Micrometer-sized ice particles for planetary-science experiments – II. Bidirectional reflectance

We have measured the bidirectional reflectance of spherical micrometer-sized water-ice particles in the visible spectral range over a wide range of incidence and emission angles. The small ice spheres were produced by spraying fine water droplets directly into liquid nitrogen. The resulting mean particle radii are 1.47 + 0.96 - 0.58 μm. Such a material shares many properties with ice in comets and at the surface of icy satellites. Measurements show that the fresh sample material is highly backscattering, contrasting with natural terrestrial snow and frost. The formation of agglomerates of particles during the sample production results in a noticeable variability of the photometric properties of the samples in their initial state. We have also observed significant temporal evolutions of the scattering behavior of the samples, shifting towards more forward scattering within some tens of hours, resulting most likely from sintering processes. All reflectance data are fitted by the Hapke photometric model (1993 and 2002 formulation) with a one/two/three-parameter Henyey-Greenstein phase function and the resulting Hapke parameters are provided. These parameters can be used to compare laboratory results with the observed photometric behaviors of astronomical objects. We show, in particular, that the optical properties of the fresh micrometer-sized ice samples can be used to reproduce the predominant backscattering in the phase curves of Enceladus and Europa.

Laboratory observations and simulations of phase reddening

The visible reflectance spectrum of many Solar System bodies changes with changing viewing geometry for reasons not fully understood. It is often observed to redden (increasing spectral slope) with increasing solar phase angle, an effect known as phase reddening. Only once, in an observation of the martian surface by the Viking 1 lander, was reddening observed up to a certain phase angle with bluing beyond, making the reflectance ratio as a function of phase angle shaped like an arch. However, in laboratory experiments this arch-shape is frequently encountered. To investigate this, we measured the bidirectional reflectance of particulate samples of several common rock types in the 400–1000 nm wavelength range and performed ray-tracing simulations. We confirm the occurrence of the arch for surfaces that are forward scattering, i.e. are composed of semi-transparent particles and are smooth on the scale of the particles, and for which the reflectance increases from the lower to the higher wavelength in the reflectance ratio. The arch shape is reproduced by the simulations, which assume a smooth surface. However, surface roughness on the scale of the particles, such as the Hapke and van Horn (Hapke, B., van Horn, H. [1963]. J. Geophys. Res. 68, 4545–4570) fairy castles that can spontaneously form when sprinkling a fine powder, leads to monotonic reddening. A further consequence of this form of microscopic roughness (being indistinct without the use of a microscope) is a flattening of the disk function at visible wavelengths, i.e. Lommel–Seeliger-type scattering. The experiments further reveal monotonic reddening for reflectance ratios at near-IR wavelengths. The simulations fail to reproduce this particular reddening, and we suspect that it results from roughness on the surface of the particles. Given that the regolith of atmosphereless Solar System bodies is composed of small particles, our results indicate that the prevalence of monotonic reddening and Lommel–Seeliger-type scattering for these bodies results from microscopic roughness, both in the form of structures built by the particles and roughness on the surface of the particles themselves. It follows from the singular Viking 1 observation that the surface in front of the lander was composed of semi-transparent particles, and was smooth on the scale of the particle size.

VIS-NIR reflectance of water ice/regolith analogue mixtures and implications for the detectability of ice mixed within planetary regoliths

Permanently shadowed regions at the poles of the Moon and Mercury have been pointed out as candidates for hosting water ice at their surface. We have measured in the laboratory the visible and near infrared spectral range (VIS-NIR) bidirectional reflectance of intimate mixtures of water ice and the JSC-1AF lunar simulant for different ice concentrations, particle sizes, and measurement geometries. The nonlinearity between the measured reflectance and the amount of ice in the mixture can be reproduced to some extent by the mixing formulas of standard reflectance models, in particular, those of Hapke and Hiroi, which are tested here. Estimating ice concentrations from reflectance data without knowledge of the mixing coefficientsstrongly dependent on the size/shape of the grainscan result in large errors. According to our results, it is possible that considerable amounts of water ice might be intimately mixed in the regolith of the Moon and Mercury without producing noticeable photometric signatures.

Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

Proton entry into the near-lunar plasma wake for magnetic field aligned flow

We report the first observation of protons in the near-lunar (100-200 km from the surface) and deeper (near anti-subsolar point) plasma wake when the interplanetary magnetic field (IMF) and solar wind velocity (vsw) are parallel (aligned flow; angle between IMF and vsw≤10°). More than 98% of the observations during aligned flow condition showed the presence of protons in the wake. These observations are obtained by the Solar Wind Monitor sensor of the Sub-keV Atom Reflecting Analyser experiment on Chandrayaan-1. The observation cannot be explained by the conventional fluid models for aligned flow. Back tracing of the observed protons suggests that their source is the solar wind. The larger gyroradii of the wake protons compared to that of solar wind suggest that they were part of the tail of the solar wind velocity distribution function. Such protons could enter the wake due to their large gyroradii even when the flow is aligned to IMF. However, the wake boundary electric field may also play a role in the entry of the protons into the wake.

