Electromagnetic Prospection via Homogeneous and Inhomogeneous Plane Waves: The Case of an Embedded Slab

This paper deals with the linear approximation of the inverse scattering problem for a dielectric slab embedded into a homogeneous half-space. After a proper normalization of the scattered field, the problem at hand is recognized to be related to a Fourier transform inversion with limited data. This permits to resort to the well-known results available in signal processing in order to discuss about the class ofthe retrievable unknowns and the resolution limits achievable by inversion. In particular, the role of both homogeneous and inhomogeneous incident plane waves in carrying out information about the profile under test is investigated and the role played by the dielectric permittivity of the host medium in determining the information content of the scattered field is pointed out.     

Analysis of the distorted Born approximation for subsurface reconstruction: truncation and uncertainties effects

The problem of determining the dielectric permittivity profile of buried objects starting from the knowledge of the scattered field is considered in the two-dimensional geometry when incomplete near-zone data are collected at a single frequency under a multiview/multistatic measurement configuration. In particular, attention is paid to the practical issues of the truncated observation domain and the presence of uncertainties on data. The problem is tackled with reference to the scalar polarization by linearization of the mathematical relationship between the unknown dielectric permittivity profile and the scattered field. A homogeneous, possibly lossy, half-space geometry for the subsurface modeling is adopted, thus leading to the so-called distorted Born approximation (DBA). A thorough investigation of the class of unknown functions that can be reliably retrieved is performed by dealing with singular value decomposition of the relevant linear operator. It results that even if sources and receivers are located at the interface, a very restricted set of profile variations can be reconstructed by a stable inversion algorithm. In particular, reduced vertical features of the buried objects with respect to the horizontal ones can be reconstructed under DBA. Moreover, the truncation of the observation domain further restricts this set, affecting mainly the vertical resolution. Numerical results confirming the validity of the analysis are also provided.     

Scattering by an arbitrary cylinder at a plane interface: broadsideincidence

The problem of the determination of the fields scattered by an infinite dielectric cylinder of arbitrary cross section located at the interface between two semi-finite dielectric media is reduced to the solution of integral equations for unknown functions defined on the boundaries. These boundary functions are chosen so as to minimize their number. The incident field is that of a plane monochromatic wave. The derivation of the integral equations is given for the transverse electric (TE) mode for a dielectric cylinder and for a perfectly conducting cylinder. The exact electromagnetic fields are obtained from the solutions of the integral equations by integration, and the radar cross section can be computed from the far-field approximation. Sample outputs of the computer programs that implement this solution are shown     

Microwave imaging within the second-order Born approximation:stochastic optimization by a genetic algorithm

This paper addresses the problem of reconstructing the location, shape, and dielectric permittivity distribution of an inhomogeneous dielectric object from measurements of the field scattered by the object. The object is an inhomogeneous infinite cylinder of arbitrary cross section illuminated by a transverse magnetic incident electric field. The approach is based on the Lippmann-Schuringer integral equation for the electromagnetic inverse scattering problem, approximated by applying the second-order Born approximation, which allows an extension of the range of contrast values that can be accurately imaged. The numerical approach is developed in the spatial domain and makes use of a multi-illumination multiview processing. In particular, the inverse problem is recast in a global nonlinear optimization problem (including a penalty function), solved by a stochastic method based on a genetic algorithm. In this paper, the mathematical formulation of the approach is described and the results of several dielectric reconstructions are reported, including comparisons with analogous reconstructions performed within the linearized (first-order) Born approximation     

Radar cross sections of dielectric or plasma coated conducting spheres and circular cylinders

Radar cross sections for a variety of spherical and cylindrical scatterers having homogeneous dielectric or plasma shells are obtained by using both the exact boundary value solutions and approximate, semi-empirical methods based on physical principles. The plasma is assumed to have the macroscopic properties of a lossless dielectric with a permittivity less than that of free space. A superposition approximation for the radar cross section of a dielectric coated conducting body is obtained by considering the scattered field to be the phasor sum of two principal components, the field scattered by the air-dielectric interface and the field scattered by an equivalent conducting body which differs from the actual body because of the lens action of the shell. This approximation yields very good agreement with the exact solutions for both spherical and cylindrical dielectric clad scatterers with radii in the Rayleigh region and in the resonant region, and for bistatic scattering as well as for backscatter. The echo area of a conducting sphere with nonconcentric spherical dielectric shell calculated by means of the superposition approximation is in excellent agreement with experimental measurements, thus demonstrating the validity of this method in a case for which the exact solution cannot be obtained.     

电介质粗糙表面光散射特性

为了研究电介质随机表面散射特性的物理产生机制,采用基于Kirchhoff近似的Monte-Carlo方法进行了数值计算,得到了一组不同粗糙程度的电介质随机表面在s线偏振光入射时的散射光强度空间分布.所有表面自相关长度相同.结果表明,随均方根高度的增加,散射光强度空间分布呈现峰值衰减、展宽和向后向移动的特征.对这些散射特...     

