Quasi-specular Reflection Research Articles

Benchmarking of the NCrystal SANS Plugin for Nanodiamonds

Nanodiamonds have attracted attention in recent years for their exceptional albedo of slow neutrons. Several theoretical models have been proposed to compute the total elastic cross section. However, these models neglect the relatively complex internal structure and chemical composition of the diamond nanoparticles, relying often on the monodisperse structureless spheres approximation. In this work, we explore the possibility of adding the small-angle neutron scattering (SANS) process for nanodiamonds to NCrystal, a library that enables calculations for Monte Carlo simulations of neutrons in polycrystalline materials and powders. This approach aims to describe the scattering process also at neutron wavelengths below the diamond Bragg cutoff where simple models usually struggle. The extension relies on modeling the SANS process through the fitting of experimental data as well as theoretical inputs. The code can then be coupled with an existing simulation framework, such as McStas, and benchmarked in different setups. We tested the plugin for two properties of diamond powder nanoparticles: the backward reflection of very cold neutrons and the quasispecular reflections of cold neutrons. The validation of this simulation tool is intended to pave the way for the design of the beam extraction system for a future high-intensity cold neutron moderator at the European Spallation Source.

Effect of Nanodiamond Sizes on the Efficiency of the Quasi-Specular Reflection of Cold Neutrons.

Nanomaterials can intensively scatter and/or reflect radiation. Such processes and materials are of theoretical and practical interest. Here, we study the quasi-specular reflections (QSRs) of cold neutrons (CNs) and the reflections of very cold neutrons (VCNs) from nanodiamond (ND) powders. The fluorination of ND increased its efficiency by removing/replacing hydrogen, which is otherwise the dominant cause of neutron loss due to incoherent scattering. The probability of the diffuse reflection of VCNs increased for certain neutron wavelengths by using appropriate ND sizes. Based on model concepts of the interaction of CNs with ND, and in reference to our previous work, we assume that the angular distribution of quasi-specularly reflected CNs is narrower, and that the probability of QSRs of longer wavelength neutrons increases if we increase the characteristic sizes of NDs compared to standard detonation nanodiamonds (DNDs). However, the probability of QSRs of CNs with wavelengths below the cutoff of ~4.12 Å decreases due to diffraction scattering on the ND crystal lattice. We experimentally compared the QSRs of CNs from ~4.3 nm and ~15.0 nm ND. Our qualitative conclusions and numerical estimates can help optimize the parameters of ND for specific practical applications based on the QSRs of CNs.

New Ku-Band Geophysical Model Function and Wind Speed Retrieval Algorithm Developed for Tiangong-2 Interferometric Imaging Radar Altimeter

A Ku-band geophysical model function for wind speed retrieval named as KuLMOD-H is proposed based on the quasi-specular reflection model for the Chinese Tiangong-2 Interferometric Imaging Radar Altimeter (TG2-InIRA), which can be used to retrieve the wind speed with 2 km resolution. The model is derived by expanding the effective nadir reflection coefficient term and the mean square slope term in the quasi-specular reflection model using quadratic polynomials with wind speed as variable. The model coefficients are obtained by fitting the radar backscattering coefficient data from TG2-InIRA to the collocated sea surface wind speed data from European Center for Medium-Range Weather Forecasts (ECMWF). For solving the problem of potential ambiguous solutions when the incidence angles are relatively large, a regularization approach is further proposed. The retrieved wind speed results have a root-mean-square error (RMSE) of 1.42 m/s compared with the collocated ECMWF wind speed data and at the same time, they are highly consistent with the buoy data. Different from the previous works on TG2-InIRA wind speed retrieval, this article derives a semiphysical model suitable for incidence angles from 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> to 8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> , by which better retrieval results are achieved. This work not only explores the wind speed retrieval capability of the instrument under low incidence-angle observation, but also provides high-resolution wind speed data for further correction of sea state bias for TG2-InIRA sea surface height measurements.

