Relative Permittivity Distribution Research Articles

Experimental evaluation of Luneburg lens using radial holes for relative permittivity distribution

In this paper, we describe a novel 3-D Luneburg lens using radial holes. A Luneburg lens can suppress the side lobe of the antenna and increase the gain. The prototype Luneburg lens was fabricated using a 30mm radius dielectric sphere with uniform permittivity by 2.1 and many holes by 1mm radius, called radial holes drilled vertically on the sphere surface. The relative permittivity distribution of the Luneburg lens is realized by changing the number and depth of five types of holes. To confirm the effectiveness of the fabricated Luneburg lens, the far-field radiation pattern at 25GHz was measured using a flanged rectangular waveguide as a wave source. It achieved a high gain of 22.4dBi. The measured radiation pattern generally agreed well with the theoretical radiation pattern of the Luneburg lens, and the validity of the Luneburg lens with radial holes at the quasi-millimeter wave was confirmed. It can be used for beam steering in 5G/6G base stations.

Full waveform inversion of common-offset ground-penetrating radar based on a special source wavelet and multiple integral wave-field transform

Ground-penetrating radar (GPR) can obtain the geological information by using the electrical difference between the abnormal body and the background field. Full waveform inversion (FWI) can process radar data and obtain a more accurate distribution of relative permittivity. However, when the electrical parameters between the anomalous body and the background field are quite different, the wavefield information is seriously disturbed. In that case, the FWI method can not obtain accurate physical parameters, which is worse for common-offset GPR because of the lack of illumination angles and of wavenumber coverage. To solve this problem, a novel GPR FWI method is proposed to improve the stability of inversion using a special source wavelet and multiple integral wave-field transform. The manuscript is composed as follows: first, a special wavelet is used to improve the gradient in FWI. Then the integral wave-field transform can provide low-frequency information of data. This process can make full use of the low-frequency components hidden in the original data, obtain the large-scale relative permittivity distribution structure, and reduce the instability of the full waveform inversion. Finally, three simulation examples and a practical example verify the effectiveness of the method. Especially when there is a large difference between the dielectric parameters of the abnormal body and the background field (more than ten times or even dozens of times), the proposed FWI algorithm can still obtain stable results.

Sub-surface stratification and dielectric permittivity distribution at the Chang’E-4 landing site revealed by the lunar penetrating radar

Context.In 2019, China’s Chang’E-4 (CE-4) probe landed on the far side of the Moon: a first in lunar exploration. The Lunar Penetrating Radar (LPR) mounted on the Yutu-2 rover allows the mapping of the near-surface structure and the dielectric permittivity of the landing area. The dielectric properties of the lunar soil affect the propagation of the LPR signals, which can be used to infer the depth of sub-surface boundaries and derive the composition of the component materials.Aims.Our objectives are to estimate the fine-resolution spatial distribution of relative permittivity and to improve the interpretation of the geological processes combined with the radargram of the CE-4 landing area.Methods.We used a modified method that combines the F-K migration and the minimum entropy of the ground penetrating radar (GPR) signals to estimate the velocity and permittivity values; this has the advantage of obtaining the appropriate velocity and permittivity, even with the incomplete or unnoticeable hyperbolic curves in the radar imageResults.The sub-surface stratification of the CE-4 landing area is seen in the first 31 lunar days of the LPR data. A fine-resolution dielectric permittivity profile ranging from ~2.3 to ~6.3 is obtained with our method, and the actual depths of the observed prominent sub-surface interfaces are determined, giving a maximum average depth of ~38 m. The thickness of the regolith layer is in the range of ~5.7–15.6 m, with an average of 11.8 m. The permittivity of the near-surface regolith (<30 cm) is ~2.78 ± 0.01, the bulk density is 1.57 ± 0.01 g cm−3, which is close to the results of ~1.61 g cm−3at the Apollo 15 landing area. The permittivity map is consistent with the radargram; the regolith and the paleo-regolith layer have relatively low permittivity and low echo strengths, while the rock debris has high permittivity and shows strong echos in the radargram. Two buried craters of different diameters beneath the navigation sites 4–11 and 16–31 are revealed in the radar profile. The permittivity distribution map can show detailed variations of material properties both inside and outside craters.