A numerical solution to full-vector electromagnetic scattering bythree-dimensional nonlinear bounded dielectrics

This paper deals with electromagnetic scattering by nonlinear dielectric objects. In particular, a numerical approach is developed that is aimed at determining the distributions of the electromagnetic field vector inside a three-dimensional nonlinear, inhomogeneous, isotropic scatterer illuminated by a time-periodic incident electric field vector. An integral-equation formulation for the full-vector scattering problem is considered, and the nonlinear effect is taken into account by introducing equivalent sources and a Fourier-series representation. A system of integral equations (for each harmonic vector component and for the static term) is obtained that includes the internal electric field distribution as the unknown. After discretization, the solution is reduced to solving an algebraic system of nonlinear equations. Some preliminary numerical results are reported concerning scatterers that exhibit a specific (quadratic) dependence of the dielectric permittivity on the total electric field. The harmonic components of the scattered electric field outside the objects are also computed     

非磁性小粒子散射的磁偶极贡献

采用磁偶极子和电四极子模型下的静场近似方法 ,得到了球形小粒子电磁散射场的两个高阶项 ,其大小正比于粒子半径的五次方 ,它和Mie级数解中对应的两项近似结果完全一致 ,从而可以将Mie级数解中这两项解释为磁偶极和电四极项散射的贡献。该方法仅要求粒子的几何尺寸的平方远小于波长的平方 ,在该条件下可将这种方法推广应用到非球形粒子 ,并给出了椭球和矩形两种非球形小粒子磁偶极散射贡献的理论计算公式 ,其结果与FDTD数值模拟结果有很好的一致性。     

On the degrees of freedom of scattered fields

Starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities, the degrees of freedom of the scattered field are introduced and then computed. The degrees of freedom are shown to be practically equal to the Nyquist number appropriate to the effective (spatial) bandwidth of the scattered field and to the extension of the observation domain. Accordingly, a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error. It is also shown that the field representation can be made in terms of field values and simple sampling functions, provided that a marginal increase in the approximation error is tolerated. The results not only completely justify the use of sampling interpolation for representing scattering fields, but also demonstrate that such representation is practically an optimal one. An algorithm for the reconstruction of scattered fields, given the maximum allowed error, is then produced     

An application of the boundary element method to the magnetic fieldintegral equation

A boundary element method (BEM) for the solution of electromagnetic scattering problems using the magnetic field integral equation (MFIE) is discussed. The discretized form of the MFIE is written in indicial notation with no limitations placed on the order of either the geometric or functional approximation. By considering several different types of boundary elements, it is determined that geometric errors can be significant and degrade the accuracy of the numerical solution. It is shown that a higher-order approximation for the current could significantly improve the accuracy of the numerical solution. The superparametric boundary element in which the geometry was given quadratic approximation and the current was given linear approximation was more efficient than elements using lower-order approximations. The BEM results are compared to the results obtained using the dielectric bodies of revolution (DBR) code     

An inexact-Newton method for short-range microwave imaging within the second-order Born approximation

A new approach to noninvasive inspection of dielectric targets at microwave frequencies is proposed. Cylindrical dielectric objects are reconstructed under the second-order Born approximation. A multi-illumination configuration is considered. The continuous model is discretized by the moment method and an efficient inexact-Newton method is applied. The dielectric profile is iteratively reconstructed starting from the measured scattered data, which are related to the unknown target through the inverse scattering equations written in a variational setting. Several numerical results are reported, which are aimed at assessing the capabilities of the approach in dealing with the nonlinear ill-posed inverse problem associated to the short-range microwave imaging. Single, multilayer, and separate cylinders are reconstructed in noiseless and noisy environments.     

Nonlinear two-dimensional velocity profile inversion using timedomain data

An iterative algorithm is developed to solve the nonlinear inverse scattering problem for two-dimensional lossless dielectric inhomogeneities using time-domain scattering data. The method is based on performing Born-type iterations on a volume integral equation and, hence, successively calculating higher-order approximations to the unknown object profile. Both the full-angle and the limited-angle problems are considered. Solutions are obtained for cases where the first-order Born approximation is severely violated. Wideband time-domain scattered field measurements make it possible to use sparse data sets and thus reduce experimental complexity and computation time. Several examples are given to show the ability of this method to invert arbitrarily shaped permittivity profiles using few transmitters and receivers. The high-resolution capability of the algorithm is also demonstrated     

Synthesis of new variable dielectric profile antennas via inverse scattering techniques: a feasibility study

