Point Scatterers Research Articles

Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti- PT -symmetry

We develop a fundamental transfer-matrix formulation of the scattering of electromagnetic (EM) waves that incorporates the contribution of the evanescent waves and applies to general stationary linear media which need not be isotropic, homogenous, or passive. Unlike the traditional transfer matrices whose definition involves slicing the medium, the fundamental transfer matrix is a linear operator acting in an infinite-dimensional function space. It is given in terms of the evolution operator for a nonunitary quantum system and has the benefit of allowing for analytic calculations. In this respect it is the only available alternative to the standard Green's-function approaches to EM scattering. We use it to offer an exact solution of the outstanding EM scattering problem for an arbitrary finite collection of possibly anisotropic nonmagnetic point scatterers lying on a plane. In particular, we provide a comprehensive treatment of doublets consisting of pairs of isotropic point scatterers and study their spectral singularities. We show that identical and $\mathcal{P}\mathcal{T}$-symmetric doublets do not admit spectral singularities and cannot function as a laser unless the real part of their permittivity equals that of the vacuum. This restriction does not apply to doublets displaying anti-$\mathcal{P}\mathcal{T}$-symmetry. We determine the lasing threshold for a generic anti-$\mathcal{P}\mathcal{T}$-symmetric doublet and show that it possesses a continuous lasing spectrum.

Radar 3-D Forward-Looking Imaging for Extended Targets Based on Attribute Scattering Model

Radar three-dimensional (3-D) forward-looking imaging has always been a difficult issue in the radar detection. In this letter, a forward-looking 3-D imaging method based on attribute scattering model (ASM) for extended targets is proposed. Firstly, an imaging model based on point scattering model (PSM) with wavefront modulation technique is constructed to achieve 3-D forward-looking imaging. Secondly, considering the fact that PSM-based imaging model assumes that the target is composed of a set of discrete points, it is not suitable for reconstructing the structure feature of extended targets, i.e. line structure and surface structure. To extract more geometry information of the target, the attribute scattering model (ASM) which includes point scatters (PSs), line-segment scatters (LSSs), and rectangular-plate scatterers (RPSs) is adapted to the 3-D imaging model. Solving the parameter sets of PSs, LSSs and RPSs with the alternating direction method of multipliers (ADMM) algorithm, the edge and surface structure of the extended target can be reconstructed. The simulation results based on electromagnetic calculation by FEKO verify the effectiveness of the proposed method.

A Novel Multiangle Images Association Algorithm Based on Supervised Areas for GNSS-Based InSAR

Global navigation satellite system-based synthetic aperture radar interferometry (GNSS-based InSAR) systems can achieve 3-D deformation retrieval by associating multiangle images of different satellites. However, the difference in the scene radar cross section (RCS) and resolution cells makes multiangle images vary considerably. In addition, low resolution will further aggravate the difference in multiangle images. In this letter, a multiangle images association algorithm is proposed for GNSS-based InSAR systems. First, the supervised area is introduced to describe the areas of the same deformation based on the persistent scatter (PS) point. Then, the initial multiangle images association results are obtained by overlapping all PS points supervised areas of all satellites. Finally, the associated areas are normalized to obtain valid associated results. The raw data from eight Beidou satellites are used to prove the effectiveness of the proposed algorithm.

Superscars for arithmetic point scatters II

Abstract We consider momentum push-forwards of measures arising as quantum limits (semiclassical measures) of eigenfunctions of a point scatterer on the standard flat torus ${\mathbb T}^2 = {\mathbb R}^2/{\mathbb Z}^{2}$ . Given any probability measure arising by placing delta masses, with equal weights, on ${\mathbb Z}^2$ -lattice points on circles and projecting to the unit circle, we show that the mass of certain subsequences of eigenfunctions, in momentum space, completely localizes on that measure and are completely delocalized in position (i.e., concentration on Lagrangian states). We also show that the mass, in momentum, can fully localize on more exotic measures, for example, singular continuous ones with support on Cantor sets. Further, we can give examples of quantum limits that are certain convex combinations of such measures, in particular showing that the set of quantum limits is richer than the ones arising only from weak limits of lattice points on circles. The proofs exploit features of the half-dimensional sieve and behavior of multiplicative functions in short intervals, enabling precise control of the location of perturbed eigenvalues.