Decorrelation of the Near-Specular Land Scattering in Bistatic Radar Systems

Signal fluctuations at the receiving antenna have been studied from decades by the radar community, especially to understand the decorrelation of the scattering in radar interferometry. This was done assuming uncorrelated point-like scatterers, leading to a simple model for the geometric decorrelation. In this case, the scattering is certainly incoherent. The quasi-specular reflections gathered under the illumination of signals of opportunity can exhibit significant temporal fluctuations. They are related to the statistical features of the surface roughness and can be observed even in almost flat regions, where a predominant coherent reflection could be expected. The presence of gentle undulations, however, i.e., those showed by surfaces having variations of the profiles comparable with the wavelength over the vertical scale, but much longer over the horizontal one, can determine transition regions where the scattering is neither coherent nor completely incoherent. In these conditions, the nature of the fluctuations of the scattering is not well understood and it requires additional studies. A discussion about the dominance of coherent or incoherent reflection in the Global Navigation Satellite System Reflectometry (GNSS-R) community is presently ongoing. To describe the nature of the scattering, and to understand the decorrelation of the near-specular components in GNSS-R, we propose a numerical study of the field collected by a moving airborne receiver based on the Kirchhoff approximation. Our study demonstrates that the near-specular scattering collected over representative natural landscapes by a GNSS-R receiver is partially coherent and essentially incoherent in most cases. Its correlation time is a function of the roughness parameters, namely standard deviation and correlation length, as well as of the system parameters (i.e., spatial resolution and height). The analysis can provide useful information for the interpretation of GNSS data, which present intrinsic variability that can significantly affect the retrieval of the relevant bio-geophysical parameters.

Understanding Ku-Band Ocean Radar Backscatter at Low Incidence Angles under Weak to Severe Wind Conditions by Comparison of Measurements and Models

The rain-free normalized radar cross-section (NRCS) measurements from the Ku-band precipitation radars (PRs) aboard the tropical rainfall measuring mission (TRMM) and the global precipitation measurement (GPM) mission, along with simultaneous sea surface wind truth from buoy observations, stepped-frequency microwave radiometer (SFMR) measurements, and H*Wind analyses, are used to investigate the abilities of the quasi-specular scattering models, i.e., the physical optics model (PO) and the classical and improved geometrical optics models (GO and GO4), to reproduce the Ku-band NRCS at low incidence angles of 0–18° over the wind speed range of 0–45 m/s. On this basis, the limitations of the quasi-specular scattering theory and the effects of wave breaking are discussed. The results show that the return caused by quasi-specular reflection is affected significantly by the presence of background swell waves at low winds. At moderate wind speeds of 5–15 m/s, the NRCS is still dominated by the quasi-specular reflection, and the wave breaking starts to work but its contribution is very small, thus, the models are found in excellent agreement with the measurements. With wind speed increasing, the impact of wave breaking increases, whereas the role of standard quasi-specular reflection decreases. The wave breaking impact on NRCS is first visible at incidence angles near 18° as wind speed exceeds about 20 m/s, then it becomes dominant when wind speed exceeds about 37 m/s where the NRCS is insensitive to wind speed and depends linearly on incidence angle, which cannot be explained by the standard quasi-specular scattering theory.

Implementation of Neutron Reflection with Nano-Dispersed Media in Geant4

A study has been carried out in order to see the feasibility of using nanodiamond particles as a reflector for cold and very cold neutrons in Geant4. Nanodiamond particles have a large scattering angle probability against very cold neutrons compared to the other materials due their high optical potential. This unique feature makes this powder a prominent candidate to be used as a reflector for very cold neutrons. Moreover, they can also be implemented for quasi-specular reflection of cold neutrons at small incidence angles due to multiple small-angle scattering of neutrons from nano-sized inhomogeneities in the scattering potential. A new process in Geant4 has been prepared in order to add cross sections of nanodiamond particles to the predefined processes. The geometry of previous experiments carried out in order to observe the reflection of nanodiamond particles has been developed in Geant4 in order to validate the implementation. The results show that there is a good agreement between the new method implemented in Geant4 and experimental data.

Firn Clutter Constraints on the Design and Performance of Orbital Radar Ice Sounders

Radar sounding is a powerful tool for constraining subglacial conditions, which influence the mass balance of polar ice sheets and their contributions to global sea-level rise. A satellite-based radar sounder, such as those successfully demonstrated at Mars, would offer unprecedented spatial and temporal coverage of the subsurface. However, airborne sounding studies suggest that poorly constrained radar scattering in polar firn may produce performance-limiting clutter for terrestrial orbital sounders. We develop glaciologically constrained electromagnetic models of radar interactions in firn, test them against in situ data and multifrequency airborne radar observations, and apply the only model we find to be consistent with observation to assess the implications of firn clutter for orbital sounder system design. Our results show that in the very high-frequency (VHF) and ultrahigh-frequency (UHF) bands, radar interactions in the firn are dominated by quasi-specular reflections at the interfaces between layers of different densities and that off-nadir backscatter is likely the result of small-scale roughness in the subsurface density profiles. As a result, high frequency (HF) or low VHF center frequencies offer a significant advantage in near-surface clutter suppression compared to the UHF band. However, the noise power is the dominant constraint in all bands, so the near-surface clutter primarily constrains the extent to which the transmit power, pulselength, or antenna gain can be engineered to improve the signal-to-noise ratio. Our analysis suggests that the deep interior of terrestrial ice sheets is a difficult target for orbital sounding, which may require optimizations in azimuth processing and cross-track clutter suppression which complement existing requirements for sounding at the margins.