In this paper, we investigate whether and how one can synthesize given far field patterns by acting on the dielectric profile of a lens antenna. In particular, an approach to design a radiating system consisting of a variable dielectric profile and a single or a low number of feeds is proposed and discussed. To properly take into account physical and practical feasibility issues, the proposed method splits the problem into two steps. The first one is aimed to fix design goals (i.e., the nominal field), in such a way to avoid super-directive or physically unfeasible antennas and properly exploits known properties of electromagnetic fields radiated by finite extent sources. The second step, dealing with the dielectric profile synthesis, is based on suitable modifications of inverse scattering techniques and can take into account constraints on the spatial behavior as well as of dielectric characteristics of the profile to be synthesized. To show the interest of the subject, as well as effectiveness of the proposed approach, the synthesis of new dielectric antennas, such as a high directivity source and a lens radiating a steerable degradation-free Chebyshev pattern, is considered in the two dimensional scalar case.     

Trigonometric approximations for the computation of Radar cross sections

Trigonometric approximation methods for the interpolation of the far field of a scatterer lit up by plane waves are presented. The Wacker method, commonly used to determine the far field of an antenna from spherical near field measurements, is adapted to decompose the scattered field in a finite series of vector spherical harmonics. The decomposition coefficients are used to assess the accuracy of the computed field and to efficiently store the far field profile. These coefficients are approximated by trigonometric functions up to a given order which can be estimated from the geometry of the scatterer. In this way an efficient procedure for the interpolation of monostatic and bistatic radar cross sections is obtained.     

A regularized Newton method for one-dimensional profile inversion of a lossy cylinder

A regularized Newton iterative method is presented for the determination of one-dimensional profile of an inhomogeneous circularly cylindrical region. The region is assumed to be filled with a lossy dielectric material of which electromagnetic parameters have an arbitrary variation in the radial direction. By using the finite Fourier transformation of field expressions, the problem is first reduced to a system of non-linear operator equations which can be solved through regularized Newton method. The method requires to solve the scattered field and the Fréchet derivatives in the inhomogeneous region in each iteration step. Numerical simulations are carried out to test the applicability and the effectiveness of the method.     

Redundant electromagnetic data for microwave imaging ofthree-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     

Electromagnetic scattering from slightly rough surfaces withinhomogeneous dielectric profiles

Remote sensing of soil moisture using microwave sensors require accurate and realistic scattering models for rough soil surfaces. In the past, much effort has been devoted to the development of scattering models for either perfectly conducting or homogeneous rough surfaces. In practice, however, the permittivity of most soil surfaces is nonuniform, particularly in depth, for which analytical solution does not exist. The variations in the permittivity of a soil medium can easily be related to its soil moisture profile and soil type using the existing empirical models. In this paper, analytical expressions for the bistatic scattering coefficients of soil surfaces with slightly rough interface and stratified permittivity profile are derived. The scattering formulation is based on a new approach where the perturbation expansion of the volumetric polarization current instead of the tangential fields is used to obtain the scattered field. Basically, the top rough layer is replaced with an equivalent polarization current and, using the volumetric integral equation in conjunction with the dyadic Green's function of the remaining stratified half-space medium, the scattering problem is formulated. Closed-form analytical expressions for the induced polarization currents to any desired order are derived, which are then used to evaluate the bistatic scattered fields up to and including the third order. The analytical solutions for the scattered fields are used to derive the complete second-order expressions for the backscattering coefficients as well as the statistics of phase difference between the scattering matrix elements. The theoretical results are shown to agree well with the backscatter measurements of rough surfaces with known dielectric profiles and roughness statistics     

A numerical simulation of scattering from one-dimensionalinhomogeneous dielectric random surfaces

An efficient numerical solution for the scattering problem of inhomogeneous dielectric rough surfaces is presented. The inhomogeneous dielectric random surface represents a bare soil surface and is considered to be comprised of a large number of randomly positioned dielectric humps of different sizes, shapes, and dielectric constants above an impedance surface. Clods with nonuniform moisture content and rocks are modeled by inhomogeneous dielectric humps and the underlying smooth wet soil surface is modeled by an impedance surface. In this technique, an efficient numerical solution for the constituent dielectric humps over an impedance surface is obtained using Green's function derived by the exact image theory in conjunction with the method of moments. The scattered field from a sample of the rough surface is obtained by summing the scattered fields from all the individual humps of the surface coherently ignoring the effect of multiple scattering between the humps. The statistical behavior of the scattering coefficient σ° is obtained from the calculation of scattered fields of many different realizations of the surface. Numerical results are presented for several different roughnesses and dielectric constants of the random surfaces. The numerical technique is verified by comparing the numerical solution with the solution based on the small perturbation method and the physical optics model for homogeneous rough surfaces. This technique can be used to study the behavior of scattering coefficient and phase difference statistics of rough soil surfaces for which no analytical solution exists