Three-dimensional Dielectric Objects Research Articles

Discrete Quasi-Helmholtz Decomposition for 3-D High-Contrast Lossy Dielectric Problems

By applying Loop-Star decomposition of basis functions to form orthogonal transformation matrices, an efficient method for the analysis of electromagnetic scattering from three-dimensional dielectric and lossy objects, especially with high-contrast parameters to the background media, has been presented in this letter. The analysis of the diagonal blocks of the impedance matrix shows that the vector potential and scalar potential subspaces scale differently in relation to the material parameters, which may have a negative effect on the conditioning of the matrix and iteration efficiency. Therefore, new equations corresponding to the exterior and interior equations have been presented, respectively, by constructing discrete quasi-Helmholtz projection operators, based on the traditional dielectric integral formulations, i.e., Poggio–Miller–Chang–Harrington–Wu–Tsai. Numerical examples show that the proposed method is effective for high-contrast lossy dielectric objects by improving the condition number and decreasing the number of iterations.

A Hybrid 3DMLUV-FIA Method for Scattering from a 3D Dielectric Object above a 2D Dielectric Rough Surface

The electromagnetic scattering from the composite model of a three-dimensional (3D) dielectric object located above a two-dimensional (2D) dielectric rough surface is analyzed in this work. Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) integral equations are discretized by the method of moments (MoM) into a matrix which is solved by Biconjugate Gradients Stabilized (BICGSTAB) method. Method of 3DMLUV was used for PEC object located above rough surface. Comparing to the case when object and rough surface are both PEC, the memory requirement and computational complexity for dielectric models are increased due to doubled unknown number. Moreover, compared to dielectric object in free space, the coupling between dielectric object and dielectric rough surface will result in complicated numerical simulation. To solve this problem, the updated rank based 3D Multilevel UV (3DMLUV) method is employed to reduce memory consumption and CPU time overhead. The 3DMLUV has been successfully applied in the scattering of PEC targets; however, when the object or rough surface becomes dielectric, the coupling between dielectric object and dielectric rough surface will lead to slow constriction. Therefore, the Fast Iterative Approach (FIA) is applied to further speed up the constricted speed of the matrix required in 3DMLUV. The efficiency, stability, and accuracy of the proposed method are demonstrated in a variety of scattering problems.

Fast Analysis of Large 3-D Dielectric Scattering Problems Arising in Remote Sensing of Forest Areas Using the CBFM

We apply the characteristic basis function method (CBFM) to compute the electromagnetic fields scattered by three-dimensional dielectric objects in the context of forest scattering simulation. We study the effect of some CBFM parameters on the accuracy of the results, and on the performance of the CBFM when compared to the classical MoM. We show that once the CBFM parameters have been appropriately chosen, this new method realizes a significant reduction both in terms of CPU time and memory use, while maintaining a level of accuracy comparable to that of the conventional MoM. Consequently, the CBFM enables us to handle electrically larger forest simulation scenes than is possible with classical MoM for higher frequencies.

Inversion of Electromagnetic Scattering for 3D Dielectric Objects Through Integral Equation Method With Nyström Discretization

Reconstruction of unknown objects requires efficient inversion for measured electromagnetic scattering data. In frequency-domain integral equation method for reconstructing dielectric objects, the volume integral equations (VIEs) are involved because the imaging domain with both true unknown objects and part of background is inhomogeneous. When solving the forward scattering integral equation (FSIE), the Nyström method is used since the traditional method of moments (MoM) with the Schaubert-Wilton-Glisson (SWG) basis function may not be convenient due to the inhomogeneity of the imaging domain. The benefits of the Nyström method include the simple implementation without using any basis and testing functions and lower requirement on geometrical discretization, so it is very suitable for inhomogeneous problems. When solving the inverse scattering integral equation (ISIE), the Gauss-Newton minimization approach (GNMA) with a multiplicative regularization method (MRM) is employed. Numerical examples for reconstructing three-dimensional dielectric objects are presented to illustrate the inversion approach.

