A multiresolution study of two-dimensional scattering by metalliccylinders

The application of wavelet transforms in method of moments (MoM) solutions for scattering problems is extended to cases involving metallic cylinders whose periphery contains a variety of length-scale features ranging from smoothly varying large-scale features (characterized by a radius of curvature of several wavelengths) to rapidly varying small scale ones (characterized by a radius of curvature that is small compared with the wavelength). The basic idea is to first consider a periodic extension of the equivalent current in the arc-length variable with a period identical to the scatterer circumference, and then to expand this representation using a set of periodic wavelets derived from a conventional basis of wavelets by a periodic extension. Using a Galerkin method and subsequently applying a threshold operation, a substantial reduction in the number of elements of the moment-method matrix is attained without virtually affecting the solution accuracy. The proposed extension is illustrated by a numerical analysis of TM (transverse magnetic) and TE (transverse electric) scattering from a cylinder of elliptic cross section. A thorough study is carried out showing how the solution accuracy improves with increasing resolution level, and how this accuracy is affected by a thresholding process which renders the moment matrix sparsely populated     

On the location and number of expansion centers for the generalizedmultipole technique

The generalized multipole technique is investigated from the perspective of determining a scheme for placing the multipole sources. The multipole technique is described using only the monopole current filament model. A limiting process is developed to determine the location and number of sources correlated to the radius of curvature of the scatterer. The ideas presented are verified by analyzing the convergence of the method using circular and elliptical cylinders. It is shown that ellipses with major to minor axis ratios up to 5:1 converge in a fashion comparable to the circular case     

A note on the radiation boundary conditions for the Helmholtzequation

The radiation boundary conditions in two dimensions are derived in the body-fitted coordinate system using the method of successive approximations for the wave envelope function. Results are valid for a convex scatterer with continuous radius of curvature on the surface of the scatterer. In the special case when the computational boundary is circular, the boundary operators derived are identical to the Bayliss operators. The on-surface radiation condition is examined. It is shown that, for a large conducting circular cylinder, a boundary operator of infinite order should be used due to the breakdown of the asymptotic expansions of the boundary operators on the surface of the scatterer. The leading order result based on the boundary operator of infinite order applied on the surface of the cylinder is the same as the result obtained by the method of physical optics     

Moment method with isoparametric elements for three-dimensionalanisotropic scatterers

A new method for computing the frequency-domain electromagnetic fields scattered from, and penetrating into, arbitrarily shaped, three-dimensional, lossy, inhomogeneous anisotropic scatterers is presented. The method is based on a general volume integro-differential formulation of the scattering problem, and consists of the numerical solution of the coupled integral equations by the moment method and point matching. A particularly powerful feature of this method is that the numerical model of the scatterer is obtained by parametric volume elements and the basis functions used to represent the field within each element are the same used in the finite-element method. Element integration problems due to the singular kernel of the integral equations are treated in some detail. Numerical results for both the isotropic and the anisotropic spherical scatterer are presented, including comparisons with results obtained by different numerical methods for the isotropic cases considered. The capability of the numerical code presented here to deal with cases where the material parameters of the scatterer are given by singular matrices is discussed for two particular examples     

A quasi-parametric algorithm for synthetic aperture radar target feature extraction and imaging with angle diversity

We present synthetic aperture radar (SAR) target feature extraction and imaging techniques with angle divesity. We first establish a flexible data model that describes each target scatterer as a two-dimensional (2D) complex sequence with arbitrary amplitude and constant phase in range and cross-range. A new algorithm, referred to as the QUasiparametric ALgorithm for target feature Extraction (QUALE), is then presented for SAR target feature extraction via data fusion through angle diversity based on the flexible data model. QUALE first estimates the model parameters, which include, for each scatterer, a 2D arbitrary real-valued amplitude sequence, a constant phase, and scatterer locations in range and cross-reange. QUALE then averages the estimated 2D real-valued amplitude sequence over range by making the assumption that the scatterer radar cross section is approximately consant. QUALE next models the so-obtained 1D sequence with a simple sinc function by assuming that the scatterer is approximately a dihedral (a trihedral is approximated as a very short dihedral) and estimates the relevant sinc function parameters by minimizing a nonlinear least-squares fitting function. Finally, the approximate 2D SAR image is reconstructed by using the estimated features. Numerical examples are given to demonstrate the perfomance of the proposed algorithm.This work was supported in part by AFRL/SNAT, Air Force Research Laboratory, Air Force Materiel Command, USAF, under grant no. F33615-99-1-1507, and the National Science Foundation Grant MIP-9457388. The U.S. Goverment is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.     

