Distortion in diffraction tomography caused by multiple scattering

In this paper, we have first presented a new computational procedure for the calculation of the "true" forward scattered fields of a multicomponent object. By "true" we mean fields that are not limited by the first-order approximations, such as those used in the first-order Born and Rytov calculations. Although the results shown will only include the second-order fields for a multicomponent object, the computational procedure can easily be generalized for higher order scattering effects. Using this procedure we have shown by computer simulation that even when each component of a two-component object is weakly scattering, the multiple scattering effects become important when the components are blocking each other. We have further shown that when strongly scattering components that are large compared to a wavelength are not blocking each other, the scattering effects can be ignored. Both these conclusions agree with intuitive reasoning. Since all the currently available diffraction tomography algorithms are based on the assumption that the object satisfies the first-order scattering assumption, it is interesting to test them under conditions when this assumption is violated. We have used the scattered fields obtained with the new computational procedure to test these algorithms, and shown the resulting artifacts. Our main conclusion drawn from this computer simulation study is that even when object inhomogeneities are as small as 5 percent of the background, multiple scattering can introduce severe distortions in multicomponent objects.     

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     

一种抑制探地/穿墙成像多径虚假目标的新型概率模型:数值研究(英文)

该文提出了一种抑制探地和穿墙成像中多径虚假目标的新方法, 虚假目标主要来源于基于伯恩近似的线性成像算法, 该方法忽略了目标之间的多次散射。相对已有抑制多径虚假目标的方法, 该文的主要贡献有两个方面:(a)目标反射率第一次用概率函数模型表征, (b)成像过程中引入随机孔径(从整个孔径中随机选取获得)的概念, 因此, 最终雷达图像可以理解为由随机子孔径得到图像相乘获得的联合概率分布。最后, 通过一组数值算例验证了该方法在探地和穿墙成像中的有效性。      

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     

The Effects of Attenuation on the Born Reconstruction Procedure for Microwave Diffraction Tomography (Short Paper)

The effects of attenuation on the Born inversion process for diffraction tomography are investigated. The exact forward scattered fields for a Iossy dielectric cylinder in a Iossy medium are calculated and are then used to reconstruct an image of the scattering object. As accurate image is produced only when the cylinder acts as a small perturbation on the dielectric constant of the external medium. Results indicate that even small losses have a significant effect on the resolution of the image. It is possible, however, to eliminate image distortion by matching the loss tangent of the outside medium to that within the cylinder.     

Microwave Subsurface Imaging Using Direct Finite-Difference Frequency-Domain-Based Inversion

We have developed a new algorithm for electromagnetic inverse scattering problems in inhomogeneous media using finite-difference frequency-domain (FDFD) forward modeling, referred to as the FDFD-based inversion method. The key issue of this method is to build a linear expression for the inverse problem from an FDFD forward model by using Born approximation to neglect mutual coupling between scattered pixels and to then solve for the inverse coefficient matrix. An important advantage of this matrix-based method is that there is no need to specify a Green's function. As such, this inverse scattering algorithm is easily implemented and is robust to the heterogeneity in the background. We test the algorithm with a microwave subsurface object detection application using cross-well radar. The new method is compared with conventional inversion using Green's function-based Born approximation. Numerical experiments are presented for a 2-D borehole geometry for buried object detection in uniform soil and in multilayered soil backgrounds.      

Planar and cylindrical active microwave temperature imaging: numerical simulations

A comparative study at 2.45 GHz concerning both measurement and reconstruction parameters for planar and cylindrical configurations is presented. For the sake of comparison, a numerical model consisting of two nonconcentric cylinders is considered and reconstructed using both geometries from simulated experimental data. The scattered fields and reconstructed images permit extraction of very useful information about dynamic range, sensitivity, resolution, and quantitative image accuracy for the choice of the configuration in a particular application. Both geometries can measure forward and backward scattered fields. The backscattering measurement improves the image resolution and reconstruction in lossy mediums, but, on the other hand, has several dynamic range difficulties. This tradeoff between forward only and forward-backward field measurement is analyzed. As differential temperature imaging is a weakly scattering problem, Born approximation algorithms can be used. The simplicity of Born reconstruction algorithms and the use of FFT make them very attractive for real-time biomedical imaging systems.     

Application of strong fluctuation random medium theory to scattering of electromagnetic waves from a half-space of dielectric mixture

The strong fluctuation random medium theory is applied to calculate scattering from a half-space of dielectric mixture. The first and second moments of the fields are calculated, respectively, by using the bilocal and the distorted Born approximations, and the low frequency limit is taken. The singularity of the dyadic Green's function is taken into account. Expressions for the effective permittivity for the full space case are derived. It is shown that the derived result of the effect permittivity is identical to that of the Polder and van Santern mixing formula. The correlation function of the random medium is obtained by using simple physical arguments and is expressed in terms of the fractional volumes and particle sizes of the constituents of the mixture. Backscattering coefficients of a half-space dielectric mixture are also calculated. Numerical results of the effective permittivity and backscattering coefficients are illustrated using typical parameters encountered in microwave remote sensing of dry and wet snow. It is also shown that experimental data can be matched with the theory by using physical parameters of the medium as obtained from ground truth measurements.     