A Multitechnique Study of Fluorinated Nanodiamonds for Low-Energy Neutron Physics Applications

Data of quasi-specular reflection of cold neutrons, prompt-γ neutron analysis, X-ray Raman scattering (XRS), and neutron pair distribution function (PDF) analysis with powder of detonation nanodiamonds are analyzed to collect their structural properties and chemical composition. Both as-synthesized and purified samples were studied using fluorination samples. Removal of both the sp2 amorphous carbon shell and the hydrogen atoms is evidenced respectively by the change of neutron-nuclei optical potentials of nanoparticles and the increase of their neutron reflectivity. Moreover, sp3 diamond cores of nanoparticles stay intact during the fluorination as revealed by similar scattering patterns, PDF, and XRS data. Quasi-specular reflection, PDF, and XRS data are complementary for the study of nanomaterials and in good agreement with conventional characterization techniques (infrared spectroscopy and solid-state NMR).

Improved success rates of rendezvous maneuvers using aerodynamic forces

Several small, unconnected satellites flying in formation are a frequently discussed option to replace large satellites due to advantages such as increased flexibility, reduced costs and enhanced reliability. Using differential aerodynamic forces as a means to maintain the formation despite present perturbations, to perform formation reconfiguration or to initiate a rendezvous maneuver is a promising propellant-less alternative to chemical and/or electric propulsion systems. Subjected to uncertainties, dynamic variations and non-linearities its implementation in a real mission is, however, challenging. A common practice to either design suitable reference trajectories for robust control strategies or to gain deeper insights into the methodology is to use linearized relative motion models and a constant density assumption. Following this practice, multiple previous studies developed and enhanced analytic control algorithms to zero out the relative position and velocity of two spacecraft utilizing differential aerodynamic forces. Even though aerodynamic lift expands the controllability to all three translational degrees of freedom, it has been frequently neglected due to the low lift coefficients experienced in orbit so far. And even if considered, analysis has shown that the feasibility range of using the differential lift for the eccentricity control of the in-plane motion is extremely limited compared to using differential drag. However, two different possible options, namely applying enhanced algorithms to decrease the eccentricity before even initializing the eccentricity control phase as well as using advanced satellite surface materials targeting specular or quasi-specular reflection and thereby increasing the differential acceleration forces, have been suggested to increase the feasibility domain of the methodology. In this article, the effectiveness of the proposed adjustments is analyzed in a Monte-Carlo approach by applying them to the analytic control algorithms introduced in the literature. Since these are based on the linearized Schweighart-Sedwick equations, so is the presented analysis. Moreover, additional modifications to the algorithms are made to reduce the maneuver time of one of the respective control phases. The results show that the analyzed options noticeably improve the success rates of the maneuvers. Especially the feasibility range of the lift-based control algorithms is enlarged considerably. In addition, the implemented modifications are shown to consistently reduce the maneuver time of the respective control phase. Consequently, the presented analysis improves the current state of the art of the analytically designed rendezvous trajectories and provides valuable new insights into the methodology of using differential aerodynamic forces as a means of relative motion control.

Directional reflection of cold neutrons using nanodiamond particles for compact neutron sources

Nanodiamond Particles (NDP) are new candidates for neutron reflection. They have a large scattering and low absorption cross-sections for low-energy neutrons. Very Cold Neutrons (VCN) are reflected from NDP with large scattering angles while Cold Neutrons (CN) have a quasi-specular reflection at small incident angles. A new scattering process has been added in Geant4 in order to examine the directional reflection of CN in an extraction beam made of NDP layer. Impurities in NDP are responsible for the up-scattered neutrons, especially hydrogen which has a large cross-section. Other impurities are also considered in Geant4 in order to produce a more accurate model for NDP scattering. The new scattering process is used to model a possible configuration of target-moderator-reflector in Compact Neutron Sources (CNS). A 13 MeV proton beam striking a beryllium target is chosen. Parahydrogen is placed as a cold moderator in order to produce CN. NDP are placed around the extraction beam for scattering the CN toward the exit of the beam. The results show that CN exiting the extraction beam can be increased thanks to the implemented NDP layer.

