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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.

Soft protons are a potential threat for X-ray missions using grazing incidence optics, as once focused onto the detectors they can contribute to increase the background and possibly induce radiation damage as well. The assessment of these undesired effects is especially relevant for the future ESA X-ray mission Athena, due to its large collecting area. To prevent degradation of the instrumental performance, which ultimately could compromise some of the scientific goals of the mission, the adoption of ad-hoc magnetic diverters is envisaged. Dedicated laboratory measurements are fundamental to understand the mechanisms of proton forward scattering, validate the application of the existing physical models to the Athena case and support the design of the diverters. In this paper we report on scattering efficiency measurements of soft protons impinging at grazing incidence onto a Silicon Pore Optics sample, conducted in the framework of the EXACRAD project. Measurements were taken at two different energies, ~470 keV and ~170 keV, and at four different scattering angles between 0.6 deg and 1.2 deg. The results are generally consistent with previous measurements conducted on eROSITA mirror samples, and as expected the peak of the scattering efficiency is found around the angle of specular reflection., 16 pages, 11 figures; accepted for publication on Experimental Astronomy

The understanding of carrier transport in metal nanostructures is indispensable for the development of nanoelectronics. In particular, Pt nanostructures have been intensively studied to realize gas sensors based on adsorbate-induced surface electron scattering. Conventionally, electron scattering at the surface of metal nanostructures has been phenomenologically described by a single specularity parameter. In this work, surface electron scattering was quantitatively studied through molecular dynamics simulations, followed by density functional nonequilibrium Green’s function calculations. Although the extracted specularity parameters qualitatively agreed with empirically treated diffusive scattering at the O-covered Pt surface and specular scattering at the H-covered Pt surface, our atomistic calculation revealed an increase in resistivity owing to H adsorption on thin Pt(111) nanosheets.

In recent years, signal of opportunity reflectometry (SoOp-R) has become a promising remote sensing technique. This emerging technique employs the reflected signals from existing Global Navigation Satellite System (GNSS) or communication satellites to estimate geophysical parameters for Earth observation, such as wind speed, altimetry, significant wave height, soil moisture, etc. While its application for forest canopy monitoring is still in the initial stage, there are still many unknown relations between vegetation parameters and actual observations, and a proper theoretical basis needs to be established for simulation and analysis of the different observation geometries. In this paper, we develop a bistatic scattering model with various polarizations at different frequency bands. Our improved model is based on the first-order radiative transfer equation, and is developed based on the wave synthesis technique, after which it can be used for circular polarization signals in bistatic radar systems, i.e. the typical configuration of SoOp-R. We analyze the simulations of the P (0.25–0.5 GHz), L (0.5–1.5 GHz), C (4–8 GHz), and X (8–12 GHz) bands at the backscattering, specular cone, bistatic scattering, and perpendicular planes. The contributions of the different components to the total scattering are also analyzed. The results show that the coherent scattering at the specular cone is larger than the non-coherent scattering, while trunk-dominated forest canopy has strong scattering at the aforementioned different directions. Variations of canopy parameters such as trunk and branch diameters, tree density, and vegetation water content are also simulated at the specular cone plane, showing strong dependence on the final bistatic scattering observation. The simulation results show that the SoOp-R technique has a great potential for monitoring of canopy parameters.

Neutron specular reflectometry (SR) and off-specular scattering (OSS) are nondestructive techniques which, through deuteration, give a high contrast even among chemically identical species and are therefore highly suitable for investigations of soft-matter thin films. Through a combination of these two techniques, the former yielding a density profile in the direction normal to the sample surface and the latter yielding a depth-resolved in-plane lateral structure, one can obtain quite detailed information on buried morphology on length scales ranging from the order of ångströms to ∼10 µm. This is illustrated via quantitative evaluation of data on SR and OSS collected in time-of-flight (ToF) measurements of a set of films composed of immiscible polymer layers, protonated poly(methyl methacrylate) and deuterated polystyrene, undergoing a decomposition process upon annealing. Joint SR and OSS data analysis was performed by the use of a quick and robust originally developed algorithm including a common absolute-scale normalization of both types of scattering, which are intricately linked, constraining the model to a high degree. This, particularly, makes it possible to distinguish readily between different dewetting scenarios driven either by the nucleation and growth of defects (holes, protrusionsetc.) or by thermal fluctuations in the buried interface between layers. Finally, the 2D OSS maps of particular cases are presented in different spaces and qualitative differences are explained, allowing also the qualitative differentiation of the in-plane structure of long-range order, the correlated roughness and bulk defects by a simple inspection of the scattering maps prior to quantitative fits.

When electromagnetic (EM) wave illuminates a target, complex structures of the target produce different scattering mechanisms, which compose the whole scattered field of the target. Decomposing and extracting different scattering mechanisms will improve the knowledge of EM scattering for complex targets, and will be of great significance for feature recognition and scattering characteristics control. In this article, we present a method to decompose and extract different scattering mechanisms such as specular scattering, multiple scattering, and creeping waves from the scattered field. The theoretical basis of the method is that the wave corresponding to different scattering mechanisms reaches the receiver at different time. Thus, we acquire the whole scattered field through simulation or experimental test at first. Then, we perform the signal processing with time-frequency analysis to obtain the arrival time of different scattering mechanisms. According to the time slot difference, the time-domain signal at each frequency can be decomposed and different scattering mechanisms can be extracted. Several examples validate the proposed method.

The physical theory of diffraction (PTD) is presented for triangular cylinders with faces consisting of soft ( electric ) and hard ( magnetic ) sections. It is shown that the specular reflections from such cylinders can be canceled and shifted with appropriate combinations of the soft and hard sections. The residual scattered field in the specular directions is produced by the fringe waves diffracted at the edges and junctions between the soft and hard sections. Due to the energy conservation law, the wave field of the canceled specular beams is distributed over the increased sidelobes. It is shown that the forward scattering is the same for the hard, soft–hard, and black cylinders.

