represents a 15% decrease in albedo is situated near the center of the trailing side of Tethys. A correlation is found between the albedo and color of the satellites: the darker objects are redder. Similarly, darker areas of each satellite are redder. Spectral reflectances of Mimas and Enceladus can be derived for the first time. After the proper calibrations to the Voyager color images are made, it is found that both satellites have remarkably flat spectra into the ultraviolet.     

Infrared (0.83-5.1 μm) photometry of Phoebe from the Cassini Visual Infrared Mapping Spectrometer

Three weeks prior to the commencement of Cassini's 4 year tour of the saturnian system, the spacecraft executed a close flyby of the outer satellite Phoebe. The infrared channel of the Visual Infrared Mapping Spectrometer (VIMS) obtained images of reflected light over the 0.83-5.1 μm spectral range with an average spectral resolution of 16.5 nm, spatial resolution up to 2 km, and over a range of solar phase angles not observed before. These images have been analyzed to derive fundamental photometric parameters including the phase curve and phase integral, spectral geometric albedo, bolometric Bond albedo, and the single scattering albedo. Physical properties of the surface, including macroscopic roughness and the single particle phase function, have also been characterized. Maps of normal reflectance show the existence of two major albedo regimes in the infrared, with gradations between the two regimes and much terrain with substantially higher albedos. The phase integral of Phoebe is 0.29±0.03, with no significant wavelength dependence. The bolometric Bond albedo is 0.023±007. We find that the surface of Phoebe is rough, with a mean slope angle of 33°. The satellite's surface has a substantial forward scattering component, suggesting that its surface is dusty, perhaps from a history of outgassing. The spectrum of Phoebe is best matched by a composition including water ice, amorphous carbon, iron-bearing minerals, carbon dioxide, and Triton tholin. The characteristics of Phoebe suggest that it originated outside the saturnian system, perhaps in the Kuiper Belt, and was captured on its journey inward, as suggested by Johnson and Lunine (2005).     

Marsshine on Phobos

The Viking Orbiters have obtained several images of Phobos at large phase angles in which the portion of the satellite not directly illuminated by the Sun is faintly visible. A photometric analysis of one such image is presented to prove that the phenomenon is real and can be explained by Marsshine (i.e., the illumination of Phobos by sunlight reflected from Mars). Such images provide cross sections of Phobos and are useful in determining the true shape and size of the satellite. The cross section observed in Picture 111A03 agrees closely with that predicted by triaxial ellipsoid model of Phobos developed by Duxbury (1974).     

Mass-Wasting Processes on the Surface of Phobos

This paper considers morphologic signatures of mass-wasting processes on the surface of Phobos. Two types of downslope movement of material are distinguished: (i) intracrater volume landslides inside impact craters and (ii) downslope near-surface movement of material. Crater statistics for the Stickney area (based on new images of Phobos) showed that the landslide in the crater Stickney could have been formed after resurfacing of the outer rim of the crater in the process of meteorite bombardment. An estimate of the volume of the landslide in Stickney (1–2 km³) and simulation of its movement allowed us to classify the landslide as a long-runout one. The possibility of forming a hummocky topographic relief to the east of Stickney due to the crater ejecta and the emplacement of the frontal part of the long-runout landslide is discussed.     

The nucleus of Comet Borrelly: a study of morphology and surface brightness

Stereo images obtained during the DS1 flyby were analyzed to derive a topographic model for the nucleus of Comet 19P/Borrelly for morphologic and photometric studies. The elongated nucleus has an overall concave shape, resembling a peanut, with the lower end tilted towards the camera. The bimodal character of surface-slopes and curvatures support the idea that the nucleus is a gravitational aggregate, consisting of two fragments in contact. Our photometric modeling suggests that topographic shading effects on Borrelly's surface are very minor (<10%) at the given resolution of the terrain model. Instead, albedo effects are thought to dominate Borrelly's large variations in surface brightness. With 90% of the visible surface having single scattering albedos between 0.008 and 0.024, Borrelly is confirmed to be among the darkest of the known Solar System objects. Photometrically corrected images emphasize that the nucleus has distinct, contiguous terrains covered with either bright or dark, smooth or mottled materials. Also, mapping of the changes in surface brightness with phase angle suggests that terrain roughness at subpixel scale is not uniform over the nucleus. High surface roughness is noted in particular near the transition between the upper and lower end of the nucleus, as well as near the presumed source region of Borrelly's main jets. Borrelly's surface is complex and characterized by distinct types of materials that have different compositional and/or physical properties.     

Surface features of Phobos and Deimos

Viking Orbiter images have provided nearly complete coverage of the two satellites of Mars and have been used to construct maps of the surface features of Phobos and Deimos. The satellites have radically different appearances although nearly all features on both objects were formed directly or indirectly by impact cratering. Phobos has an extensive network of linear depressions (grooves) that probably were formed indirectly by the largest impact recorded on Phobos. Deimos lacks grooves as well as the large number of ridges that occur on Phobos. Craters on Deimos have substantial sediment fill; those on Phobos have none. Evidence of downslope movement of debris is prominent on Deimos but is rare on Phobos. Many of the differences between Phobos and Deimos may be caused by modest differences in mechanical properties. However, the lack of a very large crater on Deimos may be responsible for its lack of grooves.     

A far-ultraviolet photometer for planetary surface analysis

The measurement of local variations in the far-ultraviolet albedo is explored as a means of detecting changes in the refractive index of rocks and dust on the surface of atmosphereless planets and satellites. Far-ultraviolet spectrophotometric measurements of the lunar surface which were obtained on the Apollo 17 orbital mission are presented to demonstrate that significant albedo variations occur in the spectral range 120 to 170 nm. These data also confirm the hypothesis that the albedo variations represent refractive index differences in the surface materials. A three-band photometer is described which, when put in orbit around a solar system object, is capable of providing refractive index maps with a sensitivity of 1 part in the second decimal place and with kilometer resolution. Comparative surface composition and surface history analyses based on such maps are discussed.Alfred P. Sloan Research Fellow.