一种用于分布式阵列的球谐波域声源定位方法

本文提出一种适用于任意阵型和阵元指向性的球谐波域声源定位方法,能够在较宽的频域范围内,尤其是低频,提供较高的空间分辨率。水下噪声源的高分辨识别具有重大意义。传统阵列信号处理方法对低频噪声源的精确定位要求阵列具有较大孔径和较多的阵元数,导致系统过于庞大且成本较高。我们基于声场的球谐波表达和变换,采用分布在一定空间区域内的多个阵列估计该区域的球谐波系数矢量,对系数矢量进行信号处理实现声源定位。理论证明了该方法具有理想的空间选择特性。在一种特定的阵元分布下,仿真研究了该算法的方位谱估计性能以及阵元不一致性和位置误差对声源定位性能的影响。仿真结果显示,该算法在低频具有较高的空间分辨率且误差对算法定位性能的影响有限。      

球谐波展开法求解玻尔兹曼方程综述

介绍3种常用的直接求解玻尔兹曼传输方程(BTE)的球谐波展开法(SHE),分别是项匹配法、Galerkin法和投影法,以及求解过程中常用的几种能带模型和H-转换、最大熵消散两种数值稳定技术,并对比了以上3种方法的异同点。综合已发表文献中的模拟结果,得出结论:高阶球谐波展开和能带模型的选取对模拟器件的传输特性具有至关重要的作用。     

A novel surface registration algorithm with biomedical modeling applications.

In this paper, we propose a novel surface matching algorithm for arbitrarily shaped but simply connected 3-D objects. The spherical harmonic (SPHARM) method is used to describe these 3-D objects, and a novel surface registration approach is presented. The proposed technique is applied to various applications of medical image analysis. The results are compared with those using the traditional method, in which the first-order ellipsoid is used for establishing surface correspondence and aligning objects. In these applications, our surface alignment method is demonstrated to be more accurate and flexible than the traditional approach. This is due in large part to the fact that a new surface parameterization is generated by a shortcut that employs a useful rotational property of spherical harmonic basis functions for a fast implementation. In order to achieve a suitable computational speed for practical applications, we propose a fast alignment algorithm that improves computational complexity of the new surface registration method from O(n3) to O(n2).     

Approximating spherical harmonic representation order

A technique is presented for approximating the spherical harmonic representation error during analysis, which in turn can be applied to determine a reasonable representation order for spherical harmonic modelling. The order is estimated according to a selected final error value instead of it having to be set in advance. In this way the modelling process is automated     

尾焰的紫外高分辨辐射图像仿真与特征提取

基于改进的球谐离散坐标法建立了飞行器尾焰的紫外辐射亮度仿真模型。在尾焰羽流的热辐射基础上，重点考虑了尾焰中气体分子的化学荧光辐射源及由尾焰中三氧化二铝簇团粒子的平均光学特性带来的多重散射源效应。基于辐射传输方程，在球谐离散坐标系中，对尾焰在不同观测角度、不同介质分布的紫外辐射亮度进行了数值计算，实现了高分辨的三维尾焰辐射亮度的空间分布图像仿真。同时，采用灰度共生矩阵算法获得尾焰辐射亮度分级分布的灰度图，结合二维超分辨旋转不变子空间算法、α-shape方法和橡皮筋算法，提出了尾焰辐射中心位置和辐射亮度峰值轮廓曲线提取的新方法，得到了尾焰辐亮度特征的准确提取，为飞行器目标和尾焰的高分辨辐射图像特征识别提供了重要的参考依据和途径。     

IMAGING OF EEG BY SPHERICAL HARMONIC ANALYSIS

A new three dimensional imaging method for electroencephalogram(EEG) is suggested. It consists of the solution of an inward spherical harmonic continuation. The principle of the new method is introduced in Section II, then a few numerical simulation tests are shown and the feasibility of the new method is confirmed by the simulation results.     

