Inhomogeneous Dielectric Objects Research Articles

Stable FFT-JVIE solvers for fast analysis of highly inhomogeneous dielectric objects

A stable volume integral equation formulation based on equivalent volumetric currents is presented for modeling electromagnetic scattering of highly inhomogeneous dielectric objects. The proposed formulation is numerically solved by means of Galerkin method of moments on uniform grids, allowing for acceleration of the matrix–vector products associated with the iterative solver with the help of FFT. In addition, the pertinent volume–volume Galerkin inner products are reduced to purely surface–surface integrals with smoother kernels, allowing for highly accurate and fast computation by readily available sophisticated cubatures. Numerical results demonstrate the convergence properties of the algorithm for scatterers with high dielectric contrast. In addition, we describe a road-map for Magnetic Resonance-specific volume integral equations fast solvers based on the proposed algorithm.

VIE-FG-FFT for Analyzing EM Scattering from Inhomogeneous Nonmagnetic Dielectric Objects

A new realization of the volume integral equation (VIE) in combination with the fast Fourier transform (FFT) is established by fitting Green’s function (FG) onto the nodes of a uniform Cartesian grid for analyzing EM scattering from inhomogeneous nonmagnetic dielectric objects. The accuracy of the proposed method is the same as that of the P-FFT and higher than that of the AIM and the IE-FFT especially when increasing the grid spacing size. Besides, the preprocessing time of the proposed method is obviously less than that of the P-FFT for inhomogeneous nonmagnetic dielectric objects. Numerical examples are provided to demonstrate the accuracy and efficiency of the proposed method.

Weakly Convex Discontinuity Adaptive Regularization for Microwave Imaging

Reconstruction of inhomogeneous dielectric objects from microwave scattering is a nonlinear and ill-posed inverse problem. In this communication, we develop a new class of weakly convex discontinuity adaptive (WCDA) models as a regularization for quantitative microwave tomography. We show that this class includes the Huber regularizer and we show how to combine these methods with electromagnetic solvers operating on the complex permittivity profile. 2D reconstructions of objects from the Institute Fresnel database and experimental data at a single frequency demonstrate the effectiveness of the proposed regularization even when employing far less transmitters and receivers than available in the database.

Marching‐on‐in‐degree solution of volume integral equations for analysis of transient electromagnetic scattering by inhomogeneous dielectric bodies with conduction loss

AbstractA time‐domain volume integral equation (TDVIE) solved by the marching‐on‐in‐degree (MOD) scheme is presented for the analysis of transient electromagentic scattering from a three‐dimensional inhomogeneous dielectric object of arbitrary shape with conduction loss.The volume of the object is discretized into curvilinear hexahedral elements, and conformal basis functions are utilized to expand the spatial variation of the electric flux density in the TDVIE. The transient variation of the electric flux density is expressed in term of weighted Laguerre polynomials so that the first, second, and third temporal derivatives of the electric flux density can be handled analytically. By applying the Galerkin spatial and temporal testing procedure, the TDVIE is converted into a recursive matrix equation in terms of the orders of the weighted Laguerre polynomials. Because of the elimination of the time variable in the MOD scheme, the proposed algorithm overcomes the late‐time instability problem that often occur in the conventional marching‐in‐on‐time (MOT) approach. Numerical results are presented to illustrate the good performance of the TDVIE algorithm. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1104–1109, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25897

A novel formulation of the volume integral equation for electromagnetic scattering

A novel method to solve the volume integral equation involving inhomogeneous and anisotropic permittivity and permeability dielectric objects is introduced. A curl-conforming edge element is used to model the electric field distributions. This simplifies the process of finding the matrix representation of the integral equations. Furthermore, the reciprocity preserving method to solve the volume integral equation is presented based on the reciprocity theorem. By introducing a delta function in the volume integral equation, this method decomposes one complicated integral into several simple integrals, which simplifies the calculation of integration. MLFMA is utilized to accelerate the matrix vector product process for large problems. Duffy's method is applied for all the surface and volume singular integrations. Representative numerical results are shown to be excellent.

Well-posedness of domain integral equations for a dielectric object in homogeneous background

An analysis of the mapping properties of three commonly used domain integro-differential operators for electromagnetic scattering by an inhomogeneous dielectric object embedded in a homogeneous background is presented in the Laplace domain. The corresponding three integro-differential equations are shown to be equivalent and well-posed under finite-energy conditions. The analysis allows for non-smooth changes, including edges and corners, in the dielectric properties. The results are obtained via the Riesz-Fredholm theory, in combination with the Helmholtz decomposition and the Sobolev embedding theorem.

Study on Electromagnetic Problems Involving Combinations of Arbitrarily Oriented Thin-Wire Antennas and Inhomogeneous Dielectric Objects with A Hybrid MoM-FDTD Method

In this paper, a novel iteration procedure of the hybrid method combining the frequency-domain MoM with the FDTD method is first presented. And then the microwave network theory is introduced into the MoM-FDTD method to calculate the mutual impedance and the isolation between antennas located near lossy dielectric objects. Numerical results have a good agreement with those obtained by the software FEKO, which validates the EMC analysis method presented in this paper. Last, interactions between human head and antenna are analyzed by the hybrid MoM-FDTD method. Not only are the near-field distributions in human head presented but also the disturbed far-field patterns of the antenna. The hybrid method in this paper supplies an effective approach to analyze the performance of antennas near inhomogeneous dielectric objects.