Solving 2D Poisson's equation based on conditional generative adversarial network

AbstractThe numerical simulation of electromagnetic problems is usually complex and time‐consuming, so a fast and accurate solver is urgently needed. In this paper, a deep learning method based on conditional generative adversarial network (CGAN) is used to solve the 2D Poisson's equation in electrostatic field. The relative permittivity distribution and source charge distribution in the two dimensional region are regarded as label of CGAN, and the potential distribution is the real image or generated image corresponding to the label. This deep learning network can be trained by reasonably designing the loss functions of generator and discriminator, and based on a large amount of samples obtained by the finite difference method. The average relative prediction error of the trained CGAN for all samples is less than 0.5%, with a significant reduction in prediction time, while that of convolution neural network (CNN) is less than 1.5%. Furthermore, the average relative prediction error of CGAN is less than 1% for the scenes different from those of training and testing samples, including triangle, square, and pentagon. The prediction results indicate that CGAN has stronger learning ability and fast prediction speed, and can be used as a fast solver for electromagnetic numerical problems.

Rock Location and Property Analysis of Lunar Regolith at Chang’E-4 Landing Site Based on Local Correlation and Semblance Analysis

The Lunar Penetrating Radar (LPR) onboard the Yutu-2 rover from China’s Chang’E-4 (CE-4) mission is used to probe the subsurface structure and the near-surface stratigraphic structure of the lunar regolith on the farside of the Moon. Structural analysis of regolith could provide abundant information on the formation and evolution of the Moon, in which the rock location and property analysis are the key procedures during the interpretation of LPR data. The subsurface velocity of electromagnetic waves is a vital parameter for stratigraphic division, rock location estimates, and calculating the rock properties in the interpretation of LPR data. In this paper, we propose a procedure that combines the regolith rock extraction technique based on local correlation between the two sets of LPR high-frequency channel data and the common offset semblance analysis to determine the velocity from LPR diffraction hyperbola. We consider the heterogeneity of the regolith and derive the relative permittivity distribution based on the rock extraction and semblance analysis. The numerical simulation results show that the procedure is able to obtain the high-precision position and properties of the rock. Furthermore, we apply this procedure to CE-4 LPR data and obtain preferable estimations of the rock locations and the properties of the lunar subsurface regolith.

Equivalent Planar Lens Ray-Tracing Model to Design Modulated Geodesic Lenses Using Non-Euclidean Transformation Optics

This article describes a design procedure that enables a time-efficient evaluation of the focusing properties of modulated geodesic lenses using ray tracing on the equivalent gradient-index planar lens. The method uses transformation optics to define the equivalent planar relative permittivity distribution of axially symmetric surfaces and a ray-tracing model to evaluate the phase distribution in the aperture of the lens. This approach is of interest to optimize modulated geodesic lenses having polynomial profiles, reducing their height while preserving their wideband behavior and wide angular focusing properties. The approach is validated with a specific lens design. The profile is optimized at 30 GHz, while the focusing properties are monitored over the complete Ka up-link frequency band allocated to satellite communications (i.e., 27.5–31 GHz). The manufactured prototype produces 21 beams equally spaced every 7.5° over the extended angular range of ±75°. The ray-tracing model results are compared in detail with the corresponding full-wave model results and experimental data. The manufactured design has return loss better than 15 dB over a fractional frequency bandwidth larger than 30%, in line with the predictions. Excellent scanning properties are demonstrated over an angular range of ±60° with scan losses below 1 dB and good pattern stability, including on sidelobe levels. A height reduction by a factor of 4, when compared to a conventional geodesic lens, is demonstrated with this specific design.