New resonant scatterer for measuring microwave magnetic-field distributions

A new resonant scatterer for measuring magnetic fields at microwave frequencies has been developed. This scatterer has the shape of a small slot antenna and is responsive only to the magnetic field.     

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     

Modeling and Migration of 2-D Georadar Data: A Stationary Phase Approach

This paper presents the basic kinematic and dynamic imaging and migration equations for zero-offset two-dimensional georadar profiling. The kinematic equations are derived from simple considerations of spatial impulse responses and a generating function. The dynamic equations follow from a multidimensional stationary phase approximation to the infinite spectral integrals. They show how the radar signal (amplitude and phase) depends on the shape and curvature of the reflector. The imaging equations are evaluated for the special cases of a point scatterer, a continuous reflector, and a terminating reflector. A general formula is developed by which to migrate an arbitrary shaped event of variable amplitude on the georadar section.     

A fast high-order solver for problems of scattering by heterogeneous bodies

A new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented. Here, a scatterer is described by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2D) bounded region; solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(Nlog(N)) operations where N is the number of discretization points. A wide variety of numerical examples provided include applications to highly singular geometries, high-contrast configurations, as well as acoustically/electrically large problems for which supercomputing resources have been used recently. Our method provides highly accurate solutions for such problems on small desktop computers in CPU times of the order of seconds.     

Dual-window dual-bandwidth spectroscopic optical coherence tomography metric for qualitative scatterer size differentiation in tissues

This study investigates the autocorrelation bandwidths of dual-window (DW) optical coherence tomography (OCT) k-space scattering profile of different-sized microspheres and their correlation to scatterer size. A dual-bandwidth spectroscopic metric defined as the ratio of the 10% to 90% autocorrelation bandwidths is found to change monotonically with microsphere size and gives the best contrast enhancement for scatterer size differentiation in the resulting spectroscopic image. A simulation model supports the experimental results and revealed a tradeoff between the smallest detectable scatterer size and the maximum scatterer size in the linear range of the dual-window dual-bandwidth (DWDB) metric, which depends on the choice of the light source optical bandwidth. Spectroscopic OCT (SOCT) images of microspheres and tonsil tissue samples based on the proposed DWDB metric showed clear differentiation between different-sized scatterers as compared to those derived from conventional short-time Fourier transform metrics. The DWDB metric significantly improves the contrast in SOCT imaging and can aid the visualization and identification of dissimilar scatterer size in a sample. Potential applications include the early detection of cell nuclear changes in tissue carcinogenesis, the monitoring of healing tendons, and cell proliferation in tissue scaffolds.     

一种改进的交互式医学图像序列分割方法

本文介绍了一种结合live wire算法和活动轮廓模型的医学图像序列的分割方法.我们通过把live wire算法和图像分割中一般的区域增长方法结合来改进live wire算法,并用改进后的算法来对医学图像序列中的单张或多张切片进行交互式的准确分割.然后计算机利用活动轮廓模型来自动分割相邻的未分割切片.我们通过在活动轮廓模型的边缘点中引入记录已分割物体边缘附近局部区域特征的灰度模型来把已分割切片中的物体与背景的局部区域特征带入相邻的未分割切片中,并用由灰度模型定义的区域相似性代替活动轮廓模型中的外能来引导边缘轮廓收敛到物体的实际边缘.本文还介绍了一种基于live wire算法思想的简单的分割结果交互式修补方法.实验表明我们的算法仅需少量用户交互就能快速准确的从医学图像序列中分割出感兴趣的物体.     

Geometric model for DSPN satellite reception in the dense scatterermobile environment

A geometric propagation model is developed for simulating the reception of direct sequence pseudonoise (DSPN) satellite signals by a directional or omni directional antenna in the dense scatterer mobile environment. The model is used to predict fading statistics. As expected, the mitigation of fading is closely related to the ratio of DSPN chip duration to delay spread of the scatterer medium for both the omni and directional antennas. The results suggest a general, frequency domain interpretation for the value of DSPN in mitigating multipath fading     

Modelling direct sequence pseudonoise(dspn) satellite reception with directional antennas in the dense scatterer mobile environment

A geometric propagation model is developed for simulating the reception of direct sequence pseudonoise (DSPN) satellite signals by a directional or omni antenna in the dense scatterer mobile environment. The model is first validated for narrowband signals by a direct comparison of both simulated cumulative signal strength statistics and simulated diffuse Doppler spectra with classical theory. The model is then used to predict fading statistics for DSPN signaling, either with omni or directional antennas. As expected, the mitigation of fading is closely related to the ratio of DSPN chip duration to delay spread of the scatterer medium for both the omni and directional antennas.     

