Inverse scattering problem for concealed objects detection

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.

We analyze the error in typical moment method scattering solutions for smooth cylindrical geometries and TM-polarized fields. We consider the magnetic field integral equation (MFIE), electric field integral equation (EFIE), and combined field integral equation. To quantify the impact of mesh element size, approximate integration of moment matrix elements, and geometrical discretization error on the accuracy of computed surface currents and scattering amplitudes, we derive error estimates analytically for the circular cylinder. For pulse functions and point testing, current and scattering amplitude errors are generally second order in the mesh element width. The convergence rate worsens to first order if low-order numerical quadrature is used to evaluate moment matrix elements with the EFIE formulation, or if a flat-facet mesh is employed with the MFIE formulation. Third-order convergence is also possible in some special cases. These results for the circular cylinder are empirically compared to computed error values for other smooth scatterer geometries. Convergence rates with respect to mesh refinement agree, but scatterers with regions of high curvature exhibit increased absolute error.

A new acceleration method is proposed for efficiently solving the problem of electromagnetic scattering from metal targets in half-space. The analysis of electromagnetic problems in any structure can be settled by the electric field integral equation. But the generated matrix condition number is large and the iterative solution has poor convergence. The number of the matrix condition generated by the magnetic field integral equation is small and iterative convergence is good. But only the closed structure problems can be worked out. The combined field integral equation is adopted because of the universality of the electric field integral equation and the convergence of the magnetic field integral equation. The gradient term of Green's function is involved in the integral equation of the mixed field. In order to further enhance the calculation efficiency, an efficient four-dimensional spatial interpolation method is introduced for half-space Green's function. Tabulation and lagrange interpolations are performed in the Sommerfeld integrals for the half-space Green's function. The improved efficiency can be 7.5 times higher than that of the traditional combined field integral equation(CFIE). Numerical results show that the computational time can be reduced significantly by the proposed method with encouraging accuracy.

Numerical solutions to the impedance boundary condition (IBC) combined source integral equation (CSIE) for scattering from impedance spheres are presented. The CSIE formulation is a well-posed alternative to the IBC electric and magnetic field integral equations which can be contaminated by spurious resonant modes. Compared with the IBC combined field integral equation (CFIE), CSIE solutions have the same accuracy when the combined source coupling admittance is chosen to be the same value as the combined field coupling admittance. However, the CSIE formulation is better suited than the CFIE for creating a general purpose computer code capable of handling aperture radiation problems and/or a scatterer which has a spatially varying surface impedance.

The “conventional” finite element‐boundary integral (FE‐BI) method suffers from two major drawbacks, one is the huge computer resources required by the dense BI submatrix; the other is the slow convergence rate of the resulting linear system of equations. In this article, both the drawbacks are investigated. First, the integral equation fast Fourier transform (IE‐FFT) algorithm with a Gaussian interpolation scheme is employed to deal with the BI part. Second, an effective and simple preconditioner is developed for solving the matrix equation obtained from FE‐BI method. Numerical results show that the proposed preconditioner can dramatically speed up the convergence of the FE‐BI system, whatever the combined field integral equation (CFIE), the electric field integral equation (EFIE), and the magnetic field integral equation (MFIE) are employed on the truncation boundary. Some examples are given to demonstrate the accuracy and efficiency of the method. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2065–2071, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24538

A highly efficient and robust scheme is proposed for analyzing electromagnetic scattering from electrically large arbitrary shaped conductors in a half space. This scheme is based on the electric field integral equation (EFIE) with a half-space Green’s function. The precorrected fast Fourier transform (p-FFT) is first extended to a half space for general three-dimensional scattering problems. A novel enhanced dual threshold incomplete LU factorization (ILUT) is then constructed as an effective preconditioner to improve the convergence of the half-space EFIE. Inspired by the idea of the improved electric field integral operator (IEFIO), the geometrical-optics current/principle value term of the magnetic field integral equation is used as a physical perturbation to stabilize the traditional ILUT perconditioning matrix. The high accuracy of EFIE is maintained, yet good calculating efficiency comparable to the combined field integral equation (CFIE) can be achieved. Furthermore, this approach can be applied to arbitrary geometrical structures including open surfaces and requires no extra types of Sommerfeld integrals needed in the half-space CFIE. Numerical examples are presented to demonstrate the high performance of the proposed solver among several other approaches in typical half-space problems.

The adaptive integral method (AIM) is applied to the solution of the combined field integral equation (CFIE) of scattering by a three-dimensional (3-D) perfect electric conductor (PEC). The employment of CFIE eliminates the interior resonance problem suffered by both the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE). Furthermore, it significantly improves the efficiency of AIM by reducing the number of iterations for convergence. It is shown that the memory requirement and computational complexity per iteration of the AIM solution of CFIE are O(N1.5) and O(N1.5log N), respectively, for 3-D PEC surface scattering problems. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 321–328, 1998.

The detection of concealed objects like weapon, explosives, and other dangerous items became very important problem for defending people against terrorist attacks. Recent time, many methods have been developed but number of methods are not efficient to effectively solve this problem. The main aim of the research in this work is devoted to the detection of concealed dangerous objects by increasing sensitivity and resolution in obtained images. In this paper, we propose to use inverse synthetic aperture radar (ISAR) technology for the detection of hidden items in the millimeter-wave length. The millimeter-wave ISAR imaging of concealed cubes and a gun are studied. The theoretical background employed for the reconstruction of measurement results is briefly described. The millimeter-wave ISAR measurement setup is presented. Then, measurements carried out for different scenarios are explained. Finally, the reconstructed results are shown for all conducted measurements.