2-D and 3-D Q-Compensated Image-Domain Least-Squares Reverse Time Migration Through the Hybrid Point Spread Functions and the Hybrid Deblurring Filter

Image-domain least-squares reverse time migration (IDLSRTM) through point spread functions (PSFs) is a suitable compromise between image quality and computational efficiency for inversion-based imaging tools. However, the conventional IDLSRTM method in acoustic approximation does not account for the subsurface attenuation effects, which may result in the unfocused migration image in attenuated geological environments. To incorporate the attenuation effects and improve the image quality, we develop a Q-compensated IDLSRTM method by using the hybrid PSFs rather than the acoustic PSFs as the blurring functions to deconvolve the adjoint migration image. These hybrid PSFs are estimated by a combination of computation between the viscoacoustic Born modeling and acoustic reverse time migration (RTM) using a series of uniform point scatterers. To further improve the quality of inverted images, we have applied a hybrid deblurring filter to the hybrid PSFs and acoustic RTM image, before the iterative inversion. Through some numerical examples of synthetic and field data, we have demonstrated that the proposed Q-IDLSRTM method combined with the hybrid PSFs and the hybrid deblurring filter can compensate for the attenuation effects and provide seismic images with improved spatial resolution and balanced image amplitudes. Relative to the conventional IDLSRTM methods through acoustic and hybrid PSFs, the proposed method can provide migration images with higher image resolution and better-balanced image amplitudes.

Lateral resolution enhanced interference microscopy using virtual annular apertures

The lateral resolution in microscopic imaging generally depends on both, the wavelength of light and the numerical aperture of the microscope objective lens. To quantify the lateral resolution Ernst Abbe considered an optical grating illuminated by plane waves. In contrast, the Rayleigh criterion holds for two point sources or point scatterers separated by a lateral distance, which are supposed to emit spherical waves. A portion of each spherical wave is collected by the objective lens and results in an Airy disc corresponding to a diffraction limited intensity point spread function (PSF). If incoherent illumination is employed the intensity PSFs related to different scatterers on an object are added resulting in the well-known Rayleigh resolution criterion. In interference microscopy instead of the intensity the electric field scattered or diffracted by an object will be affected by the transfer function of the optical imaging system. For a reflective object the lateral resolution of an interference microscope can be again characterized by the Abbe limit if the object under investigation is a grating. However, if two irregularities on a flat surface are being imaged the resolution no longer obeys the Rayleigh criterion. Instead, it corresponds to an optical system with an annular aperture and thus surpasses the prediction given by the Rayleigh criterion. This holds true for both, amplitude as well as phase objects, as it will be elucidated in this study by theoretical considerations, simulation results and an experimental proof of principle.

Analyzing of land subsidence by Sentinel-1 time-series images using PSInSAR method: A case study of Thai Nguyen, Vietnam

Natural disasters and human activities are now causing an increase in land subsidence, or surface displacement. The effects of land subsidence cause landslides and construction cracking. PSInSAR (Persistent Scatter Interferometry) was identified to estimate surface displacement from a time series of Synthetic Aperture Radar (SAR) images. This technique is a subset of the DInSAR (Differential Interferometric Synthetic Aperture Radar) method. In this article, the authors determined and analyzed land subsidence in Thai Nguyen Province, Vietnam, using time series Sentinel-1A data with VV polarization from July 2019 to December 2020 and the PSInSAR method. There are numerous mineral exploitation mines in Thai Nguyen Province. It is one of the causes of an unusual amount of land subsidence in the region. According to the results determined by the InSAR technique, the velocity of displacement along the line of sight (LOS) of the study area ranges from -23.2 mm per year to +21.0 mm per year. The analysis of time-series SAR images reveals anomalous land subsidence at persistent scatter (PS) points. By analyzing the time-series displacement at PS points using the StaMPS Visualizer tool, the land subsidence during the image acquisition period and surface displacement trends over time were determined. According to this, coal mining regions have the highest land subsidence values ranging from -40 mm to -60 mm. The city and mine regions of Thai Nguyen, where operations have stopped, are largely stable. In addition, the time-series analysis at PS points will allow us to identify unusual displacement points, enabling the implementation of early warning plans.