The results of He atom scattering experiments on KTa0.48Nb0.52O3(001) surfaces are presented and compared with similar experiments on mixed potassium tantalate/niobate perovskites with lower concentrations of Nb. The results are puzzling, unique and intriguing. Angular distributions of the He scattering intensities (the He surface diffraction pattern) are found to be very similar to those obtained from targets with lower Nb fractions. However, drift spectra (the intensity of the He specular reflection as a function of the He wave vector) are not. Whereas the drift spectra in the 〈10〉 azimuth do resemble those of the 0, 6 and 10% Nb fraction targets, in the 〈11〉 azimuth they are more similar to the strange drift spectra found from the 30% Nb-doped targets. Most intriguing are the surface temperature scans (the He specular intensity as a function of the target surface temperature); for they are quite distinct from those with lower Nb fractions. Finally, the inelastic He scattering experiments provide phonon dispersion results that are similar in most respects to those found for the lower Nb level samples. In particular, the most prominent feature is an Einstein-like mode at about 13.5 meV which spans the entire surface Brillouin zone in both 〈10〉 and 〈11〉 azimuths.

This article focuses on improving the understanding of the electromagnetic (EM) scattering from water waves modulated by shoaling effect arising from different upslope submarine topography in the nearshore zone. Simulation of EM bistatic scattering from water waves in the nearshore zone where the water depth becomes gradually shallower is presented. The shallow water waves with periodic sinusoidal type are simulated by the model that is based on Boussinesq approximation theory, which can accurately construct the detailed wave structure in the nearshore zone, and the analytical model-the second-order small slope approximation is applied to modeling the EM bistatic scattering from the shallow water waves. Comparisons of the bistatic scattering coefficient (BSC) between water waves corresponding to different submarine plane-upslope topography in the nearshore zone have shown that the angular position of harmonics of BSC will change as upslope varies: higher-order harmonics for plane-upslope cases would be far away from the specular peaks for flat topography case. Moreover, the wave height of the shallow water waves and nonlinear effect will greatly impact changing trend of the BSC. Simulations for TMA spectrum-based water waves also support the fact that the transfer of wave energy from low frequency to higher frequency wave components would be intensified in the shallow water zone with the upslope submarine topography. The results in this article indicate that shallow water waves would reflect some interesting scattering features that traditional deep-sea waves did not show, which will be helpful to the further quantitative investigation of scattering characteristics of nearshore waves.

5G mmWave communication systems have the potential to jointly estimate the positions of user equipment (UE) and mapping their propagation environments using a single base station. But such potential depends on the characteristics of the reflecting surfaces, such as a deterministic specular nature, a stochastic diffuse/scattering nature, or a combination of both. In this letter, we proposed a 5G positioning and mapping algorithm with unknown orientation and clock bias for single-bounce diffuse multipath channel models. The method is able to accurately localize, calibrate and synchronize the UE, even in the absence of line-of-sight and specular components. This enables robust positioning and mapping using only diffuse multipath.

We present the development and implementation of a novel wavelet shrinkage technique for the retrieval of obscured characteristic resonant signatures in the scattered terahertz (THz) reflectivity of molecular crystals. In this implementation, the wavelet basis functions associated with the absorption features were identified using the second-order total variation of the wavelet coefficients. Additionally, wavelet coefficients at certain scales were modified using the phase function corrections and wavelet hard thresholding. Reconstruction of the original spectra using these modified wavelet coefficients yielded the exact resonant frequencies of the chemicals, which were otherwise unrecognizable in the spectral artifacts of the rough surface scattering. We examined the robustness of this method over controlled levels of rough surface scattering, validated using the Kirchhoff approximation, in spectroscopic targets made from $\alpha $ -lactose monohydrate and 4-aminobenzoic acid (PABA), which have close spectral lines. We successfully retrieved the spectral absorption fingerprints in both specular and off-specular reflection geometries. This technique can be utilized for stand-off material characterization using the THz reflection spectroscopy in uncontrolled environments and potentially can be adopted for other broadband spectroscopic modalities.

This paper describes the calibration of the Volcano ray-tracing engine against channel measurements collected in an urban environment with a state-of-the-art 28-GHz directional channel sounder. A discrete set of rays, representing planar wavefronts propagating between the transmitter and receiver, were extracted from the measurements and characterized in path gain, delay, and 3D angle-of-arrival through super-resolution techniques, with average errors of only 1.2 dB, 0.55 ns, and 2.05° respectively. The extracted rays were then tracked over space as the receiver, mounted on a mobile rover equipped with military-grade GPS, traversed 66 m while amassing a total of 488 channel acquisitions. The tracked rays were then mapped to rays predicted from ray-tracing, originating through specular reflection or diffuse scattering from ambient objects. The mapping enabled object-specific calibration, namely calibrating distinct diffuse-scattering models for buildings, vehicles, and foliage. To our knowledge, this is the first effort to calibrate ray-tracing with object-specific diffuse scattering models against rays individually mapped in the path gain, delay, angle, and space domains. Results, in terms of calibrated ray-tracing parameters, fit-error statistics, and lessons learned, are included. Our chief finding was that, while most papers on millimeter-wave ray-tracing do not even consider diffuse scattering, it accounted for 20% of the total received power, whereas diffraction accounted for less than 1%.

The roughness scale effects on ocean radar scattering are studied using the second-order small slope approximation (SSA-II) and the method of moments (MoM). The KHCC03 spectrum is employed to represent 2-D and 1-D sea surfaces in the above two scattering methods, respectively. Criteria of full spectrum truncation are proposed for the numerical simulations of ocean scattering. Numerical results are illustrated in fully bistatic configuration at L- and C-bands. It is found that scattering at higher frequency is relatively more sensitive to the small-scale roughness but less sensitive to the large-scale roughness. At L- and C-bands, short waves with wavenumber larger than 316 rad/m have little effect on ocean scattering. The large-scale waves put more impacts on scattering in the forward directions, especially for large incidence angles. Other than the specular direction, the effects of large-scale roughness on ocean scattering are in general smaller at VV-pol than HH-pol. The bistatic scattering at cross polarizations is less sensitive to the roughness scale as compared to the copolarizations. For numerical simulations of ocean scattering with incidence angle less than 60°, using small surface profiles with size about 1/6 of those accounting for full spectrum yields results with errors less than 2 dB. Results also indicate that the incoherent parts dominate the scattered power from ocean surfaces with large-scale roughness.