Precorrected-FFT solution of the volume Integral equation for 3-D inhomogeneous dielectric objects

This work presents a fast solution to the volume integral equation for electromagnetic scattering from three-dimensional inhomogeneous dielectric bodies by using the precorrected-fast Fourier transform (FFT) method. The object is modeled using tetrahedral volume elements and the basis functions proposed by Schaubert et al. are employed to expand the unknown electric flux density. The basis functions are then projected onto a fictitious uniform grid surrounding the nonuniform mesh, enabling the FFT to be used to speed up the matrix-vector multiplies in the iterative solution of the matrix equation. The resultant method greatly reduces the memory requirement to O(N) and the computational complexity to O(NlogN), where N is the number of unknowns. As a result, this method is capable of computing electromagnetic scattering from large complex dielectric objects.

A parallel analysis of the scattering from inhomogeneous dielectric bodies by the volume integral equation and the precorrected‐FFT algorithm

AbstractIn this paper, a parallel implementation of the precorrected fast Fourier transform (FFT) algorithm is presented to efficiently solve the volume‐integral equation for scattering from inhomogeneous dielectric objects. Several examples are given to demonstrate the efficiency and correctness of the message‐passing interface (MPI)‐based parallelization algorithm. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 77–79, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20214

Volume‐integral‐equation‐based analysis of transient electromagnetic scattering from three‐dimensional inhomogeneous dielectric objects

A novel technique for analyzing transient electromagnetic scattering from three‐dimensional inhomogeneous dielectric targets is proposed. An integral equation for the electric flux density throughout the scatterer is constructed by invoking the electromagnetic volume equivalence principle. This equation is solved using a marching‐on‐in‐time scheme in which the electric flux density is expanded in space by volumetric rooftop basis functions defined on a tetrahedral mesh and in time by piecewise polynomials. The proposed method is validated for representative dielectric structures by comparison via Fourier transformation of scattering data obtained with this method and various frequency domain techniques.

Microwave imaging within the second-order Born approximation: stochastic optimization by a genetic algorithm

This paper addresses the problem of reconstructing the location, shape, and dielectric permittivity distribution of an inhomogeneous dielectric object from measurements of the field scattered by the object. The object is an inhomogeneous infinite cylinder of arbitrary cross section illuminated by a transverse magnetic incident electric field. The approach is based on the Lippmann-Schuringer integral equation for the electromagnetic inverse scattering problem, approximated by applying the second-order Born approximation, which allows an extension of the range of contrast values that can be accurately imaged. The numerical approach is developed in the spatial domain and makes use of a multi-illumination multiview processing. In particular, the inverse problem is recast in a global nonlinear optimization problem (including a penalty function), solved by a stochastic method based on a genetic algorithm. In this paper, the mathematical formulation of the approach is described and the results of several dielectric reconstructions are reported, including comparisons with analogous reconstructions performed within the linearized (first-order) Born approximation.

A new approach to the 2D inverse electromagnetic medium scattering problem: reconstruction of anisotropic objects

A new method for reconstructing the material properties of inhomogeneous lossy dielectric biaxial cylindrical objects is presented. The material properties are reconstructed using scattering data from time-harmonic electromagnetic plane waves with the electric field vector perpendicular to the cylindrical object (TE-polarization). The inverse scattering problem formulated as a nonlinear optimization problem is numerically solved using a variable metric method. This method involves exact first-order gradients, Numerical examples illustrate the efficiency of the algorithm.

Image reconstruction from TE scattering data using equation of strong permittivity fluctuation

Compared to the TM case, the inverse scattering problem for the TE incident field is more complicated due to its stronger nonlinearity. This work provides an effective method for the reconstruction of two-dimensional (2-D) inhomogeneous dielectric objects from TE scattering data. The algorithm applies the distorted Born iterative method to the integral equation of strong permittivity fluctuation to reconstruct scatterers with high-permittivity contrast. Numerical simulations are performed and the results show that the distorted Born iterative method (DBIM) for strong permittivity fluctuation (SPF-DBIM) converges faster and can obtain better reconstructions for objects with larger dimensions and higher contrasts in comparison with ordinary DBIM. A frequency hopping technique is also applied to further increase the contrast.

A novel approach to the 2D-TM inverse electromagnetic medium scattering problem

The 2D inverse electromagnetic scattering problem of reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is considered. The material properties are reconstructed using scattering data from time-harmonic TM-polarized electromagnetic plane waves. A novel method which ensures physically meaningful material properties is proposed to numerically solve this nonlinear optimization problem. Numerical examples illustrate the efficiency of the algorithm.