Influence of energy accommodation on a robust spacecraft rendezvous maneuver using differential aerodynamic forces

Differential aerodynamic forces are a promising propellant-less option to control satellite formation flight. To this day, satellite lift is the most frequently neglected and, as a consequence, the methodology of differential lift only poorly studied. This is because the adsorption of atomic oxygen on the satellite’s surfaces in Very Low Earth Orbit induces diffuse reflection and high levels of energy accommodation, both of which results in the low lift coefficients experienced in-orbit so far. Analysis has shown that surface materials which promote specular or quasi-specular reflections are able to strongly increase the magnitude of the available differential lift forces. An influence of advanced surface materials on respective maneuver sequences, however, has not yet been analyzed at all. In addition, the robustness of the differential lift-based controller proposed up to now is questionable and not able to cope with the occurring uncertainties and dynamic variations. This paper aims to address these two research gaps. To do so, a robust control approach based on Lyapunov principles developed by Perez and Bevilacqua for the differential drag-based control of the in-plane relative motion is used in a subsequent second control phase to control the out-of-plane relative motion via differential lift. In a successive second step, the influence of different levels of energy accommodation on the full rendezvous maneuver sequence is analyzed. The results show that even a modest reduction in energy accommodation strongly reduces the maneuver times as well as the resulting orbital decay. In all analyzed cases, the proposed control approach led to a successful rendezvous.

Determining Higher-Order Cumulants of Sea-Surface Slopes by Quasi-Vertical Radio Sounding Data

This paper analyzes the possibilities and constraints in determining the skewness and kurtosis of slopes by radio sounding data at angles at which the backscattered signal is determined by quasi-specular reflection. It is shown that direct recovery of skewness and kurtosis based on the dependence of the normalized backscattering cross section on the incidence angle leads to significant errors. The determination of these parameters by minimizing the discrepancies between the empirical probability density and the truncated Gram—Charlier series given a priori depends significantly on the choice of this model.

The Algorithm for Retrieving the Surface Waves Parameters Using Doppler Spectrum Measurements at Small Incident Angles

In this paper, we present an algorithm for retrieving all the second statistical moments of the sea surface that affect the scattering of waves at small angles of incidence. A feature of this algorithm is the analysis of the spectral characteristics of the reflected waves only, without taking into account the backscattering cross section. The analysis of the width and the shift of the Doppler spectrum (DS) allows us to use the obtained algorithm without the preliminary instrumental calibration, which is necessary for the backscattering cross section. We give final expressions for calculating the width and the shift of the DS in the monostatic problem statement for small angles of incidence. We obtain the expressions within the framework of the Kirchhoff approximation, which makes them reliable only in the quasi-specular reflection region. Features of these formulas are the description of the surface by five statistical moments of the second order and taking into account the anisotropic antenna pattern (AP). To solve the inverse problem of retrieving sea surface parameters, we propose a measurement scheme including three motionless transceiver antennas with different APs. For this measurement scheme, we give analytical expressions for all five unknown parameters of surface waves. Also, we give a theoretical analysis of the accuracy of the algorithm obtained for different wind speeds and wind directions. All the results are valid for the scattering of both acoustic and electromagnetic waves.

Effect of nanodiamond fluorination on the efficiency of quasispecular reflection of cold neutrons

Nanomaterials, which show large reflectivity for external radiation, are of general interest in science and technology. We report a result from our ongoing research on the reflection of low-energy neutrons from powders of detonation diamond nanoparticles. Our previous work showed a large probability for quasispecular reflection of neutrons from this medium. The model of neutron scattering from nanoparticles, which we have developed, suggests two ways to increase the quasispecular reflection probability: (1) the reduction of incoherent scattering by substitution of hydrogen with fluorine inside the nanoparticles, and (2) the sharpening of the neutron optical potential step by removal of amorphous $s{p}^{2}$ carbon from the nanoparticle shells. We present experimental results on scattering of slow neutrons from both raw and fluorinated diamond nanoparticles with amorphous $s{p}^{2}$ carbon removed by gas-solid fluorination. These results show a clear increase in quasispecular reflection probability.

Reflection of Slow Neutrons from Nanorod Powder

The possibility of increasing the effectiveness of nanostructural reflectors by replacing spherical nanoparticles with nanorods is examined. It is shown that the albedo of very cold neutrons from disordered nanorods is lower than from nanospheres of the same diameter. However, the albedo of very cold neutrons and quasispecular reflection of cold neutrons from long nanorods oriented parallel to its surface are higher than the corresponding values for a reflector comprised of nanospheres of the same diameter.

