光全散射法测量微粒尺寸分布的研究

本文从光全散射法的基本原理出发,提出了测量微粒尺寸分布的独立道模式光全散射测量法和非独立模式光全散射测量法,解决了以往光全散射法只能测量微粒的平均直径,不能给出尺寸分布,并且测量范围小,测量结果有多值性的缺陷,独立模式光全散射测量法还能用于测量多峰分布微粒的尺寸分布,数值计算和实验研究表明用本文方法,测量结果准确,可靠。     

一种新颖的用于光腔模式及光束传输模拟的特征向量法

根据有限元法单元划分的思想，提出了一种新颖的模拟光腔模式及光束传输的特征向量法. 该方法的关键之处在于基于衍射积分理论构造了一种新的光束传输矩阵，通过求解特征矩阵方程可一次性得到谐振腔的一系列特征向量，每一列特征向量即代表了腔镜上光场的一个确定模式的振幅及相位分布. 并可采用该方法模拟光场传输到腔内或腔外任意地方的场分布. 该方法将传统方法中大量的迭代过程转化成为本征积分方程特征向量的求解过程，并与初值取值无关，且可一次性求得多个模式分布，从而可方便地分析谐振腔的模式鉴别能力. 特征向量法对圆形镜共焦 关键词： 谐振腔 特征向量法 模式分布     

光腔模式及光束传输的特征向量算法

发展了一种新颖的适用于光腔模式及光束传输模拟计算的特征向量法.该方法的核心是基于菲涅耳-基尔霍夫衍射积分理论构造了一种新的光腔传输矩阵,通过求解激光谐振腔的本征积分方程,即可一次求解得到表征腔镜上多个光场模式振幅及相位分布的特征向量组;而谐振腔内或腔外任意地方的光场分布,也可采用该方法进行光束传输模拟而求得.对与该方法有关的单元划分、形函数选取、误差及稳定性分析等问题进行了论述,分析表明:合适的单元划分和形函数选取有利于提高计算速度、精度和稳定性.     

亚波长尺度下混合等离子泄漏模式激光

由于光存在衍射极限,因此传统方法不能实现亚波长尺度下的激光激射。为了打破这一衍射极限,本文设计了金属-介电层-半导体堆叠结构来实现深亚波长尺度下的激光激射,并讨论了相关结构对模式传播的影响。结构设计上,采用低介电常数金属银作为衬底、10 nm厚的LiF作为介电层、具有六边形截面的半导体纳米线ZnO作为高介电常数层,采用有限差分本征模和时域有限差分方法对所设计的结构进行光学仿真模拟。首先,通过改变ZnO纳米线的直径,使用有限本征模方法分析介电层中的光学模式,得到4种模式分布。然后,通过这4种光学模式在不同纳米线直径下的有效折射率和损耗计算了对应的波导传输距离以及激射阈值增益。最后,采用三维时域有限差分方法仿真分析纳米线稳态激光发射过程中各模式的电场分布。结果表明:在纳米线和金属衬底之间的介电层上存在混合等离子体模式和混合电模式,对于直径低于75 nm的ZnO纳米线,没有有效的物理光学模式,即混合等离子体模式和混合电模式都被切断,当ZnO纳米线的直径大于75 nm时,混合等离子体模式可以有效存在,而混合电模式在ZnO纳米线的直径达到120 nm之后才出现。虽然混合等离子体模式可以更好地限制在介电层中,但是它们的模式损耗太大,传播距离相对较小。此外,与混合等离子体模式相比,混合电模式的传播距离更长。在给定微米线的直径(D=240μm)下,混合电模式传播距离超过50μm。综上可知,在深亚波长尺度下利用混合泄漏模式可以打破光学衍射极限并实现激光激射。     

由轴锥镜折射阴影区产生的泊松衍射斑

为完善轴锥镜衍射场分布描述与认识,根据积分渐进理论处理了含大数且稳相点不在积分域中的衍射场积分函数,获得了轴锥镜折射阴影区的近轴域衍射场的近似解析解,且发现了该衍射场分布服从泊松散射分布这一新奇的现象。实验结果表明:在其阴影近轴区域的光强分布很好地服从零阶贝塞尔函数,并且中心光斑直径正比于传播距离,但其强度随纵面传播而衰减。由于照射光束与衍射斑的直径都随传播距离线性增大,二者永远不会重叠,所以理论上这个泊松衍射可传播到无穷远。相对于传统的圆屏衍射实现方式,轴锥镜透镜为超远距离空间中泊松衍射斑的产生提供了一种新的、更便捷的方法。     

夫琅和费衍射法测定微粒的大小

一、引言圆孔衍射的强度分布依赖于波长、孔径以及圆孔到图象的相互位置.我们也可以用不透明的微粒来研究这些相关现象,这样,从它们与光的相互作用就可以知道微粒的大小. 本文介绍在高等学校普通光学实验室具有的基本仪器和设备条件下,用一只钠光灯,一台分光计或测高仪,通过对石松粉的夫琅和费衍射图象的测量和计算得到石松微粒的大小.     