Prediction of groundwater level fluctuations using artificial intelligence-based models and GMS

Groundwater level fluctuations are one of the main components of the hydrogeological cycle and one of the required variables for many water resources operation models. The numerical models can estimate groundwater level (GWL) based on extensive statistics and information and using complex equations in any area. But one of the most important challenges in analyzing and predicting groundwater depletion in water management is the lack of reliable and complete data. For this reason, the use of artificial intelligence models with high predictive accuracy and due to the need for less data is inevitable. In recent years, the use of different numerical models has been noticed as an efficient solution. These models are able to estimate groundwater levels in any region based on extensive statistics and information and also various field experiments such as pumping tests, geophysics, soil and land use maps, topography and slope data, different boundary conditions and complex equations. In the current research, first, by using available statistics, information and maps, the groundwater level fluctuations of the Sonqor plain are simulated by the GMS model, and the accuracy of the model is evaluated in two stages of calibration and validation. Then, due to the need for much less data volume in artificial intelligence-based methods, the GA-ANN and ICA-ANN hybrid methods and the ELM and ORELM models are utilized. The results display that the output of the ORELM model has the best fit with observed data with a correlation coefficient equal to 0.96, and it also has the best and closest scatter points around the 45 degrees line, and in this sense, it is considered as the most accurate model. To ensure the correct selection of the best model, the Taylor diagram is also used. The results demonstrate that the closest point to the reference point is related to the ORELM method. Therefore, to predict the groundwater level in the whole plain, instead of using the complex GMS model with a very large volume of data and also the very time-consuming process of calibration and verification, the ORELM model can be used with confidence. This approach greatly helps researchers to predict groundwater level variations in dry and wet years using artificial intelligence with high accuracy instead of numerical models with complex and time-consuming structures.

Method of increasing the accuracy of the star sensor

A new algorithm for filtering distortions of the deep image of the starry sky is considered to improve the accuracy of determining the position of the star - the detection of the centroid. An increase in the accuracy of measuring the orientation parameters of the spacecraft by stellar sensors is being investigated. The method of calculations using the algorithm of exact estimation of the centroid is applied, restoring the function of the scatter of points from recorded astronomical images. Minimization of the effects of atmospheric turbulence and system noise on long-exposure images obtained by a ground-based telescope is proposed. The method was tested in the MATLAB environment for a real image of the deep sky recorded by the ground system.

Magnetoelectric‐Field Electrodynamics: Search for Magnetoelectric Point Scatterers

AbstractResonant scattering of electromagnetic (EM) waves by small particles is considered as one of the basic problems in metamaterial science. At present, special subwavelength resonators are considered as structural elements in chiral and bianisotropic metamaterials. There is a general consensus that these small scatterers behave like “artificial atoms” with strong electrical and magnetic responses and an interconnection between these responses. However, the observed effect of magnetoelectric (ME) coupling in these meta‐atoms is not associated with the near‐field manipulation properties caused by intrinsic magnetoelectricity. This arises the question whether ME point scatterers of EM radiation really exist. In this paper, we show that there are mesoscopic structures with electric and magnetic dipole‐carrying excitations that behave like point scatterers with their inherent magnetoelectricity. In such subwavelength resonators, coherent oscillations of the electric polarization and magnetization can be considered as quasistatic oscillations described by electrostatic (ES) and magnetostatic (MS) scalar wave functions. The ME resonance effect arises from the coupling of two, ES and MS, oscillations. The near fields of these resonators, called the ME near fields, are characterized by simultaneous violation of time reversal and inversion symmetry. In study of ME fields and EM problems associated with these fields, we put forward the concept of ME‐field electrodynamics.

