Effects of multiple scattering and Fresnel diffraction on random volume scattering

A wave incident on a volume of random fluctuations of medium parameters will be scattered in all directions. Two kinds of effects on random volume scattering are considered: 1) multiple scattering effect, and 2) Fresnel diffraction effect. The cumulative forward scattering is known to be responsible for the scintillation phenomenon. When strong, such cumulative or multiple scattering can drive the signal statistics into the saturated regime in which the complex amplitudes behave as a complex Gaussian process. These cumulative scattering effects on signals of a bistatic radar are investigated. Additionally, to allow for the possibility that the size of the irregularity is comparable or larger than the first Fresnel zone, Fresnel diffraction instead of Fraunhofer diffraction is considered. A generalized formula for calculating average scattered power, taking both multiple scattering and Fresnel diffraction into account, is derived. It shows that the Fresnel diffraction pattern appearing around the forward direction tends to be smeared out by multiple scattering. Also, both multiple scattering and Fresnel diffraction effects weaken and broaden the forward-scattered beam, and reduce the backscattered power when compared with the single scattering and Fraunhofer diffraction cases respectively. Under certain conditions, the enhancement effect of the backward scattered power is confirmed.     

Improving microwave imaging by enhancing diffraction tomography

In this paper, a technique for enhancing the reconstruction quality of diffraction tomography for microwave imaging is presented. The technique invokes the WKB approximation in conjunction with utilizing measurement data at more than one frequency to overcome some of the limitations of diffraction tomography. The resulting formulation has a mathematical interpretation which leads to some interesting insights into the limitations of diffraction tomography. Numerical implementation of the technique is also described and actual simulation results using this implementation for a variety of two-dimensional (2-D) objects are provided. These show that indeed significant improvements over conventional diffraction tomography are possible with our enhanced technique     

High-frequency scattering by multiple spheres

Use is made of simple geometrical optics to obtain back-scattering cross sections of arrays of identical spheres, both for broadside and end illumination. Experimental data are given for two- and three-sphere arrays for all angles of illumination and for various spacings of spheres. It is shown that a reasonable knowledge of the general behavior of the cross sections may be obtained even from simple geometrical considerations.     

Electromagnetic scattering by a curved plate--Solution by uniform asymptotic theory of diffraction

The uniform asymptotic theory (UAT) of diffraction has been applied to find the monostatic scattered field by curved plate with a plane wave illumination with electric field parallel to the edge. The solution is valid for all positions of the receiver and is uniform around the reflection boundaries. The theoretical monostatic radar cross section (RCS) shows good agreement with experimental results. The formulation works very well for arbitrary radius of curvature of the plate down to a value oflambda/2.     

EBSD花样的图像畸变及其修正

EBSD花样存在图像畸变,使得由其三维重构解析晶体Bravais点阵变得困难。本文详细介绍了EBSD衍射数据几何修正的方法：利用样品到屏幕的距离,由EBSD花样上的衍射数据修正晶体倒易矢量的长度及其夹角。使用透辉石晶体的EBSD花样,验证了几何修正的效果,结果表明衍射测量数据经过修正并用最小二乘法重新拟合后,倒易矢量偏离二维拟合网格的程度降低,其分布更接近真实情况。     

多导线散射中的广义谐振分析

利用矩量法分析了多导线散射中存在的广义谐振问题,并利用开路传输线腔理论很好地解释了这类散射结构的谐振特性。     

Near-field scattering by physical theory of diffraction andshooting and bouncing rays

This paper proposes a method to compute the near-field RCS and Doppler spectrum of a target when the distances to the antennas are comparable to the target size. By dealing with a small piece of the target surface at a time, the transmitting antenna, and the receiving antenna are in the far-field zone of the small piece of the induced currents. The electromagnetic field produced by this small piece of induced currents can be written as a spherical wave. Sum up all spherical waves produced by every small piece of induced currents and we can obtain the total scattered field at the receiving antenna. The physical theory of diffraction (PTD) and the method of shooting and bouncing rays (SBR) are modified to evaluate the received signals. Numerical results based on these techniques are obtained and discussed. The formulation applies the simple concepts of “equivalent” image and vector effective height, which are believed to be novel     

缝隙及其与边缘的相互作用对目标散射的影响

随着雷达散射截面 ( RCS)减缩技术的发展 ,缝隙对目标散射行为的影响已经日益突出。文中分析了有限目标上缝隙自身的散射 ,及缝隙与边缘的相互作用对目标散射的影响     