Purpose: In the early stages of atherosclerosis, the luminal surface of the arterial wall becomes rough due to injury and detachment of endothelial cells. This roughening can potentially be estimated with ultrasound since the electrical echo signal from the transducer is sensitive to both the angle of incidence to an extended surface as well as the roughness of the surface. Specifically, as the roughness of an interface increases, specular reflection is substituted by scattering. We propose a method that attempts separation of reflection and backscattering components in the received echo signals. Method: Assuming the predominant propagation directions of the reflected and scattered waves can be somewhat controlled by the emitted sound field, separation of those components was attempted using synthetic aperture imaging with a transmit beam, focused at a point more distant than the imaging depth. Specifically, two dedicated beamforming processes were used for generation of reflection-emphasized and backscattering-emphasized images. Result: Experimental verifications on a phantom using an ultrasound system with a limited number of active transmit–receive channels yielded a difference between these two images of 8 dB. The results further showed a similar (slightly improved) lateral spatial resolution size of 0.41 mm for the backscattering-emphasized image compared with conventional B-mode imaging (0.47 mm). Conclusion: A new technique for separation of the reflection and backscattering components using synthetic aperture beamforming with a transmit beam featuring a large focal distance was proposed. The technique demonstrated a partial separation of the reflection and backscattering components, which potentially may be used to estimate surface roughness.

The acoustic scattering from an infinitely long cylindrical shell with periodic lengthwise ribs is studied. The shell motion is described by the Donnell equations, and the lengthwise rib is modeled as an elastic beam whose motion is decomposed into longitudinal and flexural vibrations. A circumferential mode expansion is used to obtain numerical results for the scattering sound field. The backscattering characteristics in the far-field can be explained by the resonance and interference phenomena. It is shown that subsonic flexural waves can be generated and radiated by the ribs. Due to the periodical distribution of the ribs, there exist multi-order flexural Bloch waves in the circumferential direction. The multi-order flexural Bloch waves can form standing circumferential waves, which lead to a complex acoustic resonance. The attachments of the ribs to the shell can reflect an acoustic wave directly and the reflected wave will interfere with the specular reflection, which is dominant in the frequency-angle spectra with an increasing number of ribs. Furthermore, the flexural wave and flexural Bloch waves can radiate through the attachments and interfere with the specular reflection. However, the interference fringes in the frequency-angle spectra caused by the flexural wave and flexural Bloch waves are coincident at broadside.

Structural color materials, which generate colors through the interaction between light and nano-microstructures, have always been research hotspots in the fields of display, anticounterfeiting and stimuli-responsive materials. Structural colors based on scattering have received increasing attention due to their wider viewing angles than that originating from the specular reflection of photonic crystals. However, the wide scattering spectrum of an amorphous structure leads to lower purity and brightness of the appeared colors. Few researchers have focused on the scattering of ordered structures due to their strong reflection and diffraction in the visible regions. In this work, by building ordered films (OFs) using SiO2 spheres (refractive index n = 1.46) with a diameter of 300–500 nm, for the first time, sharp scattering spectra with narrow full width at half-maximum (FWHM, 24 nm) were generated. Importantly, under ambient light, brilliant colors covering the entire visible region can be observed, and a formula was proposed to calculate the scattering spectra of OFs. Moreover, rainbow structural color was realized under irradiation of the nonparallel light, and full-spectrum structural color patterns were fabricated using building blocks with a single particle size by a spraying method. Finally, a composite structure was constructed to explore possibilities in the field of flexible transparent displays.

This study examines the influence of an early lateral reflection on spatial perceptual attributes and speech reception. To this aim, a diffuse reflection is compared with a specular one. Although diffusive surfaces have widespread applications in room acoustics design, the knowledge of the perceptual and behavioral outcomes of these surfaces has yet to be fully developed. Two experiments were conducted to investigate how the reflection type, its temporal delay, and its azimuth affect spatial percepts (source distance, width, and focus) and speech intelligibility (SI) in diffuse stationary noise. The experimental setup included ecological elements: field measurements, a speaker-like source directivity, and real flat and diffusive surfaces. The results indicate that the presence of a single diffuse reflection reduces the perceived distance of a frontal speech source and makes it clearer. SI is higher with a diffuse reflection than with a specular one. Perceptual and behavioral outcomes both depend on the angle of reflection given the frequency- and angular-dependent properties of the diffusing surface and the directivity of the speech source. The results are interpreted with reference to loudness and binaural cues and to the precedence effect. Implications of the findings for acoustic design are also discussed.

Using the perturbation theory (PT), reflected field both in specular and non specular directions from a slab made of topological insulator (TI) material with rough interface is studied. The specula...

A spectrum of low-frequency (20–30 Hz) amplitude fluctuations of the ultrasonic (10 MHz) signal specularly scattered from water surfaces covered with monomolecular and thicker crude oil origin films of well-defined, oceanographically relevant viscoelastic properties was examined in laboratory and at-sea conditions. The relationship between the surface water wave (30 Hz) damping coefficient and the oil layer thickness was established, and compared to the one predicted by the classical Stokes theory. The depression of the spectral energy density of wind-driven waves by surface films was inferred from the ratio of acoustic signal fluctuations spectra with/without films, and compared to that resulting from the Marangoni damping theory applicable to monolayers of particular surface viscoelasticity. The agreement between the theory and experimental data was satisfactory. As shown in at-sea experiments performed with a free-floating, buoy-like acoustic system, and an artificial oil slick spread over the Baltic Sea surface, the film’s rheological surface properties can be recovered from acoustic surface probing, as well as oil spill edge detection. Simultaneous statistical analyses of the scattered signal amplitude distribution parameters turned out to be unequivocally related to the oil substance fraction weight, oil layer thickness, and the form of oil contamination.

Scanning helium microscopy is an emerging form of microscopy using thermal energy neutral helium atoms as the probe particle. The very low energy combined with lack of charge gives the technique great potential for studying delicate systems, and the possibility of several new forms of contrast. To date, neutral helium images have been dominated by topographic contrast, relating to the height and angle of the surface. Here we present data showing contrast resulting from specular reflection and diffraction of helium atoms from an atomic lattice of lithium fluoride. The signature for diffraction is evident by varying the scattering angle and observing sharp features in the scattered distribution. The data indicates the viability of the approach for imaging with diffraction contrast and suggests application to a wide variety of other locally crystalline materials.