Interactive Diffraction from Biological Nanostructures

We describe a technique for interactive rendering of diffraction effects produced by biological nanostructures such as snake skin surface gratings. Our approach uses imagery from atomic force microscopy that accurately captures the nanostructures responsible for structural coloration, that is, coloration due to wave interference, in a variety of animals. We develop a rendering technique that constructs bidirectional reflection distribution functions (BRDFs) directly from the measured data and leverages precomputation to achieve interactive performance. We demonstrate results of our approach using various shapes of the surface grating nanostructures. Finally, we evaluate the accuracy of our precomputation-based technique and compare to a reference BRDF construction technique.

Photometric properties of Mars soils analogs

We have measured the bidirectional reflectance of analogs of dry, wet, and frozen Martian soils over a wide range of phase angles in the visible spectral range. All samples were produced from two geologic samples: the standard JSC Mars-1 soil simulant and Hawaiian basaltic sand. In a first step, experiments were conducted with the dry samples to investigate the effects of surface texture. Comparisons with results independently obtained by different teams with similar samples showed a satisfying reproducibility of the photometric measurements as well as a noticeable influence of surface textures resulting from different sample preparation procedures. In a second step, water was introduced to produce wet and frozen samples and their photometry investigated. Optical microscope images of the samples provided information about their microtexture. Liquid water, even in relatively low amount, resulted in the disappearance of the backscattering peak and the appearance of a forward-scattering peak whose intensity increases with the amount of water. Specular reflections only appeared when water was present in an amount large enough to allow water to form a film at the surface of the sample. Icy samples showed a wide variability of photometric properties depending on the physical properties of the water ice. We discuss the implications of these measurements in terms of the expected photometric behavior of the Martian surface, from equatorial to circum-polar regions. In particular, we propose some simple photometric criteria to improve the identification of wet and/or icy soils from multiple observations under different geometries.

Interactive Diffraction from Biological Nanostructures

We describe a technique for interactive rendering of diffraction effects produced by biological nanostructures, such as snake skin surface gratings. Our approach uses imagery from atomic force microscopy that accurately captures the geometry of the nanostructures responsible for structural colouration, that is, colouration due to wave interference, in a variety of animals. We develop a rendering technique that constructs bidirectional reflection distribution functions (BRDFs) directly from the measured data and leverages pre-computation to achieve interactive performance. We demonstrate results of our approach using various shapes of the surface grating nanostructures. Finally, we evaluate the accuracy of our pre-computation-based technique and compare to a reference BRDF construction technique.

Backscattered energetic neutral atoms from the Moon in the Earth's plasma sheet observed by Chandarayaan-1/Sub-keV Atom Reflecting Analyzer instrument

We present the observations of energetic neutral atoms (ENAs) produced at the lunar surface in the Earth's magnetotail. When the Moon was located in the terrestrial plasma sheet, Chandrayaan-1 Energetic Neutrals Analyzer (CENA) detected hydrogen ENAs from the Moon. Analysis of the data from CENA together with the Solar Wind Monitor (SWIM) onboard Chandrayaan-1 reveals the characteristic energy of the observed ENA energy spectrum (the e-folding energy of the distribution function) ∼100 eV and the ENA backscattering ratio (defined as the ratio of upward ENA flux to downward proton flux) <∼0.1. These characteristics are similar to those of the backscattered ENAs in the solar wind, suggesting that CENA detected plasma sheet particles backscattered as ENAs from the lunar surface. The observed ENA backscattering ratio in the plasma sheet exhibits no significant difference in the Southern Hemisphere, where a large and strong magnetized region exists, compared with that in the Northern Hemisphere. This is contrary to the CENA observations in the solar wind, when the backscattering ratio drops by ∼50% in the Southern Hemisphere. Our analysis and test particle simulations suggest that magnetic shielding of the lunar surface in the plasma sheet is less effective than in the solar wind due to the broad velocity distributions of the plasma sheet protons.

Measurement of the production of a W boson in association with a charm quark in pp collisions at sqrts = 7 TeV with the ATLAS detector

The production of a W boson in association with a single charm quark is studied using 4.6 fb−1 of pp collision data at ps = 7TeV collected with the ATLAS detector at the Large Hadron Collider. In events in which a W boson decays to an electron or muon, the charm quark is tagged either by its semileptonic decay to a muon or by the presence of a charmed meson. The integrated and differential cross sections as a function of the pseudorapidity of the lepton from the W-boson decay are measured. Results are compared to the predictions of next-to-leading-order QCD calculations obtained from various parton distribution function parameterisations. The ratio of the strange-to-down sea-quark distributions is determined to be 0.96+0.26−0.30 at Q2 = 1.9 GeV2, which supports the hypothesis of an SU(3)-symmetric composition of the light-quark sea. Additionally, the cross-section ratio ơ(W++c)/ơ(W−+c) is compared to the predictions obtained using parton distribution function parameterisations with different assumptions about the s–s quark asymmetry.

Bounding Standard Gaussian Tail Probabilities

We review various inequalities for Mills' ratio (1 - Φ)= Ø, where Ø and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.