Emissivity simulations in passive microwave remote sensing with 3-D numerical solutions of Maxwell equations

In the numerical Maxwell-equation model (NMM3D) of rough-surface scattering, we solve Maxwell equations in three dimensions to calculate emissivities for applications in passive microwave remote sensing of soil and ocean surfaces. The difficult cases for soil surfaces are with exponential correlation functions when the surfaces have fine-scale structures of large slopes. The difficulty for ocean surfaces is that because the emissivities are close to that of a flat surface, the emissivities have to be calculated accurately to correctly assess the rough-surface effects. In this paper, the accuracies of emissivity calculations are improved by using Rao-Wilton-Glisson basis functions. We further use sparse matrix canonical method to solve the matrix equation of Poggio-Miller-Chang-Harrington-Wu integral equations. Energy conservation checks are provided for the simulations. Comparisons are made with results from the pulse basis function. Numerical results are illustrated for soil and ocean surfaces respectively with exponential correlation function and ocean spectrum. The emissivities of soil are illustrated at both L- and C-bands and at multiple incidence angles for the same physical roughness parameters. The brightness temperatures for ocean surfaces are illustrated for cases with various wind speeds. We compare results with those from the sparse matrix methods. Comparisons are also made with experimental emissivity measurements of soil surfaces. Parallel computation is also implemented. Lookup tables of emissivities based on NMM3D are provided.     

Acceleration of on-surface MEI method by new metrons and FMM for 2-D conducting scattering

A new kind of metron is proposed and rapid integration provided by fast multipole methods (FMM) is implemented to dramatically reduce the CPU time of finding the MEI coefficients in the on-surface measured equation of invariance (OSMEI) method. The numerical example of the scattering of a large conducting elliptical cylinder shows that the computation speed is at least one order of magnitude faster than that of the original OSMEI, where sinusoidal metrons are used, and about 25% faster than that of the FMM, where the iteration method is used.     

New equations for electromagnetic scattering by small perturbationsof a perfectly conducting surface

New equations are derived for the electromagnetic scattering produced by a small perturbation of a general perfectly conducting surface. These equations explicitly incorporate the magnetic field boundary condition on the general surface, which implies that the new Born term by itself leads to conventional backscatter formulas. The accuracy of the new equations is demonstrated by an example     

三维导体介质复合结构电磁辐射与散射的MLFMA分析

利用多层快速多极子方法(MLFMA)分析三维导体介质复合结构的电磁辐射与散射特性.根据等效原理,介质表面构造Poggio-Miller-Chang-Harrington-Wu(PMCHW)方程,导体表面建立电场积分方程(EFIE).分析了含介质目标MLFMA算法中远区组矩阵矢量相乘运算以及有耗媒质空间中格林函数的平面波展开.利用该方法研究了涂敷目标电磁散射特性以及天线罩对直线阵天线辐射特性的影响.MLFMA的应用降低了计算量和存储量,实现了对电大尺寸目标快速、准确的求解.     

Reconstruction of dielectric permittivity distributions in arbitrary 2-D inhomogeneous biological bodies by a multiview microwave numerical method

A numerical method for microwave imaging of two-dimensional inhomogeneous biological bodies illuminated by TM waves is presented. It is a spatial-domain multiview approach which makes use of the moment method to discretize the integral-equation formulation of inverse scattering. A pseudoinversion technique is applied to obtain a minimum-norm solution for the equivalent current density inside the cross-section of a scatterer. A multi-illumination-angle multiview process is used. The invariance of the Green matrix makes it possible to perform only one pseudoinverse (off line and once for all), independently of the number of views, thus reducing the need for computer resources. A pixel representation is adopted, and a look-up table is utilized to fast synthesize images. No plane-wave illumination is required and no first-order approximations are applied. Distortions in the dielectric reconstruction and noise effects are evaluated via some numerical simulations.     

