激光自混合干涉法亚微米及纳米颗粒测量中的反问题

基于Kaczmarz投影算法对反问题进行了详细的研究.选取颗粒线分布函数作为反演对象,改进了Kaczrnarz投影算法,使投影过程发生在较大夹角的超平面之间.数值模拟了含5%和10%的测量误差时宽单峰、窄单峰、双峰和三峰四种粒径分布的反演,结果显示改进投影算法得出的粒径分布与输入的粒径分布更好得吻合.实验测量了标称为60 mn和180 nm两种单分散颗粒,结果表明改进投影算法得出的粒径分别为54.95 nm和190.55 nm,而原先投影算法得出的粒径为83.18 nm和288.40nm,进一步显示改进投影算法提高了测量结果的准确性.     

The inverse problem of bimorph mirror tuning on a beamline

One of the challenges of tuning bimorph mirrors with many electrodes is that the calculated focusing voltages can be different by more than the safety limit (such as 500 V for the mirrors used at 17‐ID at the Advanced Photon Source) between adjacent electrodes. A study of this problem at 17‐ID revealed that the inverse problem of the tuning in situ, using X‐rays, became ill‐conditioned when the number of electrodes was large and the calculated focusing voltages were contaminated with measurement errors. Increasing the number of beamlets during the tuning could reduce the matrix condition number in the problem, but obtaining voltages with variation below the safety limit was still not always guaranteed and multiple iterations of tuning were often required. Applying Tikhonov regularization and using the L‐curve criterion for the determination of the regularization parameter made it straightforward to obtain focusing voltages with well behaved variations. Some characteristics of the tuning results obtained using Tikhonov regularization are given in this paper.     

氚钛薄膜靶中氚深度分布的反演

金属氚化物中体相氚的总量和深度分布测定是体相中氚行为研究的难点,利用氚衰变诱发X射线谱的氚分析技术分析了金属薄膜靶中体相氚的深度分布情况,建立了薄膜靶中氚深度分布计算模型,利用Tikhonov正则化方法反演了薄膜靶中体相氚的深度分布。反演结果表明,正则化数值算法能够有效提高对薄膜靶法向非均匀性的分辨。     

Particle Size Distribution Retrieval from Elastic Light Scattering Measurements by a Modified Regularization Method

Retrieval of polymeric emulsions Particle Size Distribution (PSD) from Elastic Light Scattering (ELS) measurements requires the solution of an ill conditioned inverse problem. In this paper we compare the performance of classical regularization methods such as Truncated Singular Value Decomposition and Tikhonov's, to a regularization technique due to Pike that includes positivity constraints on the PSD. We also propose a new method that combines Tikhonov's approach with Pike's method. Simulated ELS measurements for two polymeric materials were generated under different experimental noise assumptions. Uncertainties on the polymer refractive index value were also considered. The PSD estimations obtained show that the implementation of the proposed more sophisticated algorithm is convenient for this very ill‐conditioned problem.     

用于同步辐射的压电变形镜控制策略数值模拟北大核心CSCD

为了提高同步辐射中压电变形镜的控制自由度和面形精度,解决压电致动单元数量过多引起的解算电压受噪声影响异常波动(过拟合)问题,建立了变形镜模型并进行仿真控制。通过有限元仿真获得36组压电响应方程,构建面形与电压的数学模型;为补偿重力造成的镜面畸变,以获得的椭圆面形分析并比较了使用最小二乘法和Tikhonov正则化两种电压解算方案的控制效果。结果表明:采用Tikhonov正则化算法反演后,面形控制误差相比最小二乘法降低了21.7%,相邻极板间电压波动极大值从1.019 kV下降为0.174 kV,反演结果符合工程实际要求;系统对测试噪声具有鲁棒性,相比最小二乘法有更加优越的应用价值。     

Particle Systems Characterization Using a Flat Cell Static Light Scattering Apparatus