A Preliminary study of three-phase column flotation process monitoring using electrical capacitance volume tomography

A preliminary study of three-phase column flotation process using electrical capacitance volume tomography (ECVT) has been conducted. The purpose of this study is to investigate the possibility of ECVT method as a monitoring system by correlating the relative permittivity distribution (or three-dimensional image) with metallurgical performance (recovery of the process). Experiments were performed in a laboratory-scale flotation column with ECVT sensor embedded outside the pipe wall on the collection zone. The feed used was a synthetic ore consisting of sphalerite and silica with the purity of 99%. Process parameter used was air flow rate ranging from 2-4 l/m which each process was conducted for 10 minutes. The results showed that the ECVT method could observe the dynamic process of flotation, specifically in monitoring a feeding process and a separation process. They were indicated by increased and decreased relative permittivity distributions respectively. Relative permittivity signal and metallurgical performance have a good correlation and showed a positive correlation. These results show a prospect of ECVT method as the monitoring system in the flotation process, but further works need to be done for this monitoring system.

비균일 지하에 묻혀있는 유전체 충진 비금속관에 의한 지표투과레이다 응답의 특성 변화

The variation of ground-penetrating radar(GPR) signal characteristics from dielectric-filled nonmetallic pipes buried in inhomogeneous ground are compared through a numerical simulation. The relative permittivity distribution of the ground is generated by using the continuous random media(CRM) technique. As a function of the relative permittivity of the material filling the nonmetallic pipe buried in the ground media, GPR signals are simulated by using the finite-difference time-domain(FDTD) method. We show that, unlike the case for homogeneous ground, the distortion characteristics of the reflected waves caused by the front convex surface and the rear concave surface of the pipe buried in inhomogeneous ground are different depending on the permittivity contrast between the inside and outside of the pipe.

Application of ground penetrating radar to detect tunnel lining defects based on improved full waveform inversion and reverse time migration

ABSTRACTGround penetrating radar is a popular approach to detect defects in tunnel lining. However, the interpretation is usually based on the original image, which is very different from the real shape of the lining defects. Full waveform inversion and reverse time migration are helpful to solve this problem. Full waveform inversion can invert the relative permittivity distribution and reverse time migration can migrate reflection events to their proper locations. Traditional full waveform inversion method is only applicable to cross‐hole ground penetrating radar data or surface multi‐offset ground penetrating radar data. We propose an improved full waveform inversion method which offers satisfactory inversion result for surface common‐offset radar. The forward modelled waveform and the objective function curve show that our new full waveform inversion method is much more accurate than traditional full waveform inversion for common‐offset radar. Traditional reverse time migration has weaker amplitude with increasing depth; we use an energy matrix to improve the imaging effect. Moreover, our reverse time migration is based on the relative permittivity distribution obtained from full waveform inversion, which provides more accurate imaging result. Through several numerical and engineering examples, we discuss the application of both methods in tunnel lining inspection. The results show that for tunnel lining without rebars, the combined methods can give satisfactory imaging results. But the image quality deteriorates rapidly when dealing with rebars.

Effect of space charge layers on the electric field enhancement at the physical interfaces in power cable insulation

This paper intends to investigate the effect of two vented water trees w 1 and w 2 growing simultaneously from both conductor and insulation screens of medium voltage cable in the presence or not of space charge, on the electric field distribution. +12 kV DC voltage has been applied. Such simulation has been implemented under Comsol Multiphysics® environment using the finite element method. Particular interest is assigned to the effect of the polarity, density and layers thickness of the space charge as well as to the behavior of this charge initially accumulated at water trees tips. Note that for the polarity influence, the four polarities configurations related to the space charge accumulated at w 1 and w 2 have been considered. As results, the electric field enhancement at the semiconductor layers especially close to the water tree defect is strongly dependent not only upon the relative permittivity distribution inside water trees, but also on the amount, density and layers thickness of the space charge. In the absence of space charge, we show that, with regard to the inhomogeneous (linear and parabolic) distribution of the permittivity, the homogeneous one causes much more local enhancement of electric field at the trees tips. Moreover, the electric field distribution depends on the geometrical parameters (length and width) and shape of trees; the spherical form engenders a higher electric field than elliptical one. In addition, the association of the space charge could lead to the initiation of the electric trees even at lower voltages. Furthermore, the initiation of electrical trees from the physical interfaces is more probable in the case of opposite polarities especially for negative-positive configuration. Such electrical trees start not only from the tip but also from the water tree root (interface of treed region, un-treed one and semiconductor) which is particularly more vulnerable than inside.