Hybrid UTD-MM analysis of the scattering by a perfectly conducting semicircular cylinder

A hybrid UTD-MM technique which combines the uniform geometrical theory of diffraction (UTD) and the method of moments (MM) is employed to analyze efficiently the problem of electromagnetic diffraction of transverse electric (TE) and transverse magnetic (TM) waves by a perfectly conducting semicircular cylinder. An analysis of this problem is useful for understanding the coupling between the mechanisms of edge and convex surface diffraction. The accuracy of the numerical results for the far-zone fields based on this solution is established by comparison with an independent formally exact MM solution.     

Inverse scattering method for one-dimensional inhomogeneous lossymedium by using a microwave networking technique

The formulation of reflection coefficients from an inhomogeneous lossy medium illuminated by TE and TM waves is approximately derived, in closed form, by using a microwave network method. From the formulation, a novel inverse scattering scheme to reconstruct simultaneously the permittivity and conductivity profiles, is proposed. This scheme is suitable for both continuous and discontinuous profiles, under both the weak scattering and strong scattering conditions. It has also been shown that when the conductivity of the medium equals zero, the reconstructed result of this scheme will reduce to the one formulated by Ladouceur and Jordan (1985). Numerical and closed-form reconstruction examples show the validity of the scheme     

Solving the Maxwell equations by the Chebyshev method: a one-step finite-difference time-domain algorithm

We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than current finite-difference time-domain (FDTD) algorithms.     

An iterative FEM for scattering by a 3-D cavity-backed aperture

A finite-element method (FEM)-based hybrid method (or iterative FEM) is successfully applied to a three-dimensional (3-D) scattering problem without the effect of internal resonance. With only a small number of meshes around a 3-D scatterer, this FEM is shown to give an accurate result through several iterative updates of the boundary conditions. To confirm the efficiency of this method, scattering from a 3-D cavity-backed aperture is analyzed and the results obtained are compared with the same obtained by another conventional method     

3-D numerical mode-matching (NMM) method for resistivitywell-logging tools

A three-dimensional (3-D) numerical mode-matching (NMM) method is presented for Poisson's equation in general inhomogeneons media. It reduces the original 3-D problem into a series of two-dimensional (2-D) eigenvalue problems plus a one-dimensional (1-D) layered medium problem, which can be modeled efficiently by a recursion procedure. The algorithm is tested for several 3-D inhomogeneous media and an excellent agreement between the NMM and analytical solutions is obtained for all test cases. We demonstrate some typical applications of the 3-D NMM algorithm in resistivity well logging, including invasion zones of noncircular shape, vertical and horizontal fractures, and horizontal wells. The solution procedure proposed is directly applicable to wave propagation in 3-D inhomogeneous media     

Pseudo-3-D moment method for rapid calculation of electric fielddistribution in a low-loss inhomogeneous dielectric

Numerous applications of dielectric modeling require computation of the distribution of the total electric field in an inhomogeneous dielectric, in response to an applied electric field. An integral equation method would normally use an electric field volume integral technique using the moment method and hence compute the field in three-dimensional (3-D) space. For those instances where the third dimension of the region is assumed to be invariant, such as when determining the spatial sensitivity of a time-domain reflectometry sensor, the heavy resource use of calculating the additional dimension is an unnecessary burden. The new method reported in this paper sums the field contributions from the invariant third dimension at each stage of a two-dimensional (2-D) calculation, reducing the order of the model matrix by 2n² where n is the number of cells in each dimension. Thus, by accepting a small loss in accuracy of less than 3%, this procedure reduces the required memory resource by more than 2n²,and execution time is dramatically improved. Assuming an essentially lossless permittivity, we use the calculated electric field distribution from a parallel transmission line to calculate the line's propagation velocity and demonstrate favorable comparison with measured values. Moisture content measurement is used as an example     

Transient image theory for 2-D and 3-D conducting wedge problems

In the present paper, two- and three-dimensional transient scattering from a perfectly conducting wedge is studied. The exciting sources analyzed are an infinite impulsive line current parallel to edge of the conductor and an arbitrarily oriented electric dipole. The analysis presented is based on the time-harmonic image solution found for the scattered field. The frequency-domain image current corresponding to the field contribution from the wedge is an exact function expressed in terms of simple trigonometric functions. It is dependent only on the coordinates and the amplitude of the source, but it is independent of the observation point. It is shown that the transient scattering can be interpreted as arising from an image source by generalizing the time domain Green's function to complex source points     