In this article, a multiple diffuse coding metasurface (MDCM) of independent polarization is designed to control the propagation direction of diffuse reflections under different polarizations and to improve the monostatic and bistatic RCS (radar cross section) reduction effect. First, a method for controlling the distribution range and propagation direction of the diffuse field is studied, and the diffuse field distribution of the random phase metasurface is optimized by a genetic algorithm to improve the uniformity of the diffuse scattering distribution. Then, the random phase distribution is superimposed on the periodic gradient phase distributions of the linear and hedge types in the orthogonal direction so that the main propagation direction of the diffuse metasurface deviates from the specular reflection region under different polarizations, showing single and two diffuse beams. Finally, the anisotropic unit cell with a rectangle inside and an improved Jerusalem cross on the outside is employed as the basic coding element of the MDCM due to its independent polarization phase response. The numerical and experimental results show that the MDCM features multiple diffuse scattering, independent polarization and angle insensitivity and can efficiently improve the monostatic and bistatic RCS reduction effect simultaneously. Because the scattered energies are redirected away from the specular reflection direction, the specular scattering reduction effect is better than the isotropic diffuse metasurface. The proposed method increases the difficulty of detection by single or netted radar and has the potential for the applications of stealth techniques.

To develop an millimeter-waves (mm-waves) channel model for in-room access scenarios, a double-directional channel measurement campaign conducted in a conference room environment is presented. In the measurements, a custom-developed channel sounder with a 12° angle and 2.5-ns delay resolutions at 58.5 GHz was used. From the measured data, the multi-path components were extracted using a high-resolution path parameter estimation algorithm; then, they were clustered based on the actual physical propagation paths to identify the scattering processes explicitly. The cluster analysis revealed that the signal paths by line-of-sight, single-bounce, and double-bounce reflections were power-dominant and well predicted by ray-tracing, but the contribution of random clusters was not significant. In this study, to express diffuse scattering on the rough surface of an ambient reflector, an intra-cluster model of plasterboard wall reflection was parameterized. Furthermore, the proposed intra-cluster model was experimentally validated by analyzing the small-scale fading captured along the wall in the time domain which is caused by the constructive and destructive interference of the specular reflection and diffuse scattering components.

Angle of arrival (AoA) analysis is essential for the statistical characterization of the underwater (UW) channel where the acoustic signal propagation is confined to a restricted geometry. In UW channels, the acoustic signal reaches the receiver either through the line of sight path or through scattering from the sea surface and bottom. Low-frequency acoustic signals (few Hz) undergo reflection from the sea surface and bottom. This is called coherent scattering, where the scattered paths are assumed to be in phase and concentrated around the specular paths. At relatively higher frequencies (above 10 kHz), incoherent scattering occurs, resulting in an omnidirectional scattering pattern at each point of interaction with the sea surface. In this work, we derive a closed-form expression for the AoA distribution for a single bounce (SB) path that undergoes incoherent scattering from the surface/bottom in an UW channel. The analysis is extended to the case of paths involving multiple bounces (MB). The AoA distribution is further used to evaluate the Doppler spread in an UW channel.

CA Alissa The scattering phenomenon caused by rough surfaces has a dominant role in shaping the reflected field at terahertz (THz) frequencies, both in specular and non-specular directions. Most surfaces in nature are randomly rough, and the surface height obeys a certain statistical distribution. A Gaussian probability density function (PDF) for height distribution is often considered, and the correlation length is assumed to be longer than the wavelength. However, a clear understanding of how changing these assumptions affect the angular distribution of the scattered field is still lacking. In the first part of this work we investigate via microscopic measurements the statistical distribution of realistic indoor materials, and its deviation from the assumed normal distribution. After that, the influence of non-Gaussianity on the specular reflection in the low THz region is shown analytically. In the second part, a measurement campaign of diffuse scattering, caused by structured statistically-controlled surfaces, is reported. The correlation length assumption has been proven experimentally and via full-wave simulation to affect the diffuse scattering by rough samples, when the other statistical parameters are kept without changes.

The paper assesses how multiple-static scattering mitigates the effect of late-time onset on the robustness of the extracted resonance modes in the context of radar target classification. The assessment exploits the mode distribution vs onset shift to verify the sensitivity of the mode’s extraction to the selected onset, especially higher-order, to onset. However, within some bistatic directions, the modes have enhanced energies with lesser specular energy, making the modes estimate less sensitive to onset shifts. Also, the mode distribution per bistatic and polarization configuration has demonstrated different onset windows of accurate and consistent mode extraction. Notably, the distribution of the mode energy distribution reveals that classification performance degrades with poorly selected onset.

An analysis of the coherency properties of specular scattering from ocean and land surfaces as observed in global navigation satellite system-reflectometry (GNSS-R) and signals of opportunity systems is presented. This analysis applies existing approximate models for the coherent and incoherent contributions. Approximate expressions are developed for when one component of the return is likely to dominate as a function of surface and observing system properties. The model developed is then applied for sea surface returns, and the relative contribution of the coherent term is expressed as a function of the receiver height, frequency, incidence angle, and wind speed. For L-band spaceborne measurements, it is shown that coherence is expected only for wind speeds less than 2–3 m/s, while for P-band spaceborne measurements, coherence can dominate returns for wind speeds up to 5–7 m/s. For land surface measurements from space, it is shown that the surface rms height needs to be sufficiently low for coherent components to dominate returns. Coherence dominates for roughness values not exceeding a range of 5–7 cm for the L-band and 15–30 cm for the P-band. For the L-band, these conditions over land are likely to be created primarily by inland water bodies. A model for the specular scattering from a water body, including earth curvature effects, is then developed to highlight the strong dependence of the resulting coherent field on the shape of the water body and any offset in its location from the specular point. These results further clarify the significant variability that should be expected in coherent scattering from inland water bodies.