Spatial harmonic imaging of X-ray scattering--initial results

Coherent X-ray scattering is related to the electron density distribution by a Fourier transform, and therefore a window into the microscopic structures of biological samples. Current techniques of scattering rely on small-angle measurements from highly collimated X-ray beams produced from synchrotron light sources. Imaging of the distribution of scattering provides a new contrast mechanism which is different from absorption radiography, but is a lengthy process of raster or line scans of the beam over the object. Here, we describe an imaging technique in the spatial frequency domain capable of acquiring both the scattering and absorption distributions in a single exposure. We present first results obtained with conventional X-ray equipment. This method interposes a grid between the X-ray source and the imaged object, so that the grid-modulated image contains a primary image and a grid harmonic image. The ratio between the harmonic and primary images is shown to be a pure scattering image. It is the auto-correlation of the electron density distribution at a specific distance. We tested a number of samples at 60-200 nm autocorrelation distance, and found the scattering images to be distinct from the absorption images and reveal new features. This technique is simple to implement, and should help broaden the imaging applications of X-ray scattering.     

Study of resolution and super resolution in electromagnetic imaging for half-space problems

It has been observed that super resolution is possible in the electromagnetic imaging. In the first part of the paper, the possible resolution of image is investigated in the inversion of far-field data using the diffraction tomographic (DT) algorithm, where two cases are considered when the object is in a homogeneous space and in an air-earth half space. The study shows that the resolution of image for inversion of far-field data has been limited theoretically to 0.3536-0.5 wavelength using the DT algorithm in homogeneous-space problems, and it is even worse in half-space problems. If the transmitters and receivers are located in the near-field regime, however, the image resolution is less than 0.25 wavelength, which is the super-resolution phenomenon. In the second part of the paper, the physical reason for the super-resolution phenomenon is investigated using different electromagnetic inverse scattering methods. The study has demonstrated that the information of evanescent waves in the measurement data and its involvement in inversion algorithms is the main reason for the super resolution. Four inversion algorithms are considered for half-space problems: the DT algorithm, the spatial-domain Born approximation (BA), the Born iterative method (BIM), and the distorted BIM (DBIM). The first two belong to linear inverse scattering, while the last two belong to nonlinear inverse scattering. Further analysis shows that DBIM provides a better super resolution than BIM, and BIM provides a better super resolution than BA. Numerical simulations validate the above conclusions.     

A new reconstruction approach for reflection mode diffractiontomography

Reflection mode diffraction tomography (RM DT) is an inversion scheme used to reconstruct the acoustical refractive index distribution of a scattering object. In this work, we reveal the existence of statistically complementary information inherent in the backscattered data and propose reconstruction algorithms that exploit this information for achieving a bias-free reduction of image variance in RM DT images. Such a reduction of image variance can potentially enhance the detectability of subtle image features when the signal-to-noise ratio of the measured scattered data is low in RM DT. The proposed reconstruction algorithms are mathematically identical, but they propagate noise and numerical errors differently. We investigate theoretically, and validate numerically, the noise properties of images reconstructed using one of the reconstruction algorithms for several different multifrequency sources and uncorrelated data noise     

二维有耗介质目标重建的迭代－共轭梯度方法

本文提出了一种由已知的散射场数据重建二维非均匀有耗目标的复介电常数的迭代算法。连续采用多个方向的ＴＭ平面波照射目标，并分别采集目标区域外的散射场数据。本文利用矩量法．（ＭＯＭ）将积分方程变成矩阵方程，我们以Ｂｏｒｎ近似为初始值，通过多次迭代，实现目标特性的重建。通常，逆问题多是不适定的。为了克服解的不适定性，我们采用共轭梯度法（ＣＧＭ）求解逆问题。最后，通过计算机模拟，给出了一些数值重建结果。     

Diffraction Tomography with Arrays of Discrete Sources and Receivers

We present both theory and numerical simulations of diffraction tomography for arrays of line sources. The approach taken is applicable to a wide range of imaging problems where discrete sources and receivers are located near the object to be imaged rather than in its far field. As such, these new results tie into the vast body of research on inverse scattering, which to date is based largely on planewave sources. Our derivation implicitly includes a method for synthesizing plane waves; this method leads to inversion formulas based on the generalized projection-slice theorem. Although related techniues for synthesizing plane waves from discrete arrays are known, it is helpful to have available a theory that incorporates the synthesis directly into the scattering theory. The formulation is presented for propagating fields satisfying the Born and Rytov approximations in weakly inhomogeneous media and provides a convenient means for treating both forward and inverse scattering problems. Through a numerical example, we illustrate two important features of diffraction tomography inversion, i. e., 1) the effects of limited view and 2) results of probing with different signal frequencies. The example utilizes data generated by an exact forward modeling technique thus providing strong evidence supporting the usefulness of weak scattering approximations for inversion problems.     