A Frequency-Hopping Subspace-Based Optimization Method for Reconstruction of 2-D Large Uniaxial Anisotropic Scatterers With TE Illumination

Due to the nonlinear property of large uniaxial anisotropic scatterers, many iterative optimization methods have a high risk of being trapped in local minima. In this paper, a frequency-hopping subspace-based optimization method (SOM) is proposed to reconstruct the relative permittivity distribution of 2-D large uniaxial anisotropic scatterers with transverse electrical (TE) illumination. This hybrid method utilizes the results obtained at lower frequency to provide good initial guesses for higher frequency reconstruction, which reduces the occurrence of local minima for the inversion at the higher frequency. For lower frequency, it can only obtain coarse resolution image although it is unable to show the details of the scatterers. However, this coarse image provides a priori information for the reconstruction at higher frequencies to get finer resolution. Numerical examples demonstrate that the proposed hybrid method can effectively rebuild large uniaxial anisotropic scatterers (six wavelengths) with higher stability compared with conventional SOM that uses only single-frequency data.

Fabrication and simulation of permittivity graded materials for electric field grading of gas insulated power apparatus

An innovation for the higher performance and reliability of electric power apparatus can be brought about by a novel technique on electrical insulating materials. The application of functionally graded materials (FGM) with spatial distribution of dielectric permittivity in solid insulator is an effective technique to contribute to the above innovation, because FGM can control the electric field distribution with a simple shape. In this paper, we investigated the fabrication and simulation techniques of FGM with various spatial distributions of dielectric permittivity using centrifugal force. Firstly, we developed a simulation technique to estimate the dielectric permittivity distribution of FGM by considering the particle movement in a viscous fluid under centrifugal force. Secondly, based on the simulation technique, we fabricated FGM samples with various relative permittivity distribution and confirmed the validity of the simulation technique. Consequently, the fabrication results provided a good agreement with the simulation results.

電気キャパシタンス・トモグラフィ法を用いた溶融プラスチック流れ場の断面温度分布計測

This study has launched a concept to measure real time two-dimensional temperature distribution non-invasively by a combination of electrical capacitance tomography (ECT) technique and a permittivity-temperature equation for melting polyethylene (PE). The concept has two steps which are the relative permittivity calculation from the measured capacitance among the many electrodes by ECT technique, and the temperature distribution calculation from the relative permittivity distribution by permittivity-temperature equation. ECT sensor with 12-electrode was located an injection molding machine, which is designed to measure and visualize the cross sectional relative permittivity distribution. The images of the relative permittivity distribution were successfully reconstructed at every time step during the process. The images indicate that the value of wall side is difference from the centre area value.

Noninvasive real-time 2D imaging of temperature distribution during the plastic pellet cooling process by using electrical capacitance tomography

This study has launched a concept to image a real-time 2D temperature distribution noninvasively by a combination of the electrical capacitance tomography (ECT) technique and a permittivity-temperature calibration equation for the plastic pellet cooling process. The concept has two steps, which are the relative permittivity calculation from the measured capacitance among the many electrodes by the ECT technique, and the temperature distribution imaging from the relative permittivity by the permittivity-temperature calibration equation. An ECT sensor with 12 electrodes was designed to image the cross-sectional temperature distribution during the polymethyl methacrylate pellets cooling process. The images of temperature distribution were successfully reconstructed from the relative permittivity distribution at every time step during the process. The images reasonably indicate the temperature diffusion in a 2D space and time within a 0.0065 and 0.0175 time-dependent temperature deviation, as compared to an analytical thermal conductance simulation and thermocouple measurement.

