探地雷达中的衍射层析算法

给出了二维情况下进行地下目标反演的线性衍射层析算法。该方法采用线性Born近似和傅里叶变换,避免了一般非线性逆散射算法的逐步迭代,因而可用于地下目标的快速检测和位置标定。本文的衍射层析算法考虑了空气地面交界面的影响并计入了凋落场。计算结果表明,该方法可以较好地描述低对比度目标的位置、轮廓和介电参数等信息,也可用于高对比度目标的检测和定位。     

Diffraction tomographic algorithm for the detection ofthree-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     

求解埋入体电磁散射问题的矢量波函数展开法

本文利用矢量波函数展开法求解了任意激励原埋入体的电磁散射问题。通过导出圆柱和圆球矢量波函数的转换关系,使场量满足分界平面和数学球面边界条件,从而方便地利用矢量波函数展开求解了这一复杂边值问题。作为示例,本文计算了在平面波和偶极子激励下,埋入导体球和介质球的散射场。     

VECTOR WAVE FUNCTION EXPANSION FOR SOLVING ELECTROMAGNETIC SCATTERING BY BURIED OBJECTS

An analysis of solving the electromagnetic scattering by buried objects using vectorwave function expansion is presented.For expanding the boundary conditions both on the planarair-earth interface and on the spherical surface,the conversion relations between the cylindricaland spherical vector wave functions are derived.Hence the vector wave function expansion isconveniently applied to solve this complex boundary-value problem.For the excitation of the in-cident plane wave and the dipole above the earth,the scatterlng patterns of the buried conductingand dielectric spheres are presented and discussed.     

Electromagnetic imaging of underground targets using constrainedoptimization

Several high-frequency electromagnetic techniques have been used in recent years to detect and identify buried objects. Post-processing of the collected data is performed in many of these techniques to obtain high-quality images of buried targets. Accurate reconstructions of the target's constitutive parameters can be obtained by casting the imaging problem in terms of an inverse electromagnetic scattering problem. A number of techniques have been put forth recently to invert the electromagnetic data to obtain such images. The authors use a frequency-domain Born iterative method to reconstruct images of shallow targets. The Born iterative technique requires successive solutions to a forward scattering problem followed by an inverse scattering problem at each iteration step. They use a finite-difference time-domain (FDTD) algorithm to solve the forward scattering problem and constrained optimization for the inverse problem. Two-dimensional simulated data for several canonical objects buried in the ground are obtained using the FDTD technique. The same FDTD code is also used in calculating the Green's function required for solving the constrained optimization problem. Lossy, inhomogeneous ground models are used in several simulations to illustrate the use of this technique for practical situations. The inversion process can be used to reconstruct images for many realistic dielectric contrasts for which a linear Born approximation fails. Moreover, it is also shown that a small number of measurements results in accurate reconstructions with this technique. Use of multiple frequencies is also investigated     

Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface

An analytical solution is presented for the electromagnetic scattering from a dielectric circular cylinder embedded in a dielectric half-space with a slightly rough interface. The solution utilizes the spectral (plane-wave) representation of the fields and accounts for all the multiple interactions between the rough interface and the. buried cylinder. First-order coefficients from the small perturbation method are used for computation of the scattered fields from the rough surface. The derivation includes both TM and TE polarizations and can be easily extended for other cylindrical buried objects (e.g., cylindrical shell, metallic cylinder). Several scattering scenarios are examined utilizing the new solution for a dielectric cylinder beneath a flat, sinusoidal, and arbitrary rough surface profile. Results indicate that the scattering pattern of a buried object below a slightly rough surface differs from the flat surface case only when the surface roughness spectrum contains a limited range of spatial frequencies. Furthermore, the illuminated area of the incident wave is seen to be a critical factor in the visibility of a buried object below a rough surface.     

Subsurface Sensing of Buried Objects Under a Randomly Rough Surface Using Scattered Electromagnetic Field Data

This paper proposes a new inverse method for microwave-based subsurface sensing of lossy dielectric objects embedded in a dispersive lossy ground with an unknown rough surface. An iterative inversion algorithm is employed to reconstruct the geometry and dielectric properties of the half-space ground as well as that of the buried object. B-splines are used to model the shape of the object as well as the height of the rough surface. In both cases, the control points for the spline function represent the unknowns to be recovered. A single-pole rational transfer function is used to capture the dispersive nature of the background. Here, the coefficients in the numerator and denominator are the unknowns. The approach presented in this paper is based on the state-of-the-art semianalytic mode matching forward model, which is a fast and efficient algorithm to determine the scattered electromagnetic fields. Numerical experiments involving two-dimensional geometries and TM incident plane waves demonstrate the accuracy and reliability of this inverse method     

Current marching technique for electromagnetic scatteringcomputations

An iterative solver is used to compute the electromagnetic field scattered by perfectly conducting three-dimensional (3-D) objects of arbitrary shape. The unique solution of the dual-surface integral equation is approached by successive forward/backward calculations of the current. Convergence is very fast, giving accurate results in about a dozen iterations for convex objects. The method handles successfully single and multiple objects, convex objects, and cavities. Calculations can be carried out on a desktop computer for relatively large objects, with dimensions of ten wavelengths and more     

Propagation on a Ported Coaxial Cable Buried in Flat Earth

Consider a horizontal coaxial cable with periodic slots in the outer conductor. This ?leaky cable? is buried in the earth as one component of an intruder detection system. We develop the theory for surface-wave propagation on the cable in the presence of the planar air-earth interface. Numerical results are included for the phase velocity and attenuation constant as functions of the various parameters. Data are presented for the electric-field strength at the air-earth interface, and the electric-field distribution in the air region above the buried cable.     

