Homogeneous Dielectric Cylinder Research Articles

Time domain inverse scattering for a buried homogeneous cylinder in a slab medium using NU-SSGA

A time-domain inverse scattering technique for reconstructing a buried homogeneous cylinder with arbitrary cross section in a slab medium is proposed. For the forward scattering, the FDTD method is employed to calculate the scattered E fields. Base on the scattering fields, these inverse scattering problems are transformed into optimization problems. The non-uniform steady state genetic algorithm (NU-SSGA) is applied to reconstruct the location shape and permittivity of the two-dimensional homogeneous dielectric cylinder. The NU-SSGA is a population-based optimization approach that aims to minimize the objective function between measurements and computer-simulated data. A set of representative numerical results is presented for demonstrating that the proposed approach is able to efficiently reconstruct the electromagnetic properties of homogeneous dielectric scatterer even when the initial guess is far away from the exact one. In addition, the effects of Gaussian noises on the image reconstruction are also investigated.

An iterative method for a two-dimensional inverse scattering problem for a dielectric

Abstract. The inverse problem under consideration is to reconstruct the shape of a homogeneous dielectric infinite cylinder from the far field pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We propose an inverse algorithm that extends the approach suggested and investigated by Kress and Rundell for the electrostatic case and by Ivanyshyn and Kress for the time-harmonic case when the scattering object is a perfect conductor. It is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem. We present the mathematical foundations of the method and exhibit its feasibility by numerical examples.

On a two-dimensional inverse scattering problem for a dielectric

The inverse problem under consideration is to reconstruct the shape of a homogeneous dielectric infinite cylinder from the far-field pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We propose an inverse algorithm that extends the approach suggested by Johansson and Sleeman [T. Johansson and B. Sleeman, Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern, IMA J. Appl. Math. 72 (2007), pp. 96–112] for the case of the inverse problem for a perfectly conducting scatterer. It is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem. We present the mathematical foundations of the method and exhibit its feasibility by numerical examples.

Time Domain Inverse Scattering for a Homogenous Dielectric Cylinder by Asynchronous Particle Swarm Optimization

Abstract In this paper, we propose a time domain inverse scattering technique for reconstructing the electromagnetic properties of a homogeneous dielectric cylinder based on the finite difference time domain method and the asynchronous particle swarm optimization (APSO). The homogeneous dielectric cylinder with unknown electromagnetic properties is illuminated by transverse magnetic pulse and the scattered field is recorded outside. By minimizing the discrepancy between the measured and estimated scattered field data, the location, shape, and permittivity of the dielectric cylinder are reconstructed. The inverse problem is resolved by an optimization approach and the global searching scheme APSO is then employed to search the parameter space. A set of representative numerical results is presented for demonstrating that the proposed approach is able to efficiently reconstruct the electromagnetic properties of the homogeneous dielectric scatterer even when the initial guess is far away from the exact one. In addition, the effects of Gaussian noises on imaging reconstruction are also investigated.

Time domain microwave imaging for a buried dielectric cylinder by dynamic differential evolution

This paper presents the studies of time domain inverse scattering for a two dimensional homogeneous dielectric cylinder buried in a half-space which are based on the finite d ifference time domain (FDTD) method and the dynamic differential evolution (DDE). For the forward scattering, the FDTD method is employed to calculate the scattered E fields, while for th e inverse scattering the DDE scheme is utilized to determine the shape, location and the permittivity of the buried cylindrical scatterer with arbitrary cross section. The subgirdding te chnique is implemented for the FDTD code in order to model the shape of the cylinder more smoothly. In additions, in order to describe an unknown cylinder with arbitrary cross section more effectively during the course of searching, the closed cubi c-spline expansion is adopted to represent the scatterer co ntour instead of the frequently used trigonometric series. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In addition, the effects of Gaussian noise on the reconstruction res ults are investigated. Numerical results show that even the measured scattered fields are contaminated with Gaussian noise, DDE is able to yield good reconstructed quality.

Time Domain Image Reconstruction for Homogenous Dielectric Objects by Dynamic Differential Evolution

This article presents the studies of the microwave image reconstruction of two-dimensional homogeneous dielectric cylinders that are based on the finite difference time domain method and dynamic differential evolution. For forward scattering, the finite difference time domain method is employed to calculate the scattered E-fields; for inverse scattering, the dynamic differential evolution scheme is utilized to determine the shape, location, and permittivity of the cylindrical scatterers with an arbitrary cross-section. The subgirdding technique is implemented for the finite difference time domain code in order to more smoothly model the shape of the cylinder. In addition, in order to more effectively describe an unknown cylinder with an arbitrary cross-section during the course of searching, the closed cubic-spline expansion is adopted to represent the scatterer contour instead of the frequently used trigonometric series. Numerical results demonstrate that, even when the initial guess is far from exact, good reconstruction can be obtained. In addition, the effects of Gaussian noise on the reconstruction results are investigated. Numerical results show that even the measured scattered fields are contaminated with Gaussian noise, and dynamic differential evolution is able to yield good reconstructed quality.