Ray tracing as a supportive tool for interpretation of FBRM signals from spherical particles

Focused beam reflectance measurement (FBRM) is a versatile and frequently used method for in-process particle sizing. The method works with a laser beam eccentrically rotating around a parallel axis, thus describing a circular path which randomly crosses the particles in front of the probe. Chord length distributions (CLDs) are calculated from the durations of the reflected light pulses, which can be related to the particle size. As the reflection signals are strongly biased by the particles' morphology and the optical properties of the particle surface, the obtained distribution profiles are often complex and do not allow direct conclusions on the true particle size. A number of models so far developed for interpretation of CLDs account for the particle shape but they pay little regard to reflective properties. The approach of this study is based on ray tracing, which means that the luminous flux to the particle surface and the light reflected back to the detector is calculated by tracking the individual light paths for several thousand surface elements per particle and iterating this procedure for a huge number of relative detector/particle positions. The model considers three different types of reflection, Lambertian reflection, quasi-specular reflection, and subsurface scattering, which can be combined as required to fit a measured chord length profile. For reasons of simplification the calculations in this study were restricted to spherical particles. The model was shown to be able to simulate the main characteristics of CLDs obtained from three types of monodisperse spheres having different light transmission and surface properties. This simulation helps to explain how the principal features of the complex profiles are co-determined by the three basic types of reflection mentioned above. The model provides a valuable tool particularly for applications in which not only the size of spherical particles but also structural changes with impact on optical properties are monitored by FBRM.

Aerodynamic Analysis Based on Challenging Minisatellite Payload Satellite Lift-to-Drag Measurements

A lift-to-drag ratio analysis is performed based on accelerometer measurements made by the Challenging Minisatellite Payload satellite to investigate the nature of gas-surface interactions taking place in orbit. The results described are for the November 2002 satellite yaw maneuver. At this time, the satellite flew at a mean altitude of 407 km. Two types of gas–surface interaction are considered in the analysis. The first is a cosine (fully diffuse) reflection model with incomplete energy accommodation. The second is a blended cosine reflection model having full accommodation combined with a fraction of quasi-specular reflection having an accommodation coefficient dependent on the surface material. It is found that the fully diffuse model best reproduces the satellite data during the yaw maneuver, and that the accommodation coefficient is approximately 0.89 during this time.

Quasi-specular reflection from particulate media

Specular reflection is known to play an important role in many fields of scattering applications, e.g., in remote sensing, computer graphics, optimization of visual appearance of industrial products. Usually it can be assumed that the object has a solid surface and that the properties of the surface will dictate the behavior of the specular component. In this study I will show that media consisting of wavelength-sized particles can also have a quasi-specular reflection in cases where there are ordered structure in the media. I will also show that the quasi-specular reflection in particulate media is more than just a surface effect, and planar particle arrangement below the very surface can give rise to quasi-specular reflection. This study shows that the quasi-specular reflection may contribute in some cases in the backscattering direction, together with coherent backscattering and shadow-hiding effects.

Radar backscattering from breaking wind waves: field observation and modelling

In this article, the results of a field study of the Ka-band (37.5 GHz) radar backscattering from breaking wind waves are presented. Radar and a video camera were simultaneously used to measure the radar cross section (RCS) of the whitecap zone and the characteristics of wave-breaking events. A comparison is made between absolute geometrical lengths, areas and orientations of the whitecaps and the RCS of the whitecaps at moderate (45°) and high (70°) incidence angles. A thin vegetable oil film covering the illuminated area was made to minimize background Bragg backscattering from the surface free of breaking-wave features. At high incidence angles, a linear-like dependence between breaking crest length and RCS and no significant azimuthal dependence are found. At moderate angles of incidence, a prominent azimuthal variation of the whitecap's RCS is shown, while a linear-like relationship between the active breaking area and the whitecap's RCS is obtained in presence of the film on the sea surface. The results are compared to the model of quasi-specular reflection from the breaking waves. It is shown that accounting for backscattering from the droplets produced by the breaking crest improves prediction of the whitecap's RCS given by this model at high incidence angles.

Quasi-specular reflection of cold neutrons from nano-dispersed media at above-critical angles

We have predicted and observed for the first time a new phenomenon of quasi-specular reflection of cold neutrons at small incidence angles from nano-dispersed media. this is due to multiple small-angle scattering of neutrons from nano-sized inhomogeneities in the scattering potential. The reflection angle as well as the half-width of angular distribution of diffusively reflected neutrons is approximately equal to the incidence angle. For the powder of diamond nanoparticles used, the reflection probability was equal to ∼30% within the detector angular size, which corresponds to 40–50% of total probability (albedo) of quasi-specular reflection. The tangential velocity component of incident neutrons was up to an order of magnitude larger than the critical velocity for pure diamond. We provide an example of potential application of the discovered phenomenon for increasing cold neutron fluxes available for experiments.