[EN] In this work, we show that scattered acoustic vortices generated by metasurfaces with chiral symmetry present broadband unusual properties in the far-field. These metasurfaces are designed to encode the holographic field of an acoustical vortex, resulting in structures with spiral geometry. In the near field, phase dislocations with tuned topological charge emerge when the scattered waves interference destructively along the axis of the spiral metasurface. In the far field, metasurfaces based on holographic vortices inhibit specular reflections because all scattered waves also interfere destructively in the normal direction. In addition, the scattering function in the far field is unusually uniform because the reflected waves diverge spherically from the holographic focal point. In this way, by triggering vorticity, energy can be evenly reflected in all directions except to the normal. As a consequence, the designed metasurface presents a mean correlation-scattering coefficient of 0.99 (0.98 in experiments) and a mean normalized diffusion coefficient of 0.73 (0.76 in experiments) over a 4 octave frequency band. The singular features of the resulting metasurfaces with chiral geometry allow the simultaneous generation of broadband, diffuse and non-specular scattering. These three exceptional features make spiral metasurfaces extraordinary candidates for controlling acoustic scattering and generating diffuse sound reflections in several applications and branches of wave physics as underwater acoustics, biomedical ultrasound, particle manipulation devices or room acoustics., We acknowledge financial support from the Spanish Ministry of Science, Innovation and Universities through Grant "Juan de la Cierva-Incorporacion" (IJC2018-037897-I) and PID2019-111436RB-C22, and by the Agencia Valenciana de la Innovacio through grants INNVAL10/19/016. This article is based upon work from COST Action DENORMS CA15125, supported by COST (European Cooperation in Science and Technology). JPG and VRG gratefully acknowledge the ANR-RGC METARoom (ANR-18-CE08-0021) project and the project HYPERMETA funded under the program Etoiles Montantes of the Region Pays de la Loire.

International audience; Despite limiting the performance of multilayer optical thin-films, light scattering properties are not as yet controllable by current design methods. These methods usually consider only specular properties: transmittance and reflectance. Among other techniques, design of thin-film components assisted by deep neural networks have seen growing interest over the last few years. This paper presents an implementation of a deep neural network model for light scattering design and proposes an optimization process for complex multilayer thin-film components to comply with expectations on both specular and scattering spectral responses.

The past few years have witnessed the great success of artificial metamaterials with effective medium parameters to control electromagnetic waves. Herein, we present a scheme to achieve broadband microwave low specular reflection with uniform backward scattering by using a coding metasurface, which is composed of a rational layout of subwavelength coding elements, via an optimization method. We propose coding elements with high transparency based on ultrathin doped silver, which are capable of generating large phase differences (∼180°) over a wide frequency range by designing geometric structures. The electromagnetic diffusion of the coding metasurface originates from the destructive interference of the reflected waves in various directions. Numerical simulations and experimental results demonstrate that low reflection is achieved from 12 to 18 GHz with a high angular insensitivity of up to ±40° for both transverse electric and transverse magnetic polarizations. Furthermore, the excellent visible transparency of the encoding metasurface is promising for various microwave and optical applications such as electronic surveillance, electromagnetic interference shielding, and radar cross-section reduction.

While the use of diffuse surfaces is becoming increasingly common in the acoustical design of performance venues and normal rooms, there is a paucity of data on the auditory perceptual effects that characterize those finishes compared to specular ones. For instance, it is not entirely clear whether and how the aural impression is affected when first reflections are swapped from specular to diffuse. In a recent work, after revising the background knowledge on physical and perceptual effects of scattering, Visentin et al. [(2020) J. Acoust. Soc. Am. 148(1), 122–140] started a systematic analysis of how diffuse reflections influence the auditory impression by considering the simplest possible case, that is, a direct sound and one lateral reflection. The present work is a step forward in the analysis, and pairs of lateral reflections without or with a ceiling reflection are considered. By means of detailed listening tests, it is shown how diffuse reflections modulate the perception of some spatial attributes. This knowledge adds to the criteria to be employed when including diffusing surfaces in the design of first reflections in rooms.

The objects with microroughness surfaces, heterogeneous media are widely used in modern optical devices, for instance in various light guiding devices, car dashboards and other illuminating systems as elements of scenes aimed to generate images with photorealistic quality. Surface or volume scattering of these objects can have very complex shape with pronounced picks, far from ideal specular or ideal diffuse ones and typically described with Bi-Directional Scattering Functions (BSDF). If model reconstructing BSDF measuring device contains inaccurateness, it can result in errors of parameters reconstruction for scattering objects and serious damage for entire optical simulation for scattering objects. In simulation model it is very preferable simulate optical parts maximally close to real measuring device. Another problem is calculation speed of model aimed for BSDF simulation. BSDF measurement devices have very high angular and spatial resolutions that results in a very ineffective from viewpoint of simulation. Moreover, BSDF functions is multidimensional, so many calculations are required to fulfill. These problems impose careful choosing of simulation model, its reasonable simplifications, selection of proper ray tracing engine. In the paper the virtual prototyping of different industrial measurement devices is considered. These devices are quite different and thus require different approaches in computer models design. The results of virtual prototyping for several samples with complex scattering properties are presented as in numerical shape of angular intensity distribution as well in qualitative as photorealistic images. All virtual prototyping simulated results are compared with measurements to prove reliability and reasonability of built models.

International audience; The structure as well as morphology of nanoporous alumina (NP Al2O3) films on Al substrates are investigated by terahertz (THz) reflectometry and scattering imaging. An inhomogeneous area is identified in THz C-scan results off specular conditions at various angles. The thickness of NP Al2O3 films calculated based on THz results is in excellent agreement with destructive cross-sectional field emission scanning electron microscopy (FE-SEM) measurements.

For the analysis of sea surface using Global Navigation Satellite System-Reflectometry (GNSS-R), Geometrical Optics (GO) is typically adopted for modeling scattering around the specular reflection direction, where conventional GNSS-R receivers operate. However, the exploitation of GNSS-R for maritime surveillance applications, e.g., ship detection, is feasible in far-from-specular acquisition geometries, where the validity of GO is questionable. In this paper, we present the results of a link budget analysis for the sea surface return in arbitrary viewing geometries. The study is aimed at comparing GO with a more accurate closed-form bistatic two-scale model, named BA-PTSM, for the simulation of GNSS-R signals in acquisition geometries other than the conventional forward-scattering one. Numerical results show that a reliable simulation of airborne GNSS-R signals in far-from-specular acquisition geometries requires sea surface scattering models more accurate than GO, e.g., BA-PTSM.