In this work a light scattering apparatus for the study of heterogeneous liquid systems of evolving morphology is presented. A Fraunhofer configuration consisting of a linear array of photodiodes is used to detect the light scattered by thin samples illuminated by a He‐Ne laser light. Temperature control is available. The instrument is tested with the polymerization induced phase separation of a thermosetting polymer formulated with a divinylester resin copolymerized with styrene and modified with poly(methylmethacrylate). The system is successfully modeled as an arrangement of particles growing in size and number, and varying in composition. The ability of the experimental setup to provide results that can be quantitatively analyzed is checked using microspherical polystyrene standards. Different samples with nominal sizes of 0.5, 1 and 2 μm are used in different combinations of sample thickness and concentration. The analysis of the light scattering spectra is performed using inverse techniques to estimate the particle size distribution of the microspheres. The results agree with previous knowledge of the parameters of the samples.     

用Mie氏散射理论测量聚苯乙烯微球的折射率

采用全Mie氏散射理论，计算单色平行光被该球粒散射后的光强图案分布.在实验上，把聚苯乙烯小球分散在纯净水中，使其浓度满足光的透过率为70%左右的条件，然后测量单色平行光通过该样品比色皿后的远场衍射图样的第一暗环角半径的数值大小.将该测得的角半径大小同上述采用全Mie氏散射理论计算的不同折射率下的散射光强角分布曲线图相比较，选出与测得的第一暗环角半径大小符合最好者，从而得到国家标准物质聚苯乙烯小球相对于分散剂纯净水的折射率大小，最后得到聚苯乙烯小球的折射率为1.6.本研究为该标准样品提供了一个重要光学参数.     

单分散系微粒的Mie散射计算

Mie散射是公认的一种极具发展前途的微粒测试技术,应用于工厂、企业排放烟尘中微粒粒度和浓度的测试,具有非接触、精度高、重复性好和可实时在线测量的优点,是研究检测污染排放的主要技术手段,也是微粒粒度和浓度分析的理论基础.本文对Mie散射理论的多个参量进行计算并给出其数学表达式.     

德拜色散媒质的三维时域电磁逆散射技术

生物组织、土壤、水等媒质的电特性是频率相关的(称为色散媒质),常利用单极德拜(Debye)模型描述.为重建这一类媒质的色散特性,基于泛函分析和变分法,提出一种三维(3-D)时域电磁(EM)逆散射技术,主要流程为:①根据最小二乘准则,转化逆散射问题为约束最小化问题;②应用罚函数法,转化约束最小化问题为无约束最小化问题;③通过变分计算,解析导出梯度(Fréchet导数)表达式;④利用梯度法求解.此外,引入一阶吉洪诺夫(Tikhonov)正则化以应对逆问题的病态特性和噪声影响.数值应用中,将提出的目的 应用到一个简单的三维癌变乳房模型,借助PRP共轭梯度(CG)算法和时域有限差分(FDTD)法,仿真结果初步证实本文目的 的可行性、有效性和鲁棒性.     

Self‐Force in 1D Electrostatic Particle‐in‐Cell Codes for NonEquidistant Grids

Effects of non‐equidistant grids on momentum conservation is studied for simple test cases of an electrostatic 1D PIC code. The aim is to reduce the errors in energy and momentum conservation. Assuming an exact Poisson solver only numerical errors for the particle mover are analysed. For the standard electric field calculation using a central‐difference scheme, artificial electric fields at the particle position are generated in the case when the particle is situated next to a cell size change. This is sufficient to destroy momentum conservation. A modified electric field calculation scheme is derived to reduce this error. Independent of the calculation scheme additional fake forces in a two‐particle system are found which result in an error in the total kinetic energy of the system. This contribution is shown to be negligible for many particle systems. To test the accuracy of the two electric field calculation schemes numerical tests are done to compare with an equidistant grid set‐up. All tests show an improved momentum conservation and total kinetic energy for the modified calculation scheme of the electric field. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particle Size Distributions from Static Light Scattering with Regularized Non‐Negative Least Squares Constraints

Simulated data from static light scattering produced by several particle size distributions (PSD) of spherical particles in dilute solution is analyzed with a regularized non‐negative least squares method (r‐NNLS). Strong fluctuations in broad PSD's obtained from direct application of NNLS are supressed through an averaging procedure, as introduced long ago in the inversion problem in dynamic light scattering. A positive correlation between the best PSD obtained from several averaging schemes and the condition number of the respective data transfer matrices was obtained. The performance of the method is found to be similar to that of constrained regularization (CONTIN), which uses also NNLS as a starting solution, but incorporates another regularizing strategy.     