Deep learning for hetero–homo conversion in channel-domain for phase aberration correction in ultrasound imaging

Echo imaging in ultrasound computed tomography (USCT) using the synthetic aperture technique is performed with the assumption that the speed of sound is constant in the system. However, tissue heterogeneity causes a mismatch between the predicted arrival time and the actual arrival time of the echo signal, which will result in phase aberration, leading to the quality degradation of the reconstructed B-mode image. The conventional correction methods that use the correlation of each different channel require the presence of strong point scatterers and involve the problem of local solutions due to excessive correction. In this study, we propose a novel approach to correcting the signal distortion due to sound speed heterogeneity using a deep neural network (DNN). The DNN was trained to convert the distorted radio frequency (RF) inputs for the heterogeneous medium to the distortion-free RF outputs for the homogeneous medium. The network with U-net architecture using ResNet-34 as a backbone was trained using the hetero–homo corresponding channel-domain RF data generated via numerical simulations. The trained network performed phase aberration correction in the channel-domain RF, with the B-mode images reconstructed with the corrected RF demonstrating a higher contrast and an improved resolution compared with uncorrected cases. It was also demonstrated that the DNN model is robust to both varied reflection intensities and varied sound speed heterogeneities. The successful results demonstrated that the proposed DNN-based method is effective for phase aberration correction in US imaging.

Research on the Derated Power Data Identification Method of a Wind Turbine Based on a Multi-Gaussian-Discrete Joint Probability Model.

This paper focuses on how to identify normal, derated power and abnormal data in operation data, which is key to intelligent operation and maintenance applications such as wind turbine condition diagnosis and performance evaluation. Existing identification methods can distinguish normal data from the original data, but usually remove power curtailment data as outliers. A multi-Gaussian-discrete probability distribution model was used to characterize the joint probability distribution of wind speed and power from wind turbine SCADA data, taking the derated power of the wind turbine as a hidden random variable. The maximum expectation algorithm (EM), an iterative algorithm derived from model parameters estimation, was applied to achieve the maximum likelihood estimation of the proposed probability model. According to the posterior probability of the wind-power scatter points, the normal, derated power and abnormal data in the wind turbine SCADA data were identified. The validity of the proposed method was verified by three wind turbine operational data sets with different distribution characteristics. The results are that the proposed method has a degree of universality with regard to derated power operational data with different distribution characteristics, and in particular, it is able to identify the operating data with clustered distribution effectively.

A Prospective Study of Differences in the Incidence of Radiation Pneumonitis in Elderly Patients between Volumetric Arc Modulated Therapy and Step-and-Shoot Intensity-Modulated Radiation Therapy

<h3>Purpose/Objective(s)</h3> Studies have shown that the incidence of radiation pneumonitis in elderly patients with thoracic tumor radiotherapy is high, and there is a significant correlation with smoking, pulmonary dysfunction, combined chemotherapy, radiation dose and radiation site. VMAT is considered a large-scale low-dose radiation therapy modality, while Step and Shot's IMRT is a small-scale low-dose radiation therapy modality. To test whether these two radiotherapy modalities have different incidences of radiation pneumonitis in elderly lung cancer patients, we conducted this prospective randomized controlled study. <h3>Materials/Methods</h3> A total of 50 elderly patients with non-small cell lung cancer (NSCLC) diagnosed from January 2019 to January 2020 were included and randomly divided into the VMAT group and the IMRT group according to the ratio of 1:1. We collected all irradiated lung volumes from 5 to 75 Gy at the interval of 5 Gy. The occurrence of radiation pneumonitis within six months after treatment was followed up. Fisher's exact test was used to analyze the incidence of radiation pneumonitis between the two groups. In addition, linear regression was used to analyze the fitting situation of radiation pneumonitis in the two groups with an interval of 5 Gy. <h3>Results</h3> The average age was 69 yrs, lung volume was 3310±837 ml, radiation dose was 68.8±8.3 Gy. The I to V levels of radiation pneumonitis were 12, 10, 2, 1, 0 in VMAT and 10, 12, 3, 0,0 in IMRT, respectively, P=0.610 with Fisher`s exact test. Judging from the coefficient of determination (R2) of the fitted model, no matter which grouping, the dose and the inflammatory ratio were linearly correlated and negatively correlated. From the distribution of the scatter plot, the fitting degree of IMRT is higher, and the scatter points are more concentrated on both sides of the curve, while VMAT is more diffuse. The IMRT fitting model is Y=42.19-3.14x, and the VMAT fitting model is Y=36.48-2.91x. The β coefficient (3.14) of the former is greater than that of the latter (2.91), indicating that with the increase of radiation dose, The inflammatory ratio decreased more rapidly. <h3>Conclusion</h3> In this small prospective pilot experiment, we did not directly find a difference in the incidence of radiation pneumonitis between the two radiation therapy modalities. However, in further analysis of the dose distribution in the lungs, we found that the trend of pneumonia incidences in the IMRT group was lower than that in the VMAT group as the dose increased. This study warrants further conduct in elderly patients to demonstrate which radiotherapy modality is more appropriate.