Gaussian beam scattering from a dielectric cylinder, including the evanescent region

The scattering of a two-dimensional Gaussian beam from a homogeneous dielectric cylinder is analyzed using a plane-wave spectrum. Special attention is given to the computation of the evanescent field of the beam and its effect in the scattering. A comparison is made between the evanescent field in Cartesian coordinates and in cylindrical coordinates as a sum of cylindrical waves. The field given by the cylindrical wave equation is found to converge spatially as we include more Bessel modes. The evanescent field incident on the dielectric cylinder is found to cause radiating waves to form and propagate outward.

TIME DOMAIN INVERSE SCATTERING OF A TWO-DIMENSIONAL HOMOGENOUS DIELECTRIC OBJECT WITH ARBITRARY SHAPE BY PARTICLE SWARM OPTIMIZATION

This paper presents a computational approach to the two- dimensional time domain inverse scattering problem of a dielectric cylinder based on the finite difference time domain (FDTD) method andthe particle swarm optimization (PSO) to d etermine the shape, location and permittivity of a dielectric cylinder. A pulse is incident upon a homogeneous dielectric cylinder with unknown shape and d ielectric constant in free space andthe scatteredfieldis record ed outside. By using the scattered field, the shape and permittivity of the dielectric cylinder are reconstructed. The subgridding technique is implemented in the FDTD code for modeling the shape of the cylinder more closely. In order to describe an unknown cylinder with arbitrary shape more effectively, the shape function is expandedby closedcubic- spline function insteadof frequently usedtrigonometric series. The inverse problem is resolvedby an optimization approach, andthe global searching scheme PSO is then employedto search the parameter space. Numerical results demonstrate that, even when the initial guess is far away from the exact one, goodreconstruction can be obtained . In addition, the effects of Gaussian noise on the reconstruction results are investigated. Numerical results show that even the measured scattered E fields are contaminated with some Gaussian noise, PSO can still yield goodreconstructedquality.

Electromagnetic Transverse Electric-Wave Inverse Scattering of a Two-Dimensional Dielectric Object by Genetic Algorithm

In this paper, an efficient optimization algorithm for solving the TE wave imaging problem of a two-dimensional homogeneous dielectric object is investigated. The problem of reconstructing both the shape and the relative permittivity of the cylinder from the measurement of scattered fields is numerically simulated. A homogeneous dielectric cylinder of unknown permittivity scatters the incident plane wave whose electric field vector perpendicular to z-axis (TE polarization) in free space and the scattered fields are recorded. Based on the boundary condition and the incident field, a set of nonlinear surface integral equations is derived. The imaging problem is reformulated into an optimization problem and the steady-state genetic algorithm is employed to reconstruct the shape and the dielectric constant of the object. Numerical results show that the permittivity of the cylinders can be successfully reconstructed even when the permittivity is fairly large.

An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations

The solution of the two-dimensional scattering problem for an homogeneous dielectric cylinder of arbitrary shape is considered. The numerical approach is based on a two-field system of integral equations solved by a Krylov subspace method. To accelerate and to improve the convergence of this solver, an efficient and robust preconditioner, based on the Calderón formulae, is developed. Several numerical simulations, for a wide range of physical parameters, validating the choice of this preconditioner are presented.

Reconstruction of homogeneous dielectric cylinders by a supervised learning system and space‐stepped GPR electromagnetic data

AbstractThis paper addresses the problem of reconstructing homogeneous cylinders buried in a known soil, starting from the electromagnetic data collected by a subsurface radar moving on the soil surface. The proposed approach makes use of neural networks to process some data extracted from the electromagnetic time responses of the subsoil. Some numerical results are given concerning a single cylinder of circular shape. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 353–357, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20303

A quasi‐Newton reconstruction algorithm for a complex microwave imaging scanner environment

An iterative complex permittivity reconstruction technique for two‐dimensional near‐field imaging is presented. A particular feature of the algorithm is that it takes into account the complicated environment of a circular 434 MHz microwave imaging scanner, which was developed to conduct biomedical imaging experiments. This is accomplished in a computationally efficient way by means of an embedding technique. The reconstruction technique is further based on a quasi‐Newton optimization scheme with approximate line search, in which the Hessian matrix is iteratively updated with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) formula. This way, second derivative information is exploited to a large extent. The technique is illustrated with complex permittivity reconstructions of homogeneous and inhomogeneous lossy dielectric cylinders of moderate and high contrast from simulated data.

Impossibility of Recovering a Scatterer's Shape by the First Version of the “linear sampling” Method

Abstract The version of the “linear sampling” method introduced in D. Colton, A. Kirsch, Inverse Problems, 12, 383, 1996, is analyzed. It consists into the attempt to recover a scatterer's contour by determining an indicator function from the knowledge of the scattered far field data. In particular, the indicator function is determined following the solution of a certain far field equation. We show that the far field equation to solve does not have (almost anywhere) a solution for two classes of objects: Perfectly conducting cylinders and homogeneous dielectric cylinders having circular cross section. It thus follows that the indicator function is “infinite” (almost) everywhere both inside and outside the scatterer and, consequently, does not represent the shape of the object.