On a limited-view reconstruction problem in diffraction tomography

Diffraction tomography (DT) is an inversion technique that reconstructs the refractive index distribution of a scattering object. We previously demonstrated that by exploiting the redundant information in the DT data, the scattering object could be exactly reconstructed using measurements taken over the angular range [0, phimin], where pi < phimin < or = 3pi/2. In this paper, we reveal a relationship between the maximum scanning angle and image resolution when a filtered backpropagation (FBPP) reconstruction algorithm is employed for image reconstruction. Based on this observation, we develop short-scan FBPP algorithms that reconstruct a low-pass filtered scattering object from measurements acquired over the angular range [0, phi(c)], where phi(c) < phimin.     

Reconstruction in diffraction ultrasound tomography using nonuniform FFT

We show an iterative reconstruction framework for diffraction ultrasound tomography. The use of broad-band illumination allows significant reduction of the number of projections compared to straight ray tomography. The proposed algorithm makes use of forward nonuniform fast Fourier transform (NUFFT) for iterative Fourier inversion. Incorporation of total variation regularization allows the reduction of noise and Gibbs phenomena while preserving the edges. The complexity of the NUFFT-based reconstruction is comparable to the frequency-domain interpolation (gridding) algorithm, whereas the reconstruction accuracy (in sense of the L2 and the L(infinity) norm) is better.     

Elastic Multiple Scattering By Randomly Distributed Spherical Scatterers

Starting from the basic integral equation for multiple scattered fields,a set of coupledlinear equations for the expansion coefficients of elastic multiple scattered fields by randomlydistributed spherical scatterers has been derived by using the expansions of the fields and thetranslational addition theorems of vector spherical wave functions.Thus,a new theory for thiskind of problems is developed.Different from the others,this theory gives the multiple elasticallyscattered fields in all space regions.     

雷达成像和衍射层析的内在联系梳理

从方程描述、方程求解和方程解析解三个层面,对雷达成像和衍射层析的内在联系进行了系统性梳理.首先,介绍了描述成像问题的电磁散射方程,发现描述雷达的方程是二维的面积分方程,而描述衍射层析的方程是三维的体积分方程.指出成像对象不同是导致方程不同的根源,并利用等效原理建立了两种成像间的联系.其次,指出两种成像的相同点是,对非线性的电磁散射方程的线性化近似求解.最后,指出两种成像的回波信号(在空间谱域)和成像目标(在空间域)均构成一组傅里叶变换对.给出了两种成像的解析解的统一数学模型,即成像结果可表示为观测点(散射系数或散射势)卷积点扩展函数(PSF)的形式.通过PSF对两者的成像性能进行了比较.     

Wide-band microwave diffraction tomography under Born approximation

Studies of the diffraction tomography of dielectric objects in forward and backward scattering using a frequency diversity technique in the microwave region are presented. Numerical results show that the image reconstructed in the backward scattering case is better than that obtained in the forward scattering case. This shows that this cost-effective technique has potential in medical and nondestructive testing applications     

Correction for resolution nonuniformities caused by anode angulation in computed tomography

Most X-ray tubes comprise a rotating anode that is bombarded with electrons to produce X-rays. A substantial amount of heat is generated, and to increase the area of the anode exposed to the electrons, without increasing the apparent size of the focal spot, the focal track of the anode is generally beveled with a very shallow angle (typically 5 degrees-7 degrees in a computed tomography (CT) tube). Due to the line focus principle, this allows a fairly large area of the focal track to be exposed to electrons while retaining a fairly small effective projected focal spot. One side effect of anode angulation is that the focal spot appears different from different positions in the detector array; the effective focal spot size at a constant distance from the tube will be larger for a peripheral detector channel than for a central one. These differences in the effective size of the focal spot across the field-of-view lead to worse resolution in the periphery than in the center of reconstructed images. In this work we describe a method for achieving more uniform resolution in fanbeam CT images by correcting for these focal spot angulation effects. We do so by modeling the effects as a series of local blurrings in the space of transmitted CT intensities and determining the effective coefficients of the corresponding discrete convolutions. The effect of these blurrings can then be compensated for in the sinogram domain through the use of a penalized-likelihood sinogram restoration model we have recently developed.     