异轴角散射法中散射体几何模型的构建与优化

湿蒸汽参量测量对于保障汽轮机机组的高效安全运行具有重大意义。基于激光散射的异轴角散射法是湿蒸汽参数测量的光学方法之一。本文在分析异轴角散射法测量模型中激光散射的散射体几何建模存在问题的基础上,构建了CCD相机单个像元所对应的散射体的几何模型,并求解了散射体体积及与散射体相关的几何参数;并采用MATLAB软件进行了仿真计算,计算了水滴群质量中间半径r0.5、水滴数浓度N和尺寸分布系数K变化对散射光强的影响,并进行了误差分析。研究结果表明:采用新构建的散射体几何模型的异轴角散射法所得的仿真理论数据与实验数据间相对误差减小,且变化趋势更趋于一致,验证了几何模型优化的可行性和优越性,可为湿蒸汽参数测量提供更精确的数据。     

Theory and measurement of the field of a pyramidal horn

Edge-wave diffraction theory is used in an unconventional way to predict the field in the immediate vicinity of the aperture plane of a pyramidal microwave horn. The far field may then be inferred by Fourier transformation. The theoretical predictions for the near field are compared with measurements almost in the aperture plane and inside a horn made by the modulated scatterer method. The directivity on axis, which is our primary concern, is mainly determined by the curvature of the wavefront at the aperture. When computed as a function of frequency, it shows oscillations similar to those observed. They arise because edge waves, multiply reflected inside the horn, mimic the effect of a wave reflected back from the throat; this interferes with the main wave to change the curvature of the emerging wavefront, and hence, the directivity     

Polarization correction and extension of the Kennaugh-Cosgrifftarget-ramp response equation to the bistatic case and applications toelectromagnetic inverse scattering

An analytical time-domain expression derived by Kennaugh (1967) for the early time impulse response for smooth, convex, perfectly conducting scatterers under the physical optics approximation for the bistatic case is reinterpreted. The physical optics bistatic early time impulse responses can be interpreted as cross-sectional areas of the scatterer. A crude polarization correction to the leading edge of the physical optics impulse response is obtained for the bistatic case, leading to a simple asymptotic relation between the specular principal curvature difference and certain co-polarized phase terms in the bistatic scattering matrix. Applications to direct scattering are discussed. Profile reconstruction from bistatic data with a priori knowledge of the validity range of physical optics in the time domain is proposed and tested with the sphere     

A finite difference BPM analysis of bent dielectric waveguides

A new version of the scalar TE wave equation is introduced, one that is particularly useful in bent waveguide analysis. The slowly varying envelope equation in cylindrical coordinates for the field amplitude E is finite-differenced, with no other approximations made to it. It will be shown that this version of the equation has several advantages over other forms and gives good results for the power loss rates even at radii ⩽100 μm, as well as being useful for the study of curved structures with varying radii of curvature. Evidence is provided to show that the loss rates calculated from this equation using the two dimensional finite difference beam propagation method compare favorably with other numerical and analytical results found in the literature. Special care must be taken when applying transparent boundary conditions as the curvature increases     

A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section

A new method is introduced for formulating the scattering problem in which the scattered fields (and the interior fields in the case of a dielectric scatterer) are represented in an expansion in terms of free-space modal wave functions in cylindrical coordinates, the coefficients of which are the unknowns. The boundary conditions are satisfied using either an analytic continuation procedure, in which the far-field pattern (in Fourier series form) is continued into the near field and the boundary conditions are applied at the surface of the scatterer; or the completeness of the modal wave functions, to approximately represent the fields in the interior and exterior regions of the scatterer directly. The methods were applied to the scattering of two-dimensional cylindrical scatterers of arbitrary cross section and only the TM polarization of the excitation is considered. The solution for the coefficients of the modal wave functions are obtained by inversion of a matrix which depends only on the shape and material of the scatterer. The methods are illustrated using perfectly conducting square and elliptic cylinders and elliptic dielectric cylinders. A solution to the problem of multiple scattering by two conducting scatterers is also obtained using only the matrices characterizing each of the single scatterers. As an example, the method is illustrated by application to a two-body configuration.