In GNSS-R (Global Navigation Satellite System Reflectometry) land applications, bistatic scattering occurs in the vicinity of the specular direction, and the scattered waves can include both coherent and incoherent components. A description of land surfaces roughness is required to predict GNSS-R specular scattering. Here we consider roughness on three distinct length scales: a microwave roughness f 1 (x, y) with correlation lengths of ~ 10 centimeters, a coarse scale 30-meter planar topography f 3 (x,y) based on digital elevation model (DEM) data, and a fine scale topography f 2 (X,y) between these two length scales. The fine scale topography represents the length scales in which scattered waves can transition from coherence to partial coherence to incoherence. In this paper, we investigate f 2 (x, y) using recent airborne lidar measurements of land surface heights. Using f = f 1 + f 2 + f 3 , fine scale partial coherent FPCN and FPCP models are applied to predict bistatic scattering coefficients near the specular direction for 30m surface area. Here “fine scale” means the fine scale topography of f 2 (x, y) is included. The model uses complex electric field summation and Monte Carlo simulations within a large area. For non-overlapping large areas, we use intensity summations as in radiative transfer theory. We consider a fine scale partial coherent numerical model (FPCN) that applies numerical integration to the Kirchhoff integral using 2 cm discretization. The fine scale partial coherent patch model (FPCP) uses planar patches o fL size, where L is less than the correlation length of f 2 . Numerical illustrations show that the results of the FPCN and FPCP are in good agreement with each other. Comparisons are also made with geometric optics model (GO) with and without the attenuation factor of microwave roughness.

The purpose of this paper is to study the acoustic scattering characteristics of a one-dimensional random undulating interface based on the PM wind wave spectrum. The small slope approximation method is currently a more commonly used method for calculating sea surface acoustic scattering. This method is very effective in calculating the acoustic scattering of rough surfaces under the condition that the glancing angle of the incident angle is not particularly small and the surface slope is not particularly large. Therefore, this paper uses a small slope approximation method to calculate the scattering intensity of a one-dimensional random undulating interface. Moreover, most of the current researches on sea surface acoustic scattering use Gaussian spectrum, which does not conform to the real sea surface. Scientists have done many studies on real ocean waves and proposed several more mature ocean spectra. Therefore, this paper adopts the PM wind wave spectrum, uses its statistical characteristics and the small slope approximation method to analyze its variation with the scattering angle and incident frequency. The results show that as the scattering angle gets closer to the direction of specular scattering, the intensity of scattering gradually increases, and reaches the maximum in the direction of specular scattering. As the incident frequency increases, the scattering intensity in the forward scattering direction first increases and then stabilizes, and the scattering intensity in the backward scattering direction first increases and then fluctuates around the same value. The research results are of great significance to the development of underwater acoustic technology and sonar technology.

Geosynchronous Synthetic Aperture Radar (GEO SAR) has advantages of a short revisit time and large coverage for the scene of interest, so lots of theories and analysis toward the GEO SAR have been developed. However, GEO SAR systems may generate radio frequency interference (RFI) to a low earth orbit SAR (LEO SAR), causing a decrease in Signal-to-Interference-plus-Noise Ratio (SINR) of SAR images. In order to evaluate the GEO-to-LEO RFI effect on imaging, we deduce the formulas of the RFI power and image SINR, and verify them by comparing them with numerically evaluated results from simulated images. Based on the formulas, we evaluate SINRs of LEO SAR images for different bistatic scattering coefficients. The results show that when the target forms a specular bistatic scattering geometric relationship with a GEO SAR and a LEO SAR, LEO SAR image quality is poor, with a SINR worse than 5 dB, but the RFI effects can be neglected in other cases.

10 pags., 9 figs., 2 tabs., Simulation results for light transport in long tapered CsI(Tl) crystals using look-up tables (LUTs) are presented. The LUTs were derived from the topography of a polished and a lapped surface of a CsI(Tl) crystal measured with atomic force microscopy. Simulations with different combinations of polished and lapped surfaces were performed, to extract the non-uniformity of light collection depending on the interaction point, and compared to experimental results. The simulations reproduce the general trend given by the measurements, and show that more homogeneous light collection is attained when all lateral sides of the crystal are lapped. For the lapped crystal the simulation model is most sensitive to the reflectivity of the enhanced specular reflector (ESR) foil surrounding the crystal, which is one of several properties influencing the light transport examined in this study. The sensitivity of the light-output non-uniformity to variations in the absorption length observed in a batch of CsI(Tl) crystals in a previous study is also discussed. Residual differences between the simulation and the measurements can potentially be attributed to the scattering of scintillation photons inside the materials used. Additional measurements to further advance the construction of the simulation model are suggested., This work was supported by the Swedish research council (VR) grants 2017-03986, 2014-06644, 2013-04178, 2012-04550, BMBF contracts 05P15WOFNA, 05P19WOFN1, 05P15RDFN1, 05P19RDFN1, the TU Darmstadt – GSI cooperation contract HIC for FAIR, by the Spanish research council grants FPA02015-64969-P (MINDECO/FEDER/EU), FPA2015-69640-C2-1-P, PGC2018-099746-B-C21, MDM-2016.0692 (MINECO/FEDER/EU) and by ED431C-2017/54 and EDB481-2017/002 (Xunta de Galicia/FEDER/EU).

In-line inspection during the manufacturing process to evaluate topography related parameters has increasingly become important. However, it imposes strong requirements and the in-line inspection systems. Two of the most established optical metrology techniques that can cope well with different surface materials are white light interference microscopy and confocal microscopy. However, the measurement process is very time-consuming. Another technique, which offers single-shot capability and hence fast data acquisition is structured illumination, but restricted to the inspection of rough scattering surfaces only. Multiple-wavelength digital holography (MWDH) offers the possibility to overcome the aforementioned shortcomings. It can be applied on rough scattering and specular reflective surfaces in a lensless lightweight manner. However, the stability and exact knowledge of the wavelengths employed is crucial for the successful application of MWDH. In this paper, we describe a method to ensure wavelength stability for MWDH. Two VCSELs are mounted on a common heat sink with a distance of a few mm only in order to eliminate the influence of wavelength drift between the two VCSELs caused by different temperature. Moreover, the temperature is stabilized to 20C via a Peltier Element. In addition, the light-emitting surface of the two VCSEL is directly bonded to two corresponding single-mode fibers. Further fiber couplers and a fiber combiner are applied to result in a lightweight, highly robust and flexible setup. Information multiplexing via different angles of the two wavelength corresponding reference waves is introduced to enable single-shot data acquisition. In that manner, disturbances caused by changing environmental conditions as encountered in sequential acquisition are eliminated. The advantages of the VCSEL based MWDH system are demonstrated in comparison to structured illumination on non-cooperative materials (scattering and/or specular samples, samples with different colour properties).