双面声阵列波束形成的正则化改进算法

双面声阵列波束形成能够区分识别位于不同扫描平面的相干声源,然而该算法在低信噪比条件下识别精度较低。针对此问题提出一种迭代正则化改进算法,通过迭代方法更新正则化矩阵与波束形成输出,在不断提升正则化稳定性、抑制干扰旁瓣的基础上使声学云图主瓣向实际相干声源点处聚焦。数值仿真与实验算例结果显示,改进算法在中高频代表频率下能够正确区分相干声源前后方位,并具有相对原算法更高的识别精度。从而表明:从反问题正则化角度对原算法进行优化改进是理论可行的;正则化矩阵的具体形式与广义逆波束形成输出的空间分辨率紧密相关,且可通过迭代方法将二者整合以提高声源识别精度。     

空间声场全息重建的波叠加方法研究

提出了基于波叠加法的近场声场全息技术，并将其用于任意形状物体的声辐射分析.在声辐射计算问题中，边界元法是通过离散边界面上的声学和位置变量来实现，而波叠加方法则通过叠加辐射体内部若干个简单源产生的声场来完成.因而，基于波叠加法的声全息就不存在边界面上的参数插值和奇异积分等问题，而这些问题是基于边界元法的声全息所固有的.与基于边界元法的声全息相比较，基于波叠加法的声全息在原理上更易于理解，在计算机上更容易实现.实验结果表明：该种全息技术在重建声场时，具有令人满意的重建精度. 关键词： 声全息 逆问题 波叠加方法 正则化方法     

光复散射对消光法粒径测量的影响:复散射模型与数值模拟

复散射效应在光散射颗粒测量中不仅重要．且尚未得到很好解决。采用蒙特卡罗方法,对不同的光波长,颗粒浓度以及收接器条件下的光复散射进行了数值模拟．数值算法程序经与四通量模型进行对比验证,数值结果与单散射条件的郎伯-比尔模型进行比较．进而讨论了复散射效应对消光法颗粒粒径测量影响。表明复散射对消光法颗粒测量的影响不仅取决于颗粒系自身的浓度．而且接收器的几何尺寸和接收位置起着非常重要的作用,减小颗粒介质层厚度和减小光接收器接收面积．增大接收距离以及减小接收角都能减小复散射效应对消光法粒径测量的影响。     

Particle‐in‐cell simulation of an optimized high‐efficiency multistage plasma thruster

Electric propulsion attracts increasing attention in contemporary space missions as an interesting alternative to chemical propulsion because of the high efficiency it offers. The High‐Efficiency Multistage Plasma thruster, a class of cusped field thruster, is able to operate at different anode voltages and operation points and thereby generate different levels of thrust in a stable and efficient way. Since experiments of such thrusters are inherently expensive, multi‐objective design optimization (MDO) is of great interest. Several optimized thruster designs have resulted from a MDO model based on a zero‐dimensional (0D) power balance model. However, the MDO solutions do not warrant self‐consistency due to their dependency on estimation from empirical modelling based on former experimental studies. In this study, one of the optimized thruster designs is investigated by means of particle‐in‐cell (PIC) analysis to examine the predicted performance characteristics with self‐consistent simulations. The 0D power balance model is used to develop additional diagnostics for the PIC simulations to improve the physics analysis. Using input parameters for the 0D power balance model from the PIC simulations allows further improvement for the design optimization.     