基于球谐分析的脑电图映射成象方法

本文提出用球谐分析完成脑电信号内向延拓,进而实现脑电图三维映射成象的方法。文中介绍了方法原理,并进行了计算机仿真试验研究。仿真效果证明了方法的有效性和可行性。     

2-D MOSFET modeling including surface effects and impact ionizationby self-consistent solution of the Boltzmann, Poisson, andhole-continuity equations

We present a new two-dimensional (2-D) MOSFET simulation method achieved by directly solving the Boltzmann transport equation for electrons, the hole-current continuity equation, and the Poisson equation self-consistently. The spherical harmonic method is used for the solution of the Boltzmann equation. The solution directly gives the electron distribution function, electrostatic potential, and the hole concentration for the entire 2-D MOSFET. Average quantities such as electron concentration and electron temperature are obtained directly from the integration of the distribution function. The collision integral is formulated to arbitrarily high spherical harmonic order, and new collision terms are included that incorporate effects of surface scattering and electron-hole pair recombination/generation. I-V characteristics, which agree with experiment, are calculated directly from the distribution function for an LDD submicron MOSFET. Electron-hole pair generation due to impact ionization is also included by direct application of the collision integral. The calculations are efficient enough for day-to-day engineering design on workstation-type computers     

Spherical harmonics and Earth-rotation synthesis in radio astronomy

That spherical harmonic functionsY_{nm}(theta,phi)can be used to advantage in the Earth-rotation synthesis of radio astronomy maps is shown in this paper. As Earth rotates the baseline of a radio interferometer generates a cone whose angletheta, measured from theN-Spolar axis, can be varied by changing the baseline's azimuthal direction on the surface of Earth. A series of Earth-rotation measurements, at different cone angles but with baselines of equal lengthb, can be regarded as being made on a baseline sphere of radiusb, the analog of theuvplane in Fourier-type synthesis. The measured output distribution can be expanded as a spherical harmonic series on the baseline sphere. The coefficients of the series are related to the coefficients of the spherical harmonic series expansion of the source distribution on the celestial sphere by a matrix transformation. The matrix [B] is a function only of the baseline configuration (it does not vary with source declination). Inversion of the matrix leads to the solution for the source coefficients, from which a spherical harmonic map is formed of the source distribution.     

Time-domain simulation of spherical electromagnetic waves

Spherical electromagnetic waves excited by external surface electric currents in a homogeneous isotropic space are considered. It is shown that, in contrast to the harmonic excitation, in the case when the electromagnetic field is excited by external-current pulses, there is always an isolated convergent spherical wave in a bounded space-time region. The possibility of the existence of an isolated convergent spherical wave in a bounded spatial region at all instants is investigated for the cases of harmonic and pulse electromagnetic field excitations. It is proved that such a wave can exist when the divergent spherical wave arriving from the origin is compensated with the use of additional external currents. The excitation of isolated convergent spherical waves is illustrated by examples.     

由复合薄膜测定单层薄膜的杨氏模量

本文介绍了由复合薄膜测定单层薄膜的杨氏模量的一种新方法。考虑到圆膜形成时的初始变形 ,本文采用了球壳模型 ,通过测量圆形复合薄膜在集中载荷作用下的变形 ,获得其中单层薄膜材料的杨氏模量。以 PZT/Pt/Ti/Si O2 复合薄膜试样为例 ,测得单层 PZT薄膜的杨氏模量为 1 1 9± 1 2 GPa。这一数据应用于 PZT微悬臂梁的振动分析 ,发现 ANSYS谐振模拟和实验测试结果相符。     

Estimation and statistical bounds for three-dimensional polar shapes in diffuse optical tomography