Transferring laser-based sensors into industrial applications (for instance, for contact and destruction-free inline quality control of alumina alloys) is very challenging due to laser-safety regulations and the complex implementation requirements of individual technological infrastructures. In order to open laser-based sensor technology even for small to medium size enterprises, we introduce a prototyping platform for laser-based sensor technologies that enables fast, error-free, flexible and low-cost transformations in the industry. As an example, the transformation of a laser-based sensor concept using coherent light scattering at technical insulating films is shown. The transformation of this type of sensor for inline quality control is particularly demanding due to the requirements of probing transparent conversion coatings (with a thickness of less than 70 nm) that commonly applied electronic techniques fail to affect. The conversion films are produced on the top of cold-rolled, unpolished alumina so that coherently scattered laser light is regarded as superposition from diffuse scattering processes at the surfaces/interfaces, inclusions, and/or layer imperfections. Analysis is realized by extending the principal approach of reflectometry and considering the role of diffuse and specular scattering together with the concepts of light interferometry. The functionality of the transformed sensor was successfully validated using five different conversion coating thicknesses on AA3003 alumina substrates.

We present a numerical algorithm for the simulation of resonant x-ray magnetic scattering in reflection geometry for an arbitrary three-dimensional magnetization distribution over a multilayer sample utilizing the distorted-wave Born approximation. Our approach takes the medium boundary matrix approach for specular reflection, and the Born approximation typically used for off-specular reflection, combines the two, and adds the contribution from transmission through the sample before and after a reflection event. The algorithm is then tested on experimental data from an ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$/Co/Pt multilayer sample with hybrid N\'eel/Bloch/N\'eel domain walls at incidence angles at and near multilayer Bragg angles, and photon energies near the Co ${L}_{3}$ absorption edge, achieving high levels of agreement with experimental data. Incorporating the transmission components into the algorithm was found to explain the dichroism observed in scattering from Bloch-type domain walls, and uncovered the likely importance of diffuse scattering in transmission from the polycrystalline grain walls along the optical path of the x rays in the sample---a theme which deserves further investigation.

This paper presents a version of simulation program, which facilitates the calculation of changes to the intensity of RHEED oscillations in the function of the glancing angle of incidence of the electron beam, employing various models of scattering crystal potential for heteroepitaxial structure of hexagonal GaN film nucleated on AlN(0 0 0 1) and AlN(0 0 0 1 ¯ ) surfaces, including the possible existence of various diffuse scattering models through the layer parallel to the surface. Program summary Title of program: RHEED_DIFF_WW Program Files doi: http://dx.doi.org/10.17632/hn3pt6ytky.2 Licensing provisions: GNU General Public License 3 Programming language used: C++ Journal reference of previous version: Computer Physics Communications 207 (2016) 536–538 Does the new version supersede the previous version?: No. It is a supplement to the previous version. Reasons for the new version: Responding to users’ feedback we present a practical procedure of construction of simulation program, which facilitates the calculation of changes the intensity of RHEED rocking curves, employing various models of scattering crystal potential for heteroepitaxial structure of wurtzite-type GaN on AlN. The work demonstrates that the polarity of GaN/AlN heterojunctions can be investigated in real time by RHEED rocking curves measurements. Nature of problem: Aluminum nitride is a subject of intense research as a substrate material in heterojunctions for short-wavelength optoelectronics, high-power and high-frequency electronics. The lattice constants and thermal expansion coefficients of AlN and GaN are close enough to provide a low defect density in epitaxial GaN grown on the AlN substrates. Both GaN and AlN possess a wurtzite crystal structure (non-centrosymmetric), which makes it either metal or N polar along the c-axis with [0 0 0 1] or [0 0 0 1 ¯ ] direction, respectively, and which strongly influences their physical properties [1]. From the practical point of view, the distinction between these two polarities is very important for the many applications of the GaN/AlN heterostructures [2-4]. Method of solution: RHEED intensities are calculated within the general framework described in Refs. [5] and [6]. Summary of revisions: The presented version of the program implements an original algorithm for calculations of scattering potentials for regular all-metal-polar GaN(0001)/AlN(0001) and all-N-polar GaN(0 0 0 1 ¯ )/AlN(0 0 0 1 ¯ ) heterostructures, and solving a time-independent Schrodinger equation for high-energy electrons. During the numerical calculations of the changes in the intensity of the specular beam in the function of the glancing angle, it was assumed that the azimuth of the incident beam direction corresponds to the one-beam condition, the electron energy equals 10 keV, the temperature of the crystal equals 300 K, glancing angle was increased from 0.5 ∘ to 5.0 ∘ , and the value of α parameter = 0.1 and β = 0.5 for the MODEL3 of the scattering potential [6] (See Fig. 1 , Fig. 3 ). References E. S. Hellman, MRS Internet J. Nitride Semicond. Res. 3, 11 (1998). A. Onen, D. Kecik, E. Durgun, and S. Ciraci, Phys. Rev. B 95 (2017) 155435. P. Sohi, D. Martin and N. Grandjean, Semicond. Sci. Technol. 32 (2017) 075010. M. Agrawal, K. Radhakrishnan, N. Dharmarasu1, and S. S. Pramana, Jpn. J. Appl. Phys. 54 (2015) 065701-6. A. Daniluk, Comput. Phys. Commun. 207 (2016) 536-538. A. Daniluk, Comput. Phys. Commun. 185 (2014) 3001-3009.