Image reconstruction from real scattering data using an iterative scheme with incorporated a priori information

The two-dimensional inverse electromagnetic-scattering problem of reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is considered. The material properties are reconstructed from measured far-field scattering data, provided by the USAF Rome Laboratory Electromagnetic Measurement Facility in Ipswich. The targets in the Ipswich data set include perfectly electrically conducting (PEC) targets, penetrable (PEN) targets, and hybrid targets. A new method, which incorporates a priori information about the material properties, is proposed to solve the nonlinear inverse-scattering problem.

Scattering of EM waves by inhomogeneous dielectrics with the use of the method of moments and 3-D solenoidal basis functions

The solenoidal basis functions defined on tetrahedrons are modified to permit the analysis of the problem of scattering of electromagnetic waves by inhomogeneous dielectric objects. In the analysis of the scattering of EM plane waves by an inhomogeneous dielectric cube, we compare our results with those obtained using pulse basis functions. We also apply our method in the analysis of the scattering of EM plane waves by an inhomogeneous dielectric sphere, and compare the results with those obtained using the Mie's series. Finally, we apply our method in the analysis of the electromagnetic fields induced inside human tissue. We compare these results with those obtained using pulse basis functions. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 42–46, 1999.

カラーヒストグラムからの直線検出に基づいた色ベクトル推定法

This paper describes a method for estimating the color vectors of a light source and an object surface by means of line detection from a histogram of the color image. The object is supposed to be an inhomogeneous dielectric object such as plastics with a smooth surface. First, we suggest the characteristics of the color histogram in a RGB space. The histogram forms a combination of two straight clusters of highlight pixels by specular reflection, and matte pixels by diffuse reflection. The estimation of two color vectors is then reduced to finding the gradients of straight lines for the two clusters. Next, basic algorithms for extracting a line from a cluster are shown using the principal component analysis and Hough transform. Moreover, an effective algorithm is proposed based on iteratively splitting and merging the histogram on the color signal plane. Finally, the usefulness of the method is shown in an experiment.

An analysis technique for buried inhomogeneous dielectric objects in the presence of an air-Earth interface

Complex geological structures are modelled in the presence of an air-Earth interface. A cross-borehole configuration of target, source, and receiver is assumed, with the target itself not restricted as to geometrical cross section or complex permittivity value. Two-dimensional method-of-moment formulations are employed, utilizing cylindrical pulse basis functions and point matching. Scattering from buried dielectric objects is computed near the air-Earth interface for both TE and TM incident fields. A Sommerfeld-Green function is used to represent the effect of the air-Earth interface on the incident fields and the impedance matrix. The TE case is examined for scattering of both the copolarized and cross-polarized electric fields, and several examples are given for a cylindrical target at depths that vary from one to twenty four wavelengths, after which the presence of the air-Earth interface can be neglected. Some experimental results utilizing a 1/40th laboratory scale model and a tunnel-like target are also included for comparison. The technique enables the user to investigate electromagnetic scattering from a variety of complex buried objects whose dimensions are typically in or below the resonance region. The simultaneous relaxation of restrictions on cross section, material properties, and burial depth, together with experimental validation, is not found in the literature to date.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computation of electromagnetic fields inside strongly inhomogeneous objects by the weak-conjugate-gradient fast-Fourier-transform method

The computation of the electromagnetic field inside a strongly inhomogeneous dielectric object is formulated in terms of a domain-integral equation over the object. We discuss a weak form of the integral equation in which the spatial derivatives are integrated analytically. Doing so, we obtain an equation that is solved efficiently with the advantageous combination of a conjugate-gradient iterative method and a fast-Fourier-transform technique. Numerical computations are performed for a strongly inhomogeneous lossy sphere. For this case we compare the accuracy and the efficiency of the present method with the analytic solution based on the Mie series and the finite-difference time-domain approach. To show that the method is also capable of computing more-complex scattering problems, we assume the incident field to be generated by a (1/2)λ thin-wire dipole. In this case the absorbed power density is presented. All these test cases demonstrate that the weak form of the conjugate-gradient fast-Fourier-transform method can be considered as a comparatively simple and efficient tool for solving realistic electromagnetic wave-field problems.

Inverse scattering of Hz waves using local shape‐function imaging: A T‐matrix formulation

AbstractInverse scattering algorithms for Hz polarized waves are scarce, due to the added difficulties of polarization charges. Nevertheless, the polarization charges cannot be ignored for 3D problems as well as for 2D Hz problems. This work aims to reconstruct arbitrary inhomogeneous dielectric objects from Hz scattering data using a new formulation that abandons the standard integral equation model for a T‐matrix model. This new algorithm, called local shape‐function (LSF) imaging, is modified for dielectric objects with Hz incident fields, where previously the LSF algorithm was applied to metallic objects with Ez incident fields. The advantage of the LSF algorithm is a more accurate modeling of the induced interfacial polarization charges. For comparison, the Hz distorted Born iterative method using integral equations is shown to be valid only for small contrasts, while the LSF algorithm converges for much larger dielectric contrasts.©1994 John Wiley &amp; Sons Inc