粗糙面下方金属目标复合电磁散射的快速算法

为快速有效计算粗糙面下金属目标的复合电磁散射,提出了一种基于前后向迭代算法(FBM)和共轭梯度(CG)法的快速互耦迭代算(CCIA).首先建立目标与粗糙面的耦合积分方程组,并采用矩量法将其离散为矩阵方程.其次针对得到的耦合积分方程,用FBM求解粗糙面表面电流分布,用CG法求解目标表面电流分布,目标和粗糙面的相互作用通过更新两方程的激励项完成.最后,计算了高斯粗糙面下方无限长金属圆柱目标的复合电磁散射系数,当目标尺寸趋于零或目标深度趋于无穷时的结果与单独介质粗糙面相一致,验证了该数值方法的正确性;同时,讨论了不同粗糙面情况下该方法的收敛性,并分析了不同粗糙面媒质、目标尺寸和目标位置对双站散射系数的影响.     

A fast solver for the Helmholtz equation on long, thin structures

We present a fast solver for the Helmholtz equation on long, thin structures. It operates on an integral equation formulation of the problem, in which the solution is represented as a superposition of fields generated by sources on the structure (usually on the boundary or boundaries of the structure). It uses a standard iterative solver for linear equations, in conjunction with a novel method for applying the forward matrix, whose computational complexity is O(N), where N is the number of points on which the integral equation is solved. The algorithm is suitable for structures in either two dimensions (2-D) or three dimensions. It does not depend in any great detail on the specifics of the Helmholtz equation, and, thus, is also suitable for similar equations. We demonstrate the algorithm by using it to simulate scattering in 2-D from dielectric structures, using an integral equation formulation constructed using a combination of single-layer and double-layer potentials, yielding a second-kind integral equation. Numerical results show the algorithm to be efficient and accurate.     

Effective Solution of 3-D Scattering Problems via Series Expansions: Applicability and a New Hybrid Scheme

Accurate and reliable evaluation of the electromagnetic field scattered by dielectric objects is a canonical problem in the electromagnetic community. In the framework of integral equation formulations, iterative techniques, and in particular conjugate gradient (CG) schemes, are widely used. However, when the number of parameters grows, CG techniques may become too demanding from a computational point of view. In this paper, we show that many forward scattering problems can be conveniently solved by means of very simple series expansions, which allow a lower computational complexity and memory storage with respect to other iterative schemes. In particular, we consider three different series expansions, namely: 1) the traditional Born series; 2) the contrast source-extended Born series, which is recently introduced by rewriting the traditional source-type integral equations; and 3) a new series, which is a hybridization of the previous ones. Theoretical conditions for the applicability of the series expansions are discussed, and practical tools to foresee that a problem can be solved by means of these simple iterative schemes are provided. Numerical examples are reported for the sake of comparison and to assess performance     

Recursive T-matrix methods for scattering from multiple dielectricand metallic objects

We present an efficient, stable, recursive T-matrix algorithm to calculate the scattered field from a heterogeneous collection of spatially separated objects. The algorithm is based on the use of higher order multipole expansions than those typically employed in recursive T-matrix techniques. The use of these expansions introduces instability in the recursions developed by Chew (1990) and by Wang and Chew (1990), specifically in the case of near-field computations. By modifying the original recursive algorithm to avoid these instabilities, we arrive at a flexible and efficient forward solver appropriate for a variety of scattering calculations. The algorithm can be applied when the objects are dielectric, metallic, or a mixture of both. We verify this method for cases where the scatterers are electrically small (fraction of a wavelength) or relatively large (12λ). While developed for near-field calculation, this approach is applicable for far-field problems as well. Finally, we demonstrate that the computational complexity of this approach compares favorably with comparable recursive algorithms     

Three-dimensional inverse scattering of a dielectric target embedded in a lossy half-space

A modified iterative Born method is applied for three-dimensional inversion of a lossless dielectric target embedded in a lossy half-space. The forward solver employs a modified form of the extended Born method, and the half-space Green's function is computed efficiently via the complex-image technique. Example results are shown, with all scattering data based on a computational model, utilizing a rigorous forward solver distinct from that employed in the inversion. In addition, distinct gridding schemes are used in the forward and inverse solvers. Simple Tikhonov regularization is found to yield adequate results for inversion of noisy data.     