Many models used to represent the boundary condition for the separation of atmospheric scattering from the surface reflection in polarized remote sensing measurements, assuming that the polarized surface reflectance is spectrally neutral. To test this hypothesis, referred to the spectral invariance hypothesis, JPL’s Ground-based Multiangle SpectroPolarimetric Imager (GroundMSPI) was used to measure the polarized bidirectional reflectance factors (pBRFs) of different types of outdoor surfaces. GroundMSPI measures the linear polarization Stokes parameters ( $I$ , $Q$ , and $U$ ) at three wavebands centered at 470, 660, and 865 nm. Images of pBRF were acquired at the three wavelengths and the best-fitting slopes of pairwise spectral regressions were determined. The spectral invariance hypothesis predicts that these slopes should be unity. All region types, excluding grass, meet this criterion within 8% for all three wavelengths. Grass measurements show a large mean deviation of 31.1% from the expected slope when regressing 865-nm data against other wavelengths due to the differences in the spectral absorbance of chlorophyll. Angle of linear polarization (AoLP) analysis of cotton crops is presented as a method to isolate cases where the scattered light is dominated by single reflection within the plants from cases where multiple scattering plays a larger role. Spectral invariance is observed in those cases where specular reflection from the top surfaces of the leaves is primarily responsible for the measured polarization.

Vertical-cavity surface-emitting laser (VCSEL) devices operate using a variety of viewing angles to satisfy the demands of different applications. One simple and universal approach to accomplish this is by using scattering elements in the packaging process for VCSEL chips. However, inevitable backward scattering loss is introduced, which suppresses the radiant efficacy of VCSEL devices. Therefore, we have proposed an enhanced specular reflection (ESR) structure with an opening circle window (OCW) to recycle the backward scattered light. The ray-tracing method is used to optimize the diameter of the OCW, as well as the thickness of the ESR structure. Furthermore, the light extraction mechanism is discussed. According to theoretical results, VCSEL devices with optimized ESR structures are fabricated and compared with traditional VCSEL devices. The experiment results demonstrate that ESR structures can significantly enhance the radiant efficacy of VCSEL devices using scattering elements. This shows great potential for applications involving illumination and 3-D imaging.

—The kinetics of growth of a nanosized germanium film deposited by magnetron sputtering on the Si(001) surface is studied using a developed experimental X-ray reflectometry technique distinguished by the joint recording of specularly reflected and diffusely scattered radiation. By using this technique, it is possible to perform in situ both the analysis of the morphology of the growing film and the control of its thickness with an accuracy to 1 nm. Dependences of the intensity of specular reflection, diffuse scattering, rate of growth, and mean square roughness and density of the film on the deposition time are obtained. According to the results of the measurement of specularly reflected radiation, the film roughness increases with time according to a power law. However, at a thickness of the film of 4 nm, a clearly defined maximum of diffuse scattering is observed, the angular position of which corresponds to the critical angle of total external reflection of germanium of 0.31°. This pattern of distribution of scattered radiation is explained by the manifestation of the Yoneda effect that consists in the anomalous X-ray scattering, the maximum of which corresponds to the critical angle θC of total external reflection from the film. It is established experimentally that, at the initial stage of growth, the film is formed by the Volmer–Weber mechanism. It is found using in situ X-ray reflectometry that the formation of a continuous layer of a germanium film occurs at its thickness of 7 nm; the subsequent growth of the film proceeds according to the power law σf ~ tβ, where β = 0.23.

This paper proposes radar sensors operating at ${J}$ -band (220–320 GHz) for automotive applications. Operating at ${J}$ -band, at about three times higher frequency than the currently available automotive radars operating at 77 GHz, will result in three-fold improvement in cross-range resolution for the same antenna size. Since the characterization of the radar backscatter from different objects on the traffic scenes is necessary for optimizing the design of automotive sensors, the work reported in this paper is the start of a broader study that attempts to fill the lack of knowledge on radar backscatter behavior of road environment at this frequency band. Considering vehicles as the most important object for automotive radars, this paper investigates the response of vehicles from different aspects. A combination of outdoor high-resolution synthetic aperture radar imaging experiments and real-aperture imaging measurements of vehicles are performed using a 222-GHz polarimetric instrumentation radar. The aim of these experiments is to identify the scattering centers on different vehicle bodies and to determine the statistics of the radar return. The results show that significant scattering is due to a limited number of fixtures on the vehicle’s outer surfaces facing the radar. The strongest scattering phase-centers observed are due to specular reflections and, hence, have a strong dependence on the relative look angle. The statistics associated with backscatter from vehicles are found, in most cases, to best fit the Weibull distribution.

Scattering of K+ and I– ions in surface-induced dissociation of KI molecules at a diamond (110) target has been studied using the molecular beam techniques. The angular and energy distributions of the positive and negative ions were measured by a time-of-flight detector with a retarding field energy analyzer. The incident KI beam energy was equal to 12 eV while the target surface temperature was 250°C. The angular distributions of the K+ ions we observed exhibited maxima at scattering angles smaller than the specular reflection ones, in contrast to the I– ion distributions where the maxima were shifted to larger angles. The intensities of scattering of both the ions at the maxima of the distributions increased as the incident angles of the beam grew. The energy distributions of the positive and negative ions have turned out to be identical which may indicate the mechanism of rapid non-statistical dissociation of the molecules upon an impact on the target surface.

Elastic acoustic scattering is important for buried target detection and identification. For elastic spherical objects, studies have shown that a series of narrowband energetic arrivals follow the first specular one. However, in practice, the elastic echo is rather weak because of the acoustic absorption, propagation loss, and reverberation, which makes it difficult to extract elastic scattering features, especially for buried targets. To remove the interference and enhance the elastic scattering, the de-chirping method was adopted here to address the target scattering echo when a linear frequency modulation (LFM) signal is transmitted. The parameters of the incident signal were known. With the de-chirping operation, a target echo was transformed into a cluster of narrowband signals, and the elastic components could be extracted with a band-pass filter and then recovered by remodulation. The simulation results indicate the feasibility of the elastic scattering extraction and recovery. The experimental result demonstrates that the interference was removed and the elastic scattering was visibly enhanced after de-chirping, which facilitates the subsequent resonance feature extraction for target classification and recognition.