Inverse wave scattering in the time domain for point scatterers

Let Δα,Y be the bounded from above self-adjoint realization in L2(R3) of the Laplacian with n point scatterers placed at Y={y1,…,yn}⊂R3, the parameters (α1,…αn)≡α∈Rn being related to the scattering properties of the obstacles. Let ufϵα,Y and ufϵ∅ denote the solutions of the wave equations corresponding to Δα,Y and to the free Laplacian Δ respectively, with a source term given a pulse fϵ supported in ϵ-neighborhoods of the points in XN={x1,…,xN}, XN∩Y=∅. We show that, for any fixed λ>sup⁡σ(Δα,Y)≥0, there exists N∘≥1 such that the locations of the points in Y can be determined by the knowledge of a finite-dimensional scattering data operator FλN:RN→RN, N≥N∘. Such an operator is defined in terms of the limit as ϵ↘0 of the Laplace transform of ufϵα,Y(t,xk)−ufϵ∅(t,xk), k=1,…,N. We exploit the factorized form of the resolvent difference (−Δα,Y+λ)−1−(−Δ+λ)−1 and a variation on the finite-dimensional factorization in the MUSIC algorithm. Multiple scattering effects are not neglected; our model can be interpreted as the time-domain version of a frequency-domain scattering from an array of Foldy's point-like obstacles.

Symmetric flexural wave transmission and linear behaviour in a nonlinear system of two scatterers on a beam

The multiple scattering of flexural waves on a beam with two point scatterers attached to it, where one scatterer has a cubically nonlinear stiffness, is considered. The scattering behaviour is represented by first-order approximations of the reflection and transmission coefficients calculated with a perturbation approach, both at the fundamental frequency and at the generated third harmonic. Due to its nonlinearity and spatial asymmetry, such a system behaves in general nonreciprocally. By analyzing the fundamental-frequency and third-harmonic transmission coefficients, we derive conditions for particular scattering behaviours that result in transmission symmetry for the nonlinear system. We show that a sufficient condition for symmetric fundamental-frequency transmission is that the spacing between the scatterers is a multiple of half the incident wavelength, regardless of the scatterers’ properties, although the values of the reflection and transmission coefficients will still depend on the incident-wave amplitude. Such a response is also possible if the real and imaginary parts of the admittance of the linear scatterer satisfy a certain mathematical relation, regardless of spacing. A particular choice of lossless linear scatterer combined with the separation distance being a multiple of half a wavelength leads to fully linear behaviour for the nonlinear multiple scattering system.