Finite element analysis of two-dimensional EM scattering via Padé approximation for complex permittivity

[1] We present a computationally efficient algorithm which combines the finite element method with Padé approximation. The combination is used to solve the problem of transverse magnetic and transverse electric scattering from homogeneous lossy dielectric cylinders over a continuous range of the complex permittivity variable by requiring the finite element solution only at a single complex permittivity value. The proposed method is based on (1) assuming a power series expansion for the unknown solution vector, the excitation vector, and the system matrix, (2) substituting this into the system matrix equation, and (3) finding the recursion relation for the solution vectors.

A geometric optics model for high‐frequency electromagnetic scattering from dielectric cylinders

The cylinder is a fundamental shape for (2‐D) geophysical modeling, and cylindrical objects (e.g., pipes) are a common target for ground penetrating radar. This paper presents physical and theoretical model responses for a cylinder which provide insight into responses that can be anticipated in field data. We calculate the exact expressions for the scattered field components of an obliquely incident plane wave over an infinitely long homogeneous dielectric cylinder and express them in the time domain. We project the field on a horizontal plane over the dielectric cylinder and interpret them for a large range of permittivity contrasts. The high‐frequency approximation presented in this paper includes the processes of specular reflection and critical refraction, which satisfy Snell’s law. Assuming the velocity of the surface waves is equal to the velocity of the fastest medium, and assuming their travel path is the shortest one possible, we derive a geometric optics model which is valid over a wide range of permittivities. We show that the critically refracted response can be separated and measured from the specular reflections in the received signal. The identification and isolation of these different responses of the bistatic measurements enable a characterization of the target’s properties, such as its size, orientation, and formation. We confirm our theoretical results by comparison with measurements using a physical model.

Implementation of the matrix sparse decomposition technique to the scattering of two‐dimensional homogeneous dielectric cylinders

In this paper, a novel matrix‐thinning technique, matrix sparse decomposition (MSD) [Liu et al., 1998, 1999], has been implemented to solve the scattering of waves by two‐dimensional (2‐D) homogeneous dielectric cylinders for the first time. The MSD technique is a further development of the integral equation formulation of the measured equation of invariance (MEI) (IE‐MEI) [Rius et al., 1996a; Hirose et al., 1999a]. The MSD describes the local relationship between total currents and scattered fields rather than that between the scattered electric fields and the scattered magnetic fields in the IE‐MEI. The MSD directly thins a dense matrix from singular integral equations, such as method of moments (MOM), into two sparse matrices. The IE‐MEI method has difficulty in solving thin wire or thin plate structure problems. However, the MSD can do it without a hitch. Numerical examples for the scattering of 2‐D homogeneous dielectric circular and rectangular cylinders under both transverse magnetic and transverse electric plane wave incidences show that the MSD is a simple and effective technique to thin the MOM dense matrix.

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis.

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.

Inverse obstacle scattering for homogeneous dielectric cylinders using a boundary finite-element method

A method for reconstructing the shape and the permittivity of a penetrable homogeneous cylinder is described. It is the extension to penetrable cylinders of a previous work dealing with perfectly conducting cylinders. A low-frequency approximation is used to determine an initial guess. Then, a rigorous boundary integral method permits us to reconstruct arbitrary shapes and complex permittivities. It is based on an iterative conjugate gradient algorithm requiring the solving of two direct diffraction problems only. A simple and original regularization scheme is presented, which ensures the robustness of the algorithm. Numerical examples with lossy embedding media and additional random noise for both E/spl par/ and H/spl par/ polarizations are given.

A coherent scattering model to determine forest backscattering in the VHF-band

A coherent scattering model to determine the forest radar backscattering at VHF frequencies (20-90 MHz) has been developed. The motivation for studying this frequency band is the recent development of the CARABAS Synthetic Aperture Radar (SAR). In order to model the scattering from branches and trunks, homogeneous dielectric cylinders placed above a semi-infinite di-electric ground have been analyzed. An analytical approach, where the theoretically exact currents induced in an infinite cylinder are truncated, has been compared to a numerical solution using the finite difference time domain (FDTD) method. If the first-order coherent ray tracing is included in the analytical approach, the results match well with the numerically exact FDTD solution. The results show that, in order to determine the VHF-backscattering from a forest stand, the coherent ground interaction is an important part and has to be considered. In this paper, modeling results are in good agreement with CARABAS measurements.

Dielectrophoretic manipulation of rod-shaped viral particles

The dielectrophoretic manipulation of a rod-shaped virus, tobacco mosaic virus (TMV) by means of non-uniform AC electric fields is described. An expression is derived for the dielectrophoretic force on a homogeneous dielectric cylinder suspended in a liquid medium which shows that the dielectrophoretic force varies over a wide range of frequencies and medium conductivities. Measurements of the dielectrophoretic behaviour of TMV particles in microelectrode arrays have been made as a function of frequency and applied field strength. The results are shown to be in quantitative agreement with the derived expression for the dielectrophoretic force. By measuring the threshold field strength for the onset of dielectrophoresis, the force on a single TMV particle has been estimated. The results point to the potential use of dielectrophoresis for the collection and manipulation of sub-micron particles using microelectrode arrays.