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

Novel electromagnetic surface integral equations for highly accurate computations of dielectric bodies with arbitrarily low contrasts

We present a novel stabilization procedure for accurate surface formulations of electromagnetic scattering problems involving three-dimensional dielectric objects with arbitrarily low contrasts. Conventional surface integral equations provide inaccurate results for the scattered fields when the contrast of the object is low, i.e., when the electromagnetic material parameters of the scatterer and the host medium are close to each other. We propose a stabilization procedure involving the extraction of nonradiating currents and rearrangement of the right-hand side of the equations using fictitious incident fields. Then, only the radiating currents are solved to calculate the scattered fields accurately. This technique can easily be applied to the existing implementations of conventional formulations, it requires negligible extra computational cost, and it is also appropriate for the solution of large problems with the multilevel fast multipole algorithm. We show that the stabilization leads to robust formulations that are valid even for the solutions of extremely low-contrast objects.

Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies

Vector potential formulation and parametric studies of electromagnetic scattering problems of a sphere characterized by the rotationally symmetric anisotropy are studied. Both epsilon and mu tensors are considered herein, and four elementary parameters are utilized to specify the material properties in the structure. The field representations can be obtained in terms of two potentials, and both TE (TM) modes (with respect to r) inside (outside) the sphere can be derived and expressed in terms of a series of fractional-order (in a real or complex number) Ricatti-Bessel functions. The effects due to either electric anisotropy ratio (Ae=epsilont/epsilonr) or magnetic anisotropy ratio (Am=mut/mur) on the radar cross section (RCS) are considered, and the hybrid effects due to both Ae and Am are also examined extensively. It is found that the material anisotropy affects significantly the scattering behaviors of three-dimensional dielectric objects. For absorbing spheres, however, the Ae or Am no longer plays a significant role as in lossless dielectric spheres and the anisotropic dependence of RCS values is found to be predictable. The hybrid effects of Ae and Am are considered for absorbing spheres as well, but it is found that the RCS can be greatly reduced by controlling the material parameters. Details of the theoretical treatment and numerical results are presented.

Efficient low-frequency inversion of 3-D buried objects with large contrasts

An efficient inversion method is proposed using Cui et al.'s high-order extended Born approximations to reconstruct the conductivity object function of three-dimensional dielectric objects buried in a lossy Earth. High-order solutions of the object function are obtained, which have closed-form relations to the linear inverse-scattering solution. Because such relations can be evaluated quickly using the fast Fourier transform, the high-order solutions have similar simplicity as the linear inversion. When the contrasts of buried objects are large, the high-order solutions are much more accurate due to the approximate consideration of multiple-scattering effects within the objects. Hence, good-resolution images can be obtained for large-contrast objects using the new method by only solving a linear inverse problem. Numerical experiments have shown the validity and efficiency of the proposed method.

A Moment Method Solution for the Shielding Properties of Three-Dimensional Objects Above a Lossy Half Space

In this paper, a moment method (MM) solution for analyzing the electromagnetic (EM) shielding properties of three-dimensional (3-D) lossy dielectric and magnetic objects over a lossy half space is presented. An MM, based on a volume formulation and a special Green's function in the spectral domain, is developed. Plane waves with TMz and TEz polarizations incident upon 3-D lossy material structures are demonstrated for the shielding effects of those bodies in the presence of a lossy ground. Some of the results are compared with those evaluated by applying the finite difference time domain method, and good agreements are obtained. The MM solution can be used to study the shielding problems for 3-D objects located above a lossy ground.

Microwave Imaging of Three-Dimensional Dielectric Objects

An electromagnetic (EM) inverse scattering problem that involves the reconstruction of microwave images for dielectric objects is considered in this paper. This ill-posed and nonlinear problem is treated as a global optimization problem, and is solved by the application of micro-genetic algorithm (m-GA). The reconstructed results obtained by m-GA have shown that it is an effective technique for microwave imaging and satisfactory performance is achieved when compared with the conventional genetic algorithms.