Spherical Harmonic-Based Anisotropic Point Scatterer Models for Radar Applications Using Inverse Optimization

High-performance computing-based electromagnetic (EM) emulators are used to simulate real-time complex EM wave interactions between multiple radar targets, transmitters, and receivers. The radar cross section (RCS) of the radar targets are required to be stored as a table; however, the needed storage size increases dramatically with the angle and frequency sampling density. In this article, we present an innovative approach of constructing a concise spherical harmonic-based anisotropic point scatterer model that the emulators can use as part of the computations. The point scatterer model is constructed directly from the precomputed RCS data. First, we use only the monostatic RCS data and compute the spherical harmonic-based monostatic point scatterer model by solving a linear least-squares problem which has a group sparsity constraint. Then, we further compute the spherical harmonic-based bistatic point scatterer model using the full bistatic RCS data. The problem is formulated as a bilinear least-squares problem. The problem is solved using the normalized iterative algorithm, which linearly solves two parameters in a back and forth manner. The results show that the point scatterer model can effectively represent the bistatic RCS data of a radar target.

Correcting for Target Motion in Time-Reversal Spectral Focusing

It is well-known that an iterative time-reversal (TR) process, applied via a distributed sensing system, can be used to produce a space-time waveform that maximizes the energy scattered from a stationary target back to the sensors. The TR process accomplishes this by automatically focusing energy, both spatially and spectrally, on the stationary target. When scatterers are moving, however, the TR focusing can break down. This article shows how to modify the TR process so that it automatically focuses energy on a moving target. This new TR process automatically generates a distributed beam that: 1) follows the target as it moves and 2) enhances the target resonances by concentrating the energy spectrally. This focusing occurs without a priori knowledge of the target’s location or spectral response. The new TR algorithm is derived through a careful analysis of the idealized case of a single isotropic moving point scatterer. This article includes simulations that compare the TR focus both with and without the new modification. Although the simulations are carried out for the electromagnetic case, the theory applies equally well to the acoustic case when the target speed is significantly less than the ambient sound speed. Appendices are included with details of the calculations and with analysis of the range of relative velocities for which the modified TR process should be used.

Singularity-free treatment of delta-function point scatterers in two dimensions and its conceptual implications

In two dimensions, the standard treatment of the scattering problem for a delta-function potential, , leads to a logarithmic singularity which is subsequently removed by a renormalization of the coupling constant . Recently, we have developed a dynamical formulation of stationary scattering (DFSS) which offers a singularity-free treatment of this potential. We elucidate the basic mechanism responsible for the implicit regularization property of DFSS that makes it avoid the logarithmic singularity one encounters in the standard approach to this problem. We provide an alternative interpretation of this singularity showing that it arises, because the standard treatment of the problem takes into account contributions to the scattered wave whose momentum is parallel to the detectors’ screen. The renormalization schemes used for removing this singularity has the effect of subtracting these unphysical contributions, while DFSS has a built-in mechanics that achieves this goal.

Light propagation in a random three-dimensional ensemble of point scatterers in a waveguide: Size-dependent switching between diffuse radiation transfer and Anderson localization of light

Light transport in a disordered ensemble of resonant atoms placed in a waveguide is found to be very sensitive to the sizes of the cross section of a waveguide. Based on a self-consistent quantum microscopic model treating atoms as coherent radiating dipoles, we have shown that the nature of radiation transfer changes from Anderson localization regime in a single-mode waveguide to a traditional diffuse transfer in a multimode one. Moreover, the transmittance magnitude undergoes complicated steplike nonmonotonic dependence on the transverse sizes of a waveguide.

Level Repulsion for Arithmetic Toral Point Scatterers in Dimension 3

We show that arithmetic toral point scatterers in dimension three (“Šeba billiards on {mathbb R}^3/{mathbb Z}^3”) exhibit strong level repulsion between the set of “new” eigenvalues. More precisely, let Lambda := { lambda _{1}< lambda _{2} < ldots } denote the unfolded set of new eigenvalues. Then, given any gamma >0, |{i≤N:λi+1-λi≤ϵ}|N=Oγ(ϵ4-γ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\frac{|\\{ i \\le N : \\lambda _{i+1}-\\lambda _{i} \\le \\epsilon \\}|}{N} = O_{\\gamma }(\\epsilon ^{4-\\gamma }) \\end{aligned}$$\\end{document}as N rightarrow infty (and epsilon >0 small.) To the best of our knowledge, this is the first mathematically rigorous demonstration of a level repulsion phenomena for the quantization of a deterministic system.