Electromagnetic scattering by a mixture of conducting and dielectric objects: analysis using method of moments

In this paper, the method of moments is employed to solve the combined field integral equation for characterizing electromagnetic scattering by large three-dimensional structures of arbitrary shape. Unlike those discussed in the literature, these structures consist of mixed conducting and homogeneous dielectric objects. To improve the matrix conditioning number, the basis functions used to represent magnetic currents are also chosen as the popular Rao-Wilton-Glisson functions, but are multiplied by a constant number. A Galerkin's procedure is implemented, i.e., the testing functions are chosen to be the same as the basis functions.     

A quasi-wave method for determination of a general solution to the complex maxwell equations in an inhomogeneous anisotropic absorbing medium

A formal general solution to the homogeneous Maxwell equations is obtained in the form of a matrix asymptotic series for the case of a quasi-plane-layered medium in which complex tensors \(\hat \varepsilon \) and \(\hat \mu \) arbitrarily depend on Cartesian coordinate zand slowly change in the planes z=const. A recurrent system of matrix first-order linear ordinary differential equations for the coefficients of this series is derived. In contrast to the method of geometric optics, this solution, even in the first approximation, takes into account the wave polarization and has a wider range of application.     

Stationary phase method application for the analysis of radiationof complex 3-D conducting structures

The stationary phase method is used to calculate the radiation pattern of antennas on complex structures. Physical optics (PO) approximation has been applied for the induced currents. The problem is stated directly over the parametric surfaces used to model the geometry and no translation of geometrical formats is required. The integral comes from the contribution of certain points on the surface (specular, boundary and vertices) where the phase term of the integrand presents a stationary behavior. In general, the asymptotic integration behaves similar to the numerical one but being more efficient in execution time than the latter     

A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies

A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.     

A hybrid finite element method for 3-D scattering using nodal andedge elements

A hybrid finite element method for three-dimensional scattering is presented and numerical examples shown. This approach, which couples finite element discretization with the method of moments, is particularly well suited for monostatic radar cross section calculations. The method is based on a scalar and vector potential formulation of Maxwell's equations, the use of nodal elements, and a highly efficient body of revolution implementation of the method of moments. Combined nodal and edge elements are employed to accurately model fields around corners and edges. A curvature-based sampling criterion is derived and shown to ensure accurate answers for highly curved scatterers. Numerical results and Cray computer timings are compared with published results for an edge element code using radiation boundary conditions     

Two-dimensional scattering from an inhomogeneous dielectriccylinder embedded in a stratified medium: case of TM polarization

Two-dimensional scattering of a TM-polarized electromagnetic wave from a transversely inhomogeneous isotropic body buried in a homogeneous layer of an arbitrarily stratified isotropic medium has been considered using the integral equation formulation over the cross section of the body and the moment method. The arising system of linear algebraic equations is solved with the aid of the conjugate gradient method and the one-dimensional fast Fourier transform. Illustrative numerical results are presented for both an inclusion in a half space and in a layer on a homogeneous substrate     

DIRECT SOLUTION BY 2-D AND 3-D FINITE ELEMENT METHOD ON FORWARD PROBLEM OF LOW FREQUENCY CURRENT FIELDS IN INHOMOGENEOUS MEDIA

The paper adopts finite element method to analyze the forward problem of low-frequency current fields in inhomogeneous media. Firstly, the direct solution of 2-D and 3-D scalar potential is given. Secondly, the technique of covering finite elements for problems with movement has been presented; namely, when the place of testing point moved, the meshing data will be produced automatically to avoid re-meshing and distortion of the mesh. Thirdly the free and prescribed potential method is used to make the finite element coefficient matrices. Then this paper provides the result of a validity test obtained by simulating the laterolog-3 logging, compared with the numerical model-matching method. Finally, the MLL response is calculated.