Voxel-based reconstructions in diffuse optical tomography (DOT) using a quadratic regularization functional tend to produce very smooth images due to the attenuation of high spatial frequencies. This then causes difficulty in estimating the spatial extent and contrast of anomalous regions such as tumors. Given an assumption that the target image is piecewise constant, we can employ a parametric model to estimate the boundaries and contrast of an inhomogeneity directly. In this paper, we describe a method to directly reconstruct such a shape boundary from diffuse optical measurements. We parameterized the object boundary using a spherical harmonic basis, and derived a method to compute sensitivities of measurements with respect to shape parameters. We introduced a centroid constraint to ensure uniqueness of the combined shape/center parameter estimate, and a projected Newton method was utilized to optimize the object center position and shape parameters simultaneously. Using the shape Jacobian, we also computed the Cramér-Rao lower bound on the theoretical estimator accuracy given a particular measurement configuration, object shape, and level of measurement noise. Knowledge of the shape sensitivity matrix and of the measurement noise variance allows us to visualize the shape uncertainty region in three dimensions, giving a confidence region for our shape estimate. We have implemented our shape reconstruction method, using a finite-difference-based forward model to compute the forward and adjoint fields. Reconstruction results are shown for a number of simulated target shapes, and we investigate the problem of model order selection using realistic levels of measurement noise. Assuming a signal-to-noise ratio in the amplitude measurements of 40 dB and a standard deviation in the phase measurements of 0.1 degrees , we are able to estimate an object represented with an eighth-order spherical harmonic model having an absorption contrast of 0.15 cm(-1) and a volume of 4.82 cm(3) with errors of less than 10% in object volume and absorption contrast. We also investigate the robustness of our shape-based reconstruction approach to a violation of the assumption that the medium is purely piecewise constant.     

垂直电偶极子在地-电离层波导中场的球级数解

在非理想导电地面与电离层条件下,我们导出了ELF/SLF垂直电偶极子在球形地-电离层壳体中产生的电磁场的球谐级数表达式,采用一种加速收敛算法,算出了波导中的电磁场分布.根据计算结果,在SLF频段,地面与电离层之间的电磁场可理解为二个"行波"的叠加,且与SLF频段的球面二阶近似算法计算结果吻合很好.在ELF频段,壳体中的电磁场是驻波,其频率变化规律能正确反映出"舒曼"谐振现象.     

基于GNSS的武汉区域电离层TEC建模

为研究适用于区域电离层总电子含量(total electron content, TEC)建模的方法和估计策略,对传统单层假设下的几种建模方法和估计策略进行了比较分析. 基于我国中纬度武汉地区17个连续运行参考站的数据进行TEC建模,建模方法分别采用4×3阶多项式模型、2阶多项式模型、4阶球谐级数模型,估计策略使用分段常数估计策略和分段线性估计策略. 在传统单层假设的基础上,本文还提出了三层电离层TEC模型,该模型可以分别给出底部电离层、峰高电离层和顶部电离层的TEC. 研究结果表明,几种模型的天顶方向总电子含量拟合效果和欧洲轨道确定中心公布的电离层格网地图均具有较好的一致性,其中4阶球谐级数模型和分段线性估计策略效果最佳. 通过三层电离层模型,可以得到TEC与电离层高度之间的关系,多层电离层模型对空间目标监视和低轨卫星航天测控具有重要应用价值.     

Study of Mutual Coupling Between Circular Stacked-Patch Antennas on a Sphere

A rigorous mathematical analysis is given of spherical stacked-patch arrays with emphasis on the physical interpretation of mutual coupling mechanisms present in doubly- curved convex structures. The analysis method is based on electromagnetic field representation in terms of spherical harmonics where each harmonic has the same angular variation as the spectral source component. To obtain the spectral representation the vector-Legendre transformation is applied to currents and fields. A novel approach to the mutual coupling calculation within the method of moments analysis of spherical arrays is applied. By expressing the patch current in terms of two suitable potential-like auxiliary functions, it is possible to avoid the use of Euler's formulas for coordinate system rotation and the related lengthy integrations. Instead, the rotation of antenna elements and corresponding current distributions can be done in closed form with the help of Vilenkin's addition theorem for associated Legendre functions. It is shown that the new approach results in significant acceleration and improved accuracy of the analysis of spherical patch antenna arrays. The algorithm is successfully tested against a commercially available electromagnetic software and measurements performed on the developed laboratory model, confirming its accuracy for both input impedance and mutual coupling calculation and with only a small difference between the predicted and measured resonant frequencies, due to limitations in the experimental model. The influence of the structure parameters on mutual coupling level is extensively investigated, including all coupling mechanisms and leakage of energy due to curvature of the structure. It is shown that stacked-patch antennas can have reduced coupling level comparing to single patch antennas with possible deep nulls above the antenna resonant frequency.      