Fast-forward solvers for the low-frequency detection of buried dielectric objects

It is known that the extended Born approximation (ExBorn) is much faster than the method of moments (MoM) in the study of electromagnetic scattering by three-dimensional (3-D) dielectric objects, while it is much more accurate than the Born approximation at low frequencies. Hence, it is more applicable in the low-frequency numerical simulation tools. However, the conventional ExBorn is still too slow to solve large-scale problems because it requires O(N/sup 2/) computational load, where N is the number of unknowns. In this paper, a fast ExBorn algorithm is proposed for the numerical simulation of 3-D dielectric objects buried in a lossy Earth. When the buried objects are discretized with uniform rectangular mesh and the Green's functions are extended appropriately, the computational load can be reduced to O(N log N) using the cyclic convolution, cyclic correlation, and fast Fourier transform (FFT). Numerical analysis shows that the fast ExBorn provides good approximations if the buried target has a small or moderate contrast. If the contrast is large, however, ExBorn will be less accurate. In this case, a preconditioned conjugate-gradient FFT (CG-FFT) algorithm is developed, where the solution of the fast ExBorn is chosen as the initial guess and the preconditioner. Numerical results are given to test the validity and efficiency of the fast algorithms.

Application of a novel CFIE for electromagnetic scattering by dielectric objects

AbstractIn this Letter a new type of combined field integral equation (CFIE) is proposed and applied for electromagnetic scattering by three‐dimensional dielectric objects of arbitrary shape. In this formulation, traditional CFIE is applied outside the object, and inside the object the electric and magnetic field integral equations are combined by changing their roles. This formulation gives a more stable solution than the traditional CFIE when the method of moments with Galerkin's type testing and RWG functions is applied. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 3–5, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10500

A Survey of Various Frequency Domain Integral Equations for the Analysis of Scattering From Three-Dimensional Dielectric Objects - Abstract

In this paper, we present four different formulations for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) homogeneous dielectric body in the frequency domain. The four integral equations treated here are the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), the combined field integral equation (CFIE), and the PMCHW (Poggio, Miller, Chang, Harrington, and Wu) formulation. For the CFIE case, we propose eight separate formulations with different combinations of expansion and testing functions that result in sixteen different formulations of CFIE. One of the objectives of this paper is to illustrate that not all CFIE are valid methodologies in removing defects, which occur at a frequency corresponding to an internal resonance of the structure. Numerical results involving the equivalent electric and magnetic currents, far scattered fields, and radar cross section (RCS) are presented for three canonical dielectric scatterers, viz. a sphere, a cube, and a finite circular cylinder, to illustrate which formulation works and which does not.

A Survey of Various Frequency Domain Integral Equations for the Analysis of Scattering from Three-dimensional Dielectric Objects

In this paper, we present four dierent formulations for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) homogeneous dielectric body in the frequency domain. The four integral equations treated here are the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), the combined field integral equation (CFIE), and the PMCHW (Poggio, Miller, Chang, Harrington, and Wu) formulation. For the CFIE case, we propose eight separate formulations with dierent combinations of expansion and testing functions that result in sixteen dierent formulations of CFIE. One of the objectives of this paper is to illustrate that not all CFIE are valid methodologies in removing defects, which occur at a frequency corresponding to an internal resonance of the structure. Numerical results involving the equivalent electric and magnetic currents, far scattered fields, and radar cross section (RCS) are presented for three canonical dielectric scatterers, viz. a sphere, a cube, and a finite circular cylinder, to illustrate which formulation works and which does not.