This work presents a new formulation for conducting bodies of revolution (BOR) in layered media. It is derived using magnetic field integral equation (MFIE). The discrete complex image method is used to transform the Sommerfeld integrals into closed form solutions. For large closed objects, the use of the magnetic field formulation is shown to be more advantageous than the electric field integral equation (EFIE) concerning the convergence of the solution. The obtained formulation is applied to the contiguous half-spaces case. Results of both the magnetic and electric field integral equation formulations are presented.

The development of time-domain integral equation solvers with robust late-time stability properties has been a long-standing quest. Among the many methods that have been investigated, those leveraging quasi-exact integration techniques appear to be most successful. This article presents stable and accurate marching-on-in-time (MOT) solvers for time-domain electric, magnetic, and combined field integral equations (EFIE, MFIE, and CFIE) based on quasi-exact integration techniques. The novel MOT solvers exhibit excellent stability while yielding highly accurate results, as demonstrated by various numerical examples. In addition, the solvers' excellent stability and accuracy properties are used to examine spurious modes encountered when time-domain integral equations are applied to closed surfaces. It is demonstrated that MOT solutions to the time domain EFIE and MFIE often are polluted by spurious modes at the cavity's resonant frequencies whereas those of the CFIE solver are devoid of such contamination.

A discontinuous Galerkin (DG) surface integral equation method is proposed for electromagnetic scattering from targets with the impedance boundary condition (IBC). We present electric field integral equation (EFIE), magnetic field integral equation (MFIE), and self‐dual integral equation formulations for the problem and study their numerical performance. On the basis of the results of these experiments, DG is developed for EFIE and MFIE (DG‐EFIE and DG‐MFIE). The convergence of the iterative solutions and the solution accuracy of DG‐EFIE and DG‐MFIE are further investigated for a wide range of surface impedances. The numerical performance of these formulations is found to be nearly complementary with respect to the surface impedance. The capability of the proposed DG solution strategy for calculating scattering from large multiscale IBC targets is demonstrated.

An alternative method of moments discretization of the magnetic field integral equation (MFIE) uses testing functions inside the target and in a plane normal to the target surface. This approach is adapted to targets modeled with flat-faceted patches. A comparison with traditional numerical solutions of the MFIE that use testing functions on the target surface shows that the normally-integrated MFIE formulation produce far fields that are more accurate than those obtained from the traditional MFIE. The alternate approach can be made free from internal resonances and that approach is often more accurate than the combined field integral equation.

The time-domain electric, magnetic and combined field integral equations (TDEFIE, TDMFIE and TDCFIE) have been applied widely to the analysis of transient scattering from conducting bodies. The marching-on-in-time (MOT) schemes, relying on suitable spatial integral rules and an implicit time-stepping method, have been found to be always stable for solving the TDCFIE and TDMFIE. Unfortunately, the same is not true for the TDEFIE. The non-singular integral is evaluated using the standard Gaussian quadrature rules, and the transformations of the parametric coordinates and plane polar coordinates are employed to transform the singular integrals of TDEFIE into non-singular integrals, which can be accurately and efficiently evaluated by dividing the original domain of integration into sub-domains. Simulation results demonstrate that this approach produces rather stable and more accurate results without resort to any averaging processes. It is more important that this method suits any temporal basis functions and can be extended to high-order spatial basis functions.

The single-source integral equation (SSIE) technique is presented to analyze electromagnetic scattering from an arbitrarily shaped three-dimensional conducting object coated by a homogeneous dielectric body. The external and interior surface equivalence principles combined with the continuity of the tangential components of the total electric and magnetic fields on the surface of the dielectric and zero tangential component of the total electric field on the surface of the conductor are used to formulate the single-source electric and magnetic field integral equations. With a localization procedure, the Calderon preconditioned single-source electric field integral equation (SSEFIE) is constructed and combined with single-source magnetic field integral equation (SSMFIE) to produce a single-source combined field integral equation (SSCFIE), which is free from spurious resonance and dense-mesh breakdown. Numerical results validate the good performance of the proposed algorithm.

Multispectral systems for detection of concealed dangerous objects are becoming more popular because of their higher effectiveness compared to mono-spectral systems. So far, the problem of detecting objects hidden under clothing was considered only in the case of airports but it is becoming more important for public places like metro stations, and government buildings. Exploration of new spectral bands as well as development of technology result in introduction of new solutions – both mono and multispectral. It has been proved that objects hidden under clothing can be detected and visualized using terahertz (THz) cameras. However, passive THz cameras still offer too low image resolution for objects recognition. Limited range is another issue of passive imagers. On the other hand new infrared cameras offer sufficient parameters to detect objects covered with fabrics in some conditions, as well as high image quality and big pixel resolutions. The purpose of the studies is to investigate and compare the possibilities of using passive cameras operating in long wavelength infrared (LWIR) and THz spectral ranges for detection of concealed objects. For the purpose of investigations, commercial imagers operating in 6.5-11.7 μm and 250GHz (1.25mm) were used. In the article, we present the measurement setup and the results of measurements in various operating conditions. Theoretical studies of both spectral bands focused on detection of objects with passive imagers are also presented.