Particle‐Arrayed Silver Mesocubes Synthesized via Reducing Silver Oxide Mesocrystals for Surface‐Enhanced Raman Spectroscopy

In this study, we demonstrate an easy particle‐mediated protocol using the specific structure of mesocrystal Ag₂O sacrificial templates to synthesize highly rough‐cubic Ag mesocages. To the best of our knowledge, the mesocrystal particles are reported for the first time as sacrificial templates for synthesizing metal particles. The obtained Ag mesocages show high surface‐enhanced Raman scattering (SERS) sensitivity because of the highly rough topography formed by arrays of uniform individual Ag nanoparticles. Abundant “hot spots” with greatly enhanced local electromagnetic field are promoted densely on the mesocage surface by the plenty of deep and narrow gaps and the hollow structure. The single‐particle SERS signal generated by the Ag mesocage has an enhancement factor of approximately 10⁹, which is approximately four times higher than the Ag mesocage synthesized using single‐crystal Ag₂O particle as a template. Meanwhile, this signal displays a linear dependence on the detected analyte concentration, sensitively down to 1.0 × 10^?12 m .     

A One‐Dimensional Particle‐in‐Cell Model of Plasma Build‐Up in Vacuum Arcs

Understanding the mechanism of plasma build‐up in vacuum arcs is essential in many fields of physics. A one‐dimensional particle‐in‐cell computer simulation model is presented, which models the plasma developing from a field emitter tip under electrical breakdown conditions, taking into account the relevant physical phenomena. As a starting point, only an external electric field and an initial enhancement factor of the tip are assumed. General requirements for plasma formation have been identified and formulated in terms of the initial local field and a critical neutral density. The dependence of plasma build‐up on tip melting current, the evaporation rate of neutrals and external circuit time constant has been investigated for copper and simulations imply that arcing involves melting currents around 0.5–1 A/μm², evaporation of neutrals to electron field emission ratios in the regime 0.01 – 0.05, plasma build‐up timescales in the order of ～ 1 – 10 ns and two different regimes depending on initial conditions, one producing an arc plasma, the other one not. Also the influence of the initial field enhancement factor and the external electric field required for ignition has been explored, and results are consistent with the experimentally measured local field value of ～ 10 GV/m for copper (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synchrotron X‐ray tests of an L‐shaped laterally graded multilayer mirror for the analyzer system of the ultra‐high‐resolution IXS spectrometer at NSLS‐II

Characterization and testing of an L‐shaped laterally graded multilayer mirror are presented. This mirror is designed as a two‐dimensional collimating optics for the analyzer system of the ultra‐high‐resolution inelastic X‐ray scattering (IXS) spectrometer at National Synchrotron Light Source II (NSLS‐II). The characterization includes point‐to‐point reflectivity measurements, lattice parameter determination and mirror metrology (figure, slope error and roughness). The synchrotron X‐ray test of the mirror was carried out reversely as a focusing device. The results show that the L‐shaped laterally graded multilayer mirror is suitable to be used, with high efficiency, for the analyzer system of the IXS spectrometer at NSLS‐II.     

皮肤组织可见与近红外Mie散射光学特性分析

依据Mie单次散射理论, 并考虑到皮肤组织复折射率实部的色散, 分析了在可见与近红外波段皮肤组织对光的吸收、散射及散射的方向特性。研究表明, 散射系数和吸收系数均随皮肤组织中散射粒子半径的增加而增加, 而且, 对于大粒子, 在某一波长处表现出强烈的散射和吸收特性。当粒子半径大于临界半径时, 散射系数呈现振荡特性, 随着折射率虚部的增加, 振幅减小。皮肤组织呈现前向散射特性, 且散射粒子的半径越大, 前向散射特性越明显。     

热损耗条件下导热系数反演模型及实验研究

通过导热反问题反演求解导热系数通常误差较大,本文构建考虑热损耗条件下的虚拟薄板模型精确求解导热系数。首先通过数值算例验证模型的准确性和稳定性,正向问题使用有限差分法进行求解,反问题求解采用人工蜂群算法进行目标函数最优化。然后搭建第二类边界条件下导热正向装置,进行导热系数实例反演和实验研究,并将新模型与理论模型反演结果对比分析。结果表明理论模型反演结果的相对误差约为-14.76%,而新模型下导热系数反演相对误差达到-4.67%。新模型较理论模型反演结果更精确,有效降低了热损耗对反演的影响,提高了反演精度,更符合实际工况。