Method of moments evaluation of the two-dimensionalquasi-crystalline approximation

In remote sensing, the propagation of electromagnetic fields through random media is often of concern. We may wish to characterize the effects of clouds or water droplets along the line of sight between an airplane and a radar installation, or we may be interested in using radar to probe the random medium itself, such as in determining snow depth and particle size. In all of these problems it is necessary to predict the propagation constant in the “random” medium. The purpose of this paper is to characterize the accuracy of the quasi-crystalline approximation and other associated methods of determining the effective permittivity for two-dimensional (2-D) random media. A numerical method based on the method of moments is used as a gauge for comparison with the theoretical methods. After deriving the 2-D quasi-crystalline approximation and presenting the numerical method, the behavior of the effective permittivity is analyzed for a range of particle sizes, volume fractions and dielectric losses. From this analysis, regions of validity for the theoretical methods are determined. An investigation is also given which explores the effect of particle arrangement methods on the pair distribution function which, in turn, is shown to have a significant effect on the imaginary component of the effective permittivity     

Experimental characterization of the effective propagation constantof dense random media

A new technique for measuring the effective propagation constant of dense random media is presented. This technique involves two major steps: (1) measurement of the mean bistatic scattered field of a cluster of the random medium confined in a spherical boundary and (2) characterization of the complex permittivity for a homogeneous dielectric sphere having identical radius and bistatic scattered field as those of the spherical cluster of the random medium. Using this measurement technique, not only the effective propagation constant of complex dense random media for which an analytical solution does not exist can be characterized, but it can also be used to establish the validity region of the existing models. The sensitivity analyses of the proposed algorithm show that the imaginary part of the effective propagation constant can be measured very accurately. It is also shown that the effective complex permittivity of media with very low dielectric contrast or volume fractions can be characterized accurately. Measurements of the effective propagation constant of different dense random media comprised of homogeneous spherical particles of different packing densities are reported and compared with the existing analytical models     

Quasi-static effective permittivity of periodic compositescontaining complex shaped dielectric particles

A methodology is described for computing the quasi-static effective permittivity of a two-dimensional (2-D) or three-dimensional (3-D) lattice of dielectric particles. The particles in this composite material may have complicated shapes. This methodology uses a moment method based technique to determine the electric dipole moments of the particles immersed in a uniform electric field. The effective permittivity is then obtained using an appropriate macroscopic model. With this methodology, the mutual interaction between particles can be accounted for accurately. The computed effective permittivity for round cylinders and spheres suspended in a host are compared with our previous T-matrix method results as well as the Maxwell Garnett (MG) formula predictions. Three additional examples involving square (2-D), rounded square (2-D), and spherical (3-D) dielectric inclusions are also given, illustrating the shape effects on the computation of the quasi-static effective permittivity. While the square- and cubic-shaped particles can possess great mutual interaction, surprisingly their effective permittivity is well predicted for all volume fractions by the simple MG formula in both 2-D and 3-D problems     

Estimation of Incoherent Scattered Field by Multiple Scatterers in Random Media

This paper proposes a method to estimate directly the incoherent scattered intensity and radar cross section (RCS) from the effective permittivity of a random media. The proposed method is derived from the original concept of incoherent scattering. The incoherent scattered field is expressed as a simple formula. Therefore, to reduce computation time, the proposed method can estimate the incoherent scattered intensity and RCS of a random media. To verify the potential of the proposed method for the desired applications, we conducted a Monte‐Carlo analysis using the method of moments; we characterized the accuracy of the proposed method using the normalized mean square error (NMSE). In addition, several medium parameters, such as the density of scatterers and analysis volume, were studied to understand their effect on the scattering characteristics of a random media. The results of the Monte‐Carlo analysis show good agreement with those of the proposed method, and the NMSE values of the proposed method and Monte‐Carlo analysis are relatively small at less than 0.05.     

Scattering by a Cylindrical Post of Complex Permittivity in a Waveguide

An exact solution of the discontinuity problem of a circular cylindrical post of arbitrary complex permittivity centered in a rectangular waveguide with the axis parallel to the electric field vector of the dominant mode has been set up and numerical results based directly on this solution have been found rising an electronic computer. The method used divides the waveguide up into three different regions by introducing two imaginary plane walls perpendicular to the waveguide walls. In the center region, which contains the cylindrical rod, the electromagnetic field is expanded in cylindrical waves and in the outer regions the field is expanded in waveguide modes. By setting up the boundary conditions at all discontinuity surfaces and performing numerical matching of the fields at the two imaginary walls, a system of linear equatious determining the coefficients of reflection, transmission, and absorption of the field due to the cylindrical rod is found. The structure which is of most interest in the case of a plasma column is a coaxial structure consisting of an inner dielectric cylinder with complex permittivity (the plasma) surrounded by a dielectric sleeve with real, positive permittivity (the glass tube). The theory is therefore developed to apply generally for such structures. From the numerical results, curves have been obtained showing the relationship between the coefficients of reflection and transmission and the (complex) permittivity of the rod material. Such curves maybe used for deducing the microwave properties of a cylindrical rod from measurements of the reflection and transmission coefficient of the rod.     