New approximate formulations for EM scattering by dielectric objects

The extended Born approximation (ExBorn) has been shown an efficient formulation in the electromagnetic (EM) scattering by dielectric objects in both free-space and air-Earth half-space problems. In most cases, ExBorn is much more accurate than the conventional Born approximation at low frequencies. When the frequency is high or the contrast of dielectric objects is large, however, the ExBorn approximation becomes inaccurate. In this paper, new approximations are proposed for the EM scattering by dielectric objects buried in a lossy Earth, which are also suitable for the case of free space. It has been shown that the zeroth-order form of new approximations is completely equivalent to ExBorn. Hence, high-order approximations can be regarded as high-order ExBorn. Closed-form formulations are derived for the new approximations. Using the fast Fourier transform (FFT), these formulations can be implemented efficiently at a cost of CNlogN, where N is the number of unknowns and C is a small number. Numerical simulations show that high-order ExBorn approximations are much more accurate than the ExBorn approximation.     

The range limitation on radar-acoustic sounding systems (RASS) due to atmospheric refractive turbulence

The effects of acoustic refractivity fluctuations on the operation of a radar-acoustic sounding system (RASS) have been calculated. Using the Born approximation, the electromagnetic field scattered from a spherical acoustic pulse whose sphericity is perturbed by transmission through the turbulent medium between the source and scattering volume was determined. The resultant system gain reduction factor changes the dependence on rangeRof the total received power from anR^{-2}dependence for a homogeneous atmosphere toR^{-18/5}in strong turbulence. This new range dependence can occur at distances of the order of a few hundred meters for sufficiently strong turbulence.     

High-order generalized extended Born approximation for electromagnetic scattering

Previous work on the subject of electromagnetic scattering has shown that the extended Born approximation (EBA) is more accurate than the first-order Born approximation with approximately the same operation count. However, the accuracy of the EBA degrades in cases when the source is very close to the scatterer, or when the electric field exhibits significant spatial variations within the scatterer. This paper introduces a generalized extended Born approximation (GEBA) and its high-order variants (Ho-GEBA) to efficiently and accurately simulate electromagnetic scattering problems. We make use of a generalized series expansion of the internal electric field to construct high-order terms of the generalized extended Born approximation (Ho-GEBA). A salient feature of the Ho-GEBA is its enhanced accuracy over the Born approximation and the EBA, even when only the first-order term of the series expansion is considered in the approximation. This behavior is not conditioned by either the source location or the spatial distribution of the internal electric field. A unique feature of the Ho-GEBA is that it can be used to simulate electromagnetic scattering due to electrically anisotropic media. Such a feature is not possible with approximations of the internal electric field that are based on the behavior of the background electric field. Three-dimensional (3-D) models of electromagnetic scattering are used to benchmark the efficiency and accuracy of the Ho-GEBA, including comparisons against the first-order Born approximation and the EBA.     

Imaging of strongly-scattering targets from real data

Measured bistatic scattered fields for five new targets were added to the Ipswich data set. Three of the targets remained a mystery until revealed at a special session on image reconstruction from real data, at the 1996 IEEE AP-S International Symposium and URSI Radio Science Meeting in Baltimore. We provided coherent scattered-field data for more complicated scattering structures, as well as many more transmit-illumination directions, or views, than we had previously. Reconstructions corresponding to the first. We show back-propagated images of all five targets, using aspect diversity in diffraction tomography at a 3 cm wavelength. As expected, those targets that possess multiple-scattering effects, and/or have high contrast, fail to image properly. Targets from the Ipswich data set may serve as a useful standard against which researchers, involved in inverse scattering, can compare the merits of their inversion algorithms     

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     

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.     

Electromagnetic scattering model for a tree trunk above a tiltedground plane

An efficient and realistic electromagnetic scattering model for a tree trunk above a ground plane is presented. The trunk is modeled as a finite-length stratified dielectric cylinder with a corrugated bark layer. The ground is considered to be a smooth homogeneous dielectric with an arbitrary slope. The bistatic scattering response of the cylinder is obtained by invoking two approximations. In the microwave region, the height of the tree trunks are usually much larger than the wavelength. Therefore the interior fields in a finite length cylinder representing a tree trunk can be approximated with those of an infinite cylinder with the same physical and electrical radial characteristics. Also an approximate image theory is used to account for the presence of the dielectric ground plane which simply introduces an image excitation wave and an image scattered field. An asymptotic solution based on the physical optics approximation is derived which provides a fast algorithm with excellent accuracy when the radii of the tree trunks are large compared to the wavelength. The effect of a bark layer is also taken into account by simply replacing the bark layer with an anisotropic layer. It is shown that the corrugated layer acts as an impedance transformer which may significantly decrease the backscattering radar cross section depending on the corrugation parameters. It is also shown that for a tilted ground plane a significant cross-polarized backscattered signal is generated while the co-polarized backscattered signal is reduced