Diffraction tomographic algorithm for the detection of three-dimensional objects buried in a lossy half-space

A diffraction tomographic (DT) algorithm has been proposed for detecting three-dimensional (3-D) dielectric objects buried in a lossy ground, using electric dipoles or magnetic dipoles as transmitter and receiver, where the air-earth interface has been taken into account and the background is lossy. To derive closed-form reconstruction formulas, an approximate generalized Fourier transform is introduced. Using this algorithm, the locations, shapes, and dielectric properties of buried objects can be well reconstructed under the low-contrast condition, and the objects can be well detected even when the contrast is high. Due to the use of fast Fourier transforms to implement the problem, the proposed algorithm is fast and quite tolerant to the error of measurement data, making it possible to solve realistic problems. Reconstruction examples are given to show the validity of the algorithm.

Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface

A numerical model for computing scattering from a three-dimensional (3D) dielectric object above or below a rough interface is described. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. To improve computational efficiency, the canonical grid method and the discrete dipole approach (DDA) are used to compute surface to surface and object to object point couplings, respectively, in O(N log N), where N is the number of surface or object sampling points. Two distinct iterative approaches and a preconditioning method for the resulting matrix equation are discussed, and the solution is verified through comparison with a Sommerfeld integral-based solution in the flat surface limit. Results are illustrated for a sample landmine detection problem and show that a slight surface roughness can modify object backscattering returns.

Solution of Electromagnetic Scattering Problems Involving Three-Dimensional Homogeneous Dielectric Objects by the Single Integral Equation Method

The problem of electromagnetic scattering by a homogeneous dielectric object is usually formulated as a pair of coupled integral equations involving two unknown currents on the surface S of the object. In this paper, however, the problem is formulated as a single integral equation involving one unknown current on S. Unique solution at resonance is obtained by using a combined field integral equation. The single integral equation is solved by the method of moments using a Galerkin test procedure. Numerical results for a dielectric sphere are in good agreement with the exact results. Furthermore, the single integral equation method is shown to have superior convergence speed of iterative solution compared with the coupled integral equations method.

Redundant electromagnetic data for microwave imaging of three-dimensional dielectric objects

The possibilities of reconstructing the dielectric characteristics of unknown three-dimensional dielectric objects located inside a known volume are studied by means of numerical computer simulations. A numerical approach is proposed that is based on the moment method and on the utilization of redundant data (i.e., the values of the components of the scattered electric field measured outside the investigation volume) in order to strictly constrain the solution. In particular, a multi-illumination-angle multiview approach is proposed, which is based on an integrodifferential formulation of the three-dimensional inverse electromagnetic scattering problem. The analytical model is discretized using the moment method, and a regularization procedure is employed to find a solution, in a least-squares sense, to the resulting rectangular ill-conditioned linear system of algebraic equations. Since the heaviest computations can be performed off line, the computer resources required by the approach are entirely independent of the number of views. Numerical simulations have been performed to assess the effectiveness of the approach in dielectric reconstruction, in particular, by evaluating the distortions due to the ill-posedness of the inverse-scattering formulation. >

The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems

The problem of electromagnetic scattering by a three-dimensional dielectric object can be formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free space Green's function and the contrast source over the domain of interest. A weak form of the integral equation for the relevant unknown quantity is obtained by testing it with appropriate testing functions. The vector potential is then expanded in a sequence of the appropriate expansion functions and the grad-div operator is integrated analytically over the scattering object domain only. A weak form of the singular Green's function has been used by introducing its spherical mean. As a result, the spatial convolution can be carried out numerically using a trapezoidal integration rule. This method shows excellent numerical performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computation of electromagnetic wave scattering from an arbitrary three-dimensional inhomogeneous dielectric object

A scattering matrix formulation for scattering of electromagnetic fields by an arbitrary three-dimensional dielectric objects is presented. It is based on an extended moment method that digitizes the scattering equation by dividing the scatterer as well as the measurement region into small cells. The Green's function within each cell is derived analytically by integrating over the cell. The accuracy of the method is demonstrated by computing vector scattering fields from a uniform dielectric sphere and comparing the results with those calculated using the Mie scattering formula. The formulation also provides an inverse solution, namely, determination of the dielectric profile of the scatterer from the scattering field measured in a finite region outside the scatterer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>