2.45GHz微波频率下有机二元体系溶液等效介电系数新特性的实验研究

介质混合物的等效介电系数是微波化学研究中的一个重要内容.本文在微波频率下,利用微扰法测量了有机二元体系的等效介电系数.测试结果显示:在二元混合体系中,当两组元的等效介电系数实部接近而虚部相差较大或虚部接近而实部相差较大时,介质混合物的等效介电系数的实部(或虚部)随体积比变化过程中,会出现大于其中任何一种组份的介电系数实部(或虚部)的峰值.本文中,利用对称Bruggeman理论对这一与Clausius-Mossotti、 Onsager和Kirkwood等传统理论相悖的新特性进行了合理的解释与分析.     

A homomorphic filtering method for imaging strongly scatteringpenetrable objects

This paper describes a new method for determining the structure of strongly scattering penetrable objects having permittivity fluctuations with scales comparable to the illuminating wavelength. We are concerned with the case when small wavelength or weakly scattering approximations, such as the Born or distorted wave Born approximations, or slowly varying approximations such as the Rytov approximation, are not valid. The problem is formulated as one of recovering, in principle, a quantitative image of the object's permittivity distribution function from a set of perturbed images. Each perturbed image is obtained by backpropagating the scattered field measured around the object for different illumination directions. These backpropagated images are filtered in the differential cepstral domain to recover the object permittivity distribution, and we show reconstructions from both simulated and real microwave scattered data     

A high order renormalization method for radar backscatter from arandom medium

The problem of radar backscattering from a half-space random medium is formulated in terms of a series solution to Dyson's equation for the mean field in the random medium. The renormalization method is applied to given an approximate solution through the use of Feynman diagrams. An improved approximation is then obtained by including two additional summations of infinite series of these diagrams. The results from this improved approximation are used to calculate the radar backscattering cross sections and compared with those of a previous paper (1980). For comparison with experimental data, a field of vegetation is modeled as a random medium with an average complex permittivity as well as fluctuations in the real and imaginary parts of the permittivity. The values of the average permittivity and the variance of the fluctuations are estimated by the use of dielectric mixture theory     

Three-Dimensional Through-Wall Imaging Under Ambiguous Wall Parameters

A through-wall imaging problem for a 3-D geometry is considered. Scatterers are located beyond a wall represented by a dielectric slab whose features are unknown or known with some degree of uncertainty. A two-step imaging procedure is presented. First, the thickness and the dielectric permittivity of the wall are estimated by a simple procedure which takes into account that actual measurements concern the total scattered field (i.e., the field reflected by the wall plus the one scattered by the obscured scatterers). Then, the problem is cast as a linear inverse scattering problem and solved by means of a truncated-singular value decomposition algorithm. In particular, a 2-D sliced approach is employed to obtain the 3-D scene. Numerical examples are shown to assess the effectiveness of the reconstruction procedure.     

Effective permittivity of mixtures: numerical validation by theFDTD method

The present paper reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of a two-dimensional (2-D) dielectric mixture is calculated by FDTD simulations of such a sample in a TEM waveguide. Various theoretical bounds are tested in light of the numerical simulations. The results show how the effective permittivity of a mixture with random inclusion positionings is distributed. All possible permittivity values lie between Wiener limits, and according to FDTD simulations the values are almost always between Hashin-Shtrikman limits. Calculated permittivity distribution is also compared with theoretical mixture models. No model seems to be able to predict the simulated behavior over the whole range of volume fraction     

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     

Monte Carlo simulations for clutter statistics in minefields: AP-mine-like-target buried near a dielectric object beneath 2-D random rough ground surfaces

A rigorous three-dimensional (3-D) electromagnetic model is developed to analyze the scattering from anti-personnel (AP) nonmetallic mine-like target when it is buried near a clutter object under two-dimensional (2-D) random rough surfaces. The steepest descent fast multipole method (SDFMM) is implemented to solve for the unknown electric and magnetic surface currents on the ground surface, on the target and on the clutter object. A comprehensive numerical investigation of two clutter sources; the ground roughness and the nearby benign object, is presented based on using more than 800 random rough surface realizations which could not be achieved without using fast algorithms such as the SDFMM. The statistics of the scattered near-electric fields are computed using the Monte Carlo simulations for both polarizations. For the parameters used here, the results show that the average and the standard deviation of the target signature represent 5-7% and 3-3.5% of the total scattered signal, respectively, while they represent 16-20% and 7-12% of the signal for the clutter object, respectively. This study indicates the high possibility of a false alarm during the detection process when the target is located nearby a realistic object such as a piece of a tree root.     