An abrupt change detection algorithm for buried landmines localization

Ground-penetrating radars (GPRs) are very promising sensors for landmine detection as they are capable of detecting landmines with low metal contents. GPRs deliver so-called Bscan data which are, roughly, vertical slice images of the ground. However, due to the high dielectric permittivity contrast at the air-ground interface, a strong response is recorded at early time by GPRs. This response is the main component of the so-called clutter noise and it blurs the responses of landmines buried at shallow depths. The landmine detection task is therefore quite difficult. This paper proposes a new method for automated detection and localization of buried objects from Bscan records. A support vector machine algorithm for online abrupt change detection is implemented and proves to be efficient in detecting buried landmines from Bscan data. The proposed procedure performance is evaluated using simulated and real data.     

Quasi-ray Gaussian beam algorithm for time-harmonic two-dimensionalscattering by moderately rough interfaces

Gabor-based Gaussian beam (GB) algorithms, in conjunction with the complex source point (CSP) method for generating beam-like wave objects, have found application in a variety of high-frequency wave propagation and diffraction scenarios. Of special interest for efficient numerical implementation is the noncollimated narrow-waisted species of GB, which reduces the computationally intensive complex ray tracing for collimated GB propagation and scattering to quasi-real ray tracing, without the failure of strictly real ray field algorithms in caustic and other transition regions. The Gabor-based narrow-waisted CSP-GB method has been applied previously to two-dimensional (2-D) propagation from extended nonfocused and focused aperture distributions through arbitrarily curved 2-D layered environments. In this 2-D study the method is applied to aperture-excited field scattering from, and transmission through, a moderately rough interface between two dielectric media. It is shown that the algorithm produces accurate and computationally efficient solutions for this complex propagation environment, over a range of calibrated combinations of the problem parameters. One of the potential uses of the algorithm is as an efficient forward solver for inverse problems concerned with profile and object reconstruction     

Conjugate-gradient algorithm with edge-preserving regularizationfor image reconstruction from Ipswich data for mystery objects

This paper presents some evidence of the effectiveness of adding edge preserving (EP) regularization to the conjugate radient (CG) method, in reconstructing the shape and permittivity profile of dielectric objects. Without any a priori information, our CG algorithm is also still efficient, and succeeded in reconstructing two mystery targets. As the two targets are now known, we hope we can greatly enhance the reconstruction quality by choosing better values for the calibration factors, and by applying our EP regularization to these data     

Electromagnetic scattering by multiple three-dimensional scatterersburied under multilayered media. II. Numerical implementations andresults

For pt.I see ibid., vol.36, no.2, p.526-34 (1998). In part I of this paper, coupled electric-field integral equations for dielectric objects, conducting objects, and multiple dielectric and/or conducting objects were derived when they were buried under one-dimensional (1D) multilayered media. In part II of this paper, numerical implementations for these integral equations are developed by use of the method of moments, in which the “self-actions” in the method are treated special because of the presence of singularity. Sample numerical results are presented for several cases of interest, which show the validity of the scheme     

A Single-Boundary Implicit and FFT-Accelerated Time-Domain Finite Element-Boundary Integral Solver

A novel time-domain finite-element boundary integral (FE-BI) solver for analyzing broadband scattering and radiation from free-standing electromagnetically large and perfect electrically conducting platforms supporting inhomogeneous and geometrically intricate structures is presented. The solver has three distinctive features that render it especially attractive for broadband analysis of installed antennas. i) The FE and BI solver components are hybridized using a single-surface interface. ii) The hybrid equations are solved by an implicit time-marching scheme accelerated by an (outer) Jacobi iterative solver that leverages (inner) direct FE and iterative BI solvers. iii) The BI solver component is accelerated by a distributed memory parallel implementation of the time-domain adaptive integral method based on the message-passing interface. The accuracy, late-time stability, and performance of the proposed time-domain FE-BI solver are demonstrated via its application to various scattering and radiation problems; moreover, the solver is used to characterize conformally mounted antennas on several platforms including an aircraft     

An Improved Weak-Form BCGS-FFT Combined With DCIM for Analyzing Electromagnetic Scattering by 3-D Objects in Planarly Layered Media

Fast algorithms for electrically large objects buried in layered media are mainly hindered by two time-consuming processes. One is the table filling of Green's function, and the other is the solving of the impedance matrix equation. For the first, to accelerate the evaluation of the time-consuming Sommerfeld integral in the dyadic Green's function (DGF), the discrete complex image method (DCIM) is introduced to get a closed-form DGF. To further accelerate the calculation of DGF for the volume electric field integral equation (EFIE), DGF is split before applying DCIM. For the second, the iterative solver stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) is combined with DCIM for solving the matrix equations. Meanwhile, the closed-form DGF enables the "spherical-mean" Green's function, which eliminates the singularity of Green's function. Numerical results show that the weaker singularity results in a faster and steadier convergence rate for iterative solvers