Quantitative cross-sectional measurement of solid concentration distribution in slurries using a wire-mesh sensor

Wire-mesh sensors have so far been widely applied in gas–liquid flows where resistance or capacitance distributions are measured and converted into gas or liquid holdup distributions. In this work we report on the qualification of the wire-mesh imaging technique for the measurement of cross-sectional solid concentrations in solid–liquid mixtures. As the dielectric constants of solid particles are different from those of gas, water or oil in the flow, measuring this property can be used as an indication of solid distribution. Experiments were performed in a stirred tank of 100 mm diameter equipped with a capacitance wire-mesh sensor. The wire-mesh sensor was operated at an acquisition speed of 4000 frames per second and has a spatial resolution of 6.25 mm. As solids we used silica sand particles (diameter ~250 μm) which were suspended in water in a volume concentration range of 1% to 35% to form slurries. By varying the stirring speed, different solid concentration distributions were produced and investigated. In order to convert the measured relative permittivity distribution into a solid concentration distribution, an empirical approach was employed.

J0510203 インピーダンス計測による高分子の比誘電率と温度との関係([J051-01]流れの高次元化可視化に向けて(2),流体工学部門)

Temperature is one of the important factors in polymer molding processes. A non-intrusive technique which obtains temperature distribution in dies or nozzles is expected. Electrical Capacitance Tomography (ECT) is a suitable system for satisfying the requirement to acquire two-dimensional capacitance distribution. However, it also draws relative permittivity distribution because capacitance is a function of relative permittivity. The relative permittivity distribution probably indicates the temperature distribution, because relative permittivity has temperature dependence. There are number of previous reports about temperature dependence of polymeric relative permittivity. The temperature ranges are usually lower than the point where polymers are melted. We describe polymeric relative permittivity under such high temperature. Capacitance is determined with an impedance analyzer which has a two-electrode cell, and relative permittivity is calculated from the capacitance. Sample polymers are polypropylene (PP), polycarbonate (PC) and polymethyl methacrylate (PMMA). The temperature dependence is changed complicatedly. It depended on the polarity existence or the measuring frequency. Some points where showed same values of relative permittivity in spite of different temperature were found. Capacitance distribution does not mean temperature distribution directly. There is necessary of considering new measurement method with a combination of relative permittivity and other electrical properties, such as dielectric loss or dielectric loss tangent.

Microwave imaging of dielectric cylinders from experimental scattering data based on the genetic algorithms, neural networks and a hybrid micro genetic algorithm with conjugate gradient

The application of three techniques for the reconstruction of the permittivity profile of cylindrical objects from scattered field measurements is studied in the present paper. These approaches are applied to two-dimensional configurations. After an integral formulation, a discretization using the method of moments (MoM) is applied. Considering that the microwave imaging is recast as a nonlinear optimization problem, a cost functional is defined by the norm of a difference between the measured scattered electric field and that calculated for an estimated relative permittivity distribution. Thus, the permittivity profile can be obtained by minimizing the cost functional. In order to solve this inverse scattering problem, three techniques are employed. The first is based on a basic real coded genetic algorithms (GAs). The second is a hybrid technique (mGA-CG) which is based on a conjunction of a micro genetic algorithm (mGA) approach with the conjugate gradient based method (CG). The third is an application of an artificial neural network (ANN) having multilayered perceptrons architecture (MLPs). Three algorithms: conjugate gradient with Polak–Ribiere updates (CGP), Levenberg–Marquardt (LM) and gradient descent (GD) are used to train the ANN. Computer simulations of these methods are performed for reconstruction of circular cylinders against laboratory-controlled microwave data.

Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method

The aim of the present work is to validate a full vectorial electromagnetic inverse scattering algorithm against experimental data. Data were provided courtesy of Institut Fresnel, Marseille, France. These data were carried out in an anechoic chamber and correspond to different canonical targets as well as one mysterious object which is known only by experimentalists who measured the associated scattered field. The inverse algorithm was first developed in the optical domain and is adapted herein to the microwave domain. It is an iterative approach where the parameter of interest, namely the relative permittivity distribution, is updated gradually by minimizing a cost function describing the discrepancy between data and those that would be obtained via a forward solver for the best available estimate of the relative permittivity. The forward solver is based on the coupled dipole method which was introduced in the seventies to study the scattering of light by non-spherical dielectric grains. The forward and inverse schemes are briefly described and various examples are presented that demonstrate the efficiency of the inverse algorithm.