Microwave image reconstruction from 3-D fields coupled to 2-D parameter estimation

An efficient Gauss-Newton iterative imaging technique utilizing a three-dimensional (3-D) field solution coupled to a two-dimensional (2-D) parameter estimation scheme (3-D/2-D) is presented for microwave tomographic imaging in medical applications. While electromagnetic wave propagation is described fully by a 3-D vector field, a 3-D scalar model has been applied to improve the efficiency of the iterative reconstruction process with apparently limited reduction in accuracy. In addition, the image recovery has been restricted to 2-D but is generalizable to three dimensions. Image artifacts related primarily to 3-D effects are reduced when compared with results from an entirely two-dimensional inversion (2-D/2-D). Important advances in terms of improving algorithmic efficiency include use of a block solver for computing the field solutions and application of the dual mesh scheme and adjoint approach for Jacobian construction. Methods which enhance the image quality such as the log-magnitude/unwrapped phase minimization were also applied. Results obtained from synthetic measurement data show that the new 3-D/2-D algorithm consistently outperforms its 2-D/2-D counterpart in terms of reducing the effective imaging slice thickness in both permittivity and conductivity images over a range of inclusion sizes and background medium contrasts.     

“Blind” shape reconstruction from experimental data

A method for reconstructing the shape of a bounded impenetrable object from measured scattered field data is presented. The reconstruction algorithm is, in principle, the same as that used before for reconstructing the conductivity of a penetrable object and uses the fact that for high conductivity the skin depth of the scatterer is small, in which case the only meaningful information produced by the algorithm is the boundary of the scatterer. A striking increase in efficiency is achieved by incorporating into the algorithm the fact that for large conductivity, the contrast is dominated by a large positive imaginary part. This fact together with the knowledge that the scatterer is constrained in some test domain constitute the only a priori information about the scatterer that is used. There are no other implicit assumptions about the location, connectivity, convexity, or boundary conditions. The method is shown to successfully reconstruct the shape of an object from experimental scattered field data in a “blind” test     

Analytical solution for electromagnetic diffraction on 2-Dperfectly conducting scatterers of arbitrary shape

A method is developed to receive a rigorous analytical solution of the external stationary two-dimensional (2-D) boundary value problem for the Helmholtz equation for perfectly conducting scatterers of an arbitrary shape. The rigorous expression for the scattered field is represented by the sum of integrals along piece-wise contours in a complex plane. In case of necessity a simple analytical asymptotic expression can be obtained     

Image reconstruction from TE scattering data using equation ofstrong 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     

Numerical modeling of disordered mixture using pseudorandom simulations

The electrostatic effective permittivity of samples of three-dimensional random material consisting of equisized spheres is analyzed numerically. The electric field inside a cubical computation domain is calculated by using finite-element method and field calculation software Opera in a supercomputer. The spheres occupy random positions in the cubic computation cell. As the effective permittivity is analyzed numerically, the finite calculation domain makes the structure infinite and periodic. This kind of structure is called pseudorandom material. This study suggests that a relatively small computational domain (around five times the inclusion sphere radius) could be used when modeling random mixture, if the same samples are analyzed using three orthogonal field orientations. The effective permittivity as a function of the volume fraction of inclusions can be described with generalized mixing formula containing a parameter, which is fitted to numerical results.     

Shadow boundary incremental length diffraction coefficients appliedto scattering from 3-D bodies

Shadow boundary incremental length diffraction coefficients (SBILDCs) are high-frequency fields designed to correct the physical optics (PO) field of a three-dimensional (3-D) perfectly electrically conducting scatterer. The SBILDCs are integrated along the shadow boundary of the 3-D object to approximate the field radiated by the nonuniform shadow boundary current (the difference between the exact and PO currents near the shadow boundary). This integral is added to the PO field to give an approximation to the exact scattered field that takes into account both PO and nonuniform shadow boundary currents on the scatterer. Like other incremental length diffraction coefficients, any SBILDC is based on the use of a 2-D canonical scatterer to locally approximate the surface of the 3-D scatterer to which it is applied. Circular cylinder SBILDCs are, to date, the only SBILDCs that have been obtained in closed form. In this paper, these closed-form expressions are validated by applying them for the first time to a 3-D scatterer with varying radius of curvature-the prolate spheroid. The results obtained clearly demonstrate that for bistatic scattering the combined PO-SBILDC approximation is considerably more accurate than the PO field approximation alone     

Renormalization of EM fields in application to large-angle scattering from randomly continuous media and sparse particle distributions

The conventional wave-integral equation in electromagnetic scattering, consisting of a sum of directly received vacuum field plus a scattered field that sums weighted vacuum spherical waves from each scatterer, is replaced by one in which renormalized fields containing part of the multiply scattered energy replace the vacuum fields. A first-order approximation in the renormalized equation is applied to bistatic (large-angle) scattering from weak random fluctuations of the permittivity in a distant volume, and to a sparse monodisperse distribution of isotropic particles to yield scattering cross sections with extended validity for the direct polarization. A similar correction is introduced for the cross polarization in the case of backscatter. Differences with other calculations are noted.