Parameterization-invariant shape comparisons of anatomical surfaces

We consider 3-D brain structures as continuous parameterized surfaces and present a metric for their comparisons that is invariant to the way they are parameterized. Past comparisons of such surfaces involve either volume deformations or nonrigid matching under fixed parameterizations of surfaces. We propose a new mathematical representation of surfaces, called q-maps, such that L2 distances between such maps are invariant to re-parameterizations. This property allows for removing the parameterization variability by optimizing over the re-parameterization group, resulting in a proper parameterization-invariant distance between shapes of surfaces. We demonstrate this method in shape analysis of multiple brain structures, for 34 subjects in the Detroit Fetal Alcohol and Drug Exposure Cohort study, which results in a 91% classification rate for attention deficit hyperactivity disorder cases and controls. This method outperforms some existing techniques such as spherical harmonic point distribution model (SPHARM-PDM) or iterative closest point (ICP).     

Scattering-Based Tomography for HRR and SAR Prediction

This paper introduces a method for predicting HRR radar signatures and SAR images by creating a parametric three-dimensional scattering model from existing measured or model-based HRR signatures and/or SAR images. The method identifies potential three-dimensional persistent scatterers and estimates their scattering patterns. The results are parametric HRR signature and SAR image reconstruction functions of range, azimuth, and elevation.The modeling is accomplished through a scattering-based tomography technique. This technique localizes potential scatterers by using a filtered back-projection algorithm for the inverse radon transform. Once found, potential scatterers may then have their two-dimensional (azimuth and elevation) scattering patterns parameterized through the use of a truncated spherical harmonic series.Results using the reconstructions from HRR data are presented. A M109 model is reconstructed based on HRR signatures. The model allows us to predict what the vehicle would look like from any arbitrary orientation using SAR. Finally an M548 vehicle is modeled using 26 measured HRR signatures. The model is shown to be better than the synthetic model data. Additionally we show that the new model results can be combined with the synthetic data to provide a better target model for signature matching.     

SLF/ELF垂直电偶极子在理想导电地-电离层中的场

在理想导电地面与电离层条件下,我们导出了SLF/ELF垂直电偶极子在球形地-电离层壳体中产生的电磁场的球谐级数表达式,并提出了一种加速收敛算法。利用此算法分别算出了电场分量随传播距离、高度及工作频率的变化,所得计算结果与Barrick方法所得结果基本吻合。由于地面和电离层没有吸收损耗,地面与电离层之间产生的场是＂驻波＂,在ELF频段,其频率变化规律能正确反映出＂舒曼＂谐振现象。     

Geoid undulation accuracy

For use in oceanographic applications the geoid is ideally needed to a high accuracy and to a high resolution. In 1979 the cumulative geoid undulation error to spherical harmonic degree 20 was ±1.4 m for the GEM10 potential coefficient model. Today the corresponding value has been reduced to ±25 cm for GEM-T3 or ±11 cm for the OSU91A model. Similar improvements are noted in harmonic degree (wavelength) and in resolution. The accuracy of the determination of the geoid is discussed from several points of views. Some comparisons are made with information available 12 years ago and that now available in the time framework of the TOPEX launch. It is noted that the accuracies described are subject to constant improvement. This is especially true as new satellite tracking data (e.g. DORIS data) are used in the potential coefficient models and more satellite altimeter data become available from the ERS-1 and TOPEX/Poseidon missions