Maximum entropy image reconstruction in X-ray and diffraction tomography

The authors propose a Bayesian approach with maximum-entropy (ME) priors to reconstruct an object from either the Fourier domain data (the Fourier transform of diffracted field measurements) in the case of diffraction tomography, or directly from the original projection data in the case of X-ray tomography. The objective function obtained is composed of a quadratic term resulting from chi(2) statistics and an entropy term that is minimized using variational techniques and a conjugate-gradient iterative method. The computational cost and practical implementation of the algorithm are discussed. Some simulated results in X-ray and diffraction tomography are given to compare this method to the classical ones.     

Consistency conditions and linear reconstruction methods in diffraction tomography

Because an image can be reconstructed from knowledge of its Radon transform (RT), the task of reconstructing an image is tantamount to that of estimating its RT. Based upon the Fourier diffraction projection (FDP) theorem, from the statistical perspective of unbiased reduction of image variance, we previously proposed an infinite family of estimation methods for obtaining the RT from the scattered data in diffraction tomography (DT). In this work, using the FDP theorem, we define the diffraction Radon transform (DRT), which can be treated as the data function in DT. Subsequently, using strategies similar to those that analyze the consistency conditions on the exponential Radon transform in two-dimensional (2-D) single-photon emission computed tomography with uniform attenuation, we studied the consistency condition on the DRT and we show that there is a hierarchy of estimation methods that actually project the noisy data function onto its consistency space in different ways. In terms of a weighted inner product of the consistency and inconsistency parts of a noisy data function, we further demonstrate that a subset of the family of estimation methods can be interpreted as orthogonal projections onto the consistency space of the DRT. In particular, the statistically suboptimal estimation method in the family corresponds to an orthogonal projection associated with an ordinary inner product of the consistency and inconsistency parts of a noisy data function.     

一种分析多目标散射问题的区域分解方法

提出了一种用于分析复杂多目标散射问题的区域分解方法. 在该方法中,每个目标作为一个独立的计算区域采用矢量有限元方法进行分析;各个区域之间通过基于格林函数的边界积分方程进行耦合;所得到的耦合矩阵方程采用基于Foldy-Lax多径散射方程的特征基函数方法进行求解. 由于矢量有限元方法的灵活性,该区域分解方法特别适合于求解多个具有相同结构复杂目标的散射问题. 数值算例验证了该方法的准确性和处理复杂多目标散射问题的能力.     

INELASTIC MULTIPLE SCATTERING BY ACTIVE RANDOMLY DISTRIBUTED SPHERICAL SCATTERERS

According to the model of equivalent dipoles for active molecules, the analysisof inelastic EM scattering by active molecules embedded in a sphere is given by the method ofdyadic Green's functions at the first, and then based on the theory of elastic multiple scattering byrandomly distributed spherical scatterers, a new theory for analysis of inelastic multiple scatteringby active molecules embedded in randomly distributed spherical scatterers also is developed. Thistheory gives the expansions of the multiple scattering fields in all space region in terms of vectorspherical wave functions in which the expansion coefficients can be solved from a set of coupledlinear equations.     

High-frequency multiple diffraction by a flat strip: Higher order asymptotics

By including correction terms in inverse powers of the wavenumberk, one may hope to extend the range of applicability of multiple edge diffracted geometrical theory of diffraction (GTD) to lower frequencies, and also to extend thereby the range of validity of the corresponding time domain solutions. The correction can be applied to each of the surface rays in the hierarchy that has been proposed by us recently as a model for multiple interaction between parallel edges separated by a plane surface segment on a two-dimensional perfectly conducting scatterer. The surface rays, which were found to explain the structure of the complex resonances in transient scattering, are excited for each interaction by equivalent line sources, dipole line sources, and their derivatives, with strengths determined from the asymptotic expansion of the edge diffracted field. This procedure is applied in detail toE- andH- polarized plane wave scattering by a perfectly conducting flat strip, up to quadruple diffraction, including consistentO(k^{-2})corrections with respect to the dominant term. The procedure is applied also to generate corrected multiple diffracted individual surface ray fields, which lead to an improved equation for the complex resonances in the "layer" synthesized in the complex frequency plane by a surface ray of a particular order. Inclusion of the low frequency corrections reduces further the already small discrepancy between the ray optically calculated low frequency resonances and those computed numerically by the moment method.