光散射法测量微粒直径分布的分析与计算

一、前言液滴微粒(以下简称微粒)是分割状态下的液体,由于分割,微粒表现出许多在整体状态下不需要考虑的特性,其中最主要的是微粒的平均直径以及直径的分布规律。在许多工业生产过程中都碰到过微粒的测量问题。蒸汽透平运行中饱和蒸汽膨胀凝结,出现水滴,沉积在动、静叶片表面形成水膜,高速气流扯裂水膜成较大的水滴,导致叶片的水蚀,发生叶片断裂事故及降低透平的效率。为保证透平运行安全,提高效率,需检测蒸汽中的水滴直径及湿度。在各种燃     

激光衍射粒度分析仪粒度分布求解方法的研究

本文介绍了激光衍射粒度分析仪的基本原理,给出了光电探测器上的光能分布公式,对其求解方法进行了详细分析,提出了利用改进的最小二乘法求解粒度分布的新方法.最后分别利用函数限制解法和自由分布解法对两种情况的粒度分布进行了数值模拟计算.     

用激光衍射测量群体微粒尺寸分布的计算机模拟和拟合

介绍了群体微粒激光衍射现象的原理,建立了相应的数学模型;报导了相应的计算机模拟和最小二乘法拟合结果,以确定群体微粒的尺寸分布。     

空气中一维声栅对微粒的声操控

本文对一维空气声栅表面微粒受到的声辐射力进行了详细的理论研究.首先采用有限元方法研究一维声栅的透射性质及表面声场分布,然后将有限元与动量张量积分结合研究处于一维声栅表面微粒受到的声辐射力特征.声栅共振透射增强是表面周期衍射波与狭缝Fabry-Perot共振耦合形成的,并且与声栅周期和厚度密切相关.研究发现,当共振波长与声栅周期相当时,微粒在其表面可受到指向声栅板面的声吸引力;当共振波长为声栅周期的二倍及以上,微粒可受到指向狭缝中的吸引力,且强度远小于第一种情况的吸引力.因此,在声栅处于共振波长与周期相当的共振模式时,可以在空气中利用声栅表面操控、吸引和排列微粒.     

Three-dimensional emission tomography of a scattering plasma

The three-dimensional emission ray tomography of a plasma partially scattering its self-radiation is considered. The spatial distribution of scattering density and its angular distribution are assumed to be known. The model of projection-data acquisition taking into account single and multiple scattering is constructed. In terms of this model, the problem of determining the distribution of local emission coefficients is posed. For solving this problem, the algorithm based on the Neumann-series expansion of the product of the radiative-transfer operator for a scattering medium and the operator for solving the pure emission problem was proposed. The algorithm was investigated in detail using numerical simulation.     

Fokker-Planck方程在快波加热中的应用

快波加热算法，一般都是假定托卡马克中粒子为麦克斯韦分布.其实由于准线性扩散效应，共振粒子的平行温度与垂直温度不相等，这样必然产生一定的计算误差.针对这种情况，本文引入Fokker-Planck方程，采用叠代算法较好地解决了这一问题. 关键词：     

基于单次傅里叶变换的分段衍射算法

针对单次傅里叶变换算法(S-FFT算法)受到采样定理的约束,衍射面画幅尺寸和有效内容像素数无法灵活控制,很容易出现衍射面画幅尺寸大小与衍射距离不匹配的情况,本文提出了一种分段衍射算法。首先,在采样数、光的波长、初始衍射面大小确定的情况下,利用拆分的衍射距离比控制最终衍射面画幅尺寸。然后,对单次衍射计算结果与分段衍射计算结果进行了图像相似度对比。实验表明,分段衍射算法可在画面强度分布不变的情况下,提高有效像素数目,数据量增加了2~3个数量级。此外,文章分析了造成误差的一个主要原因来自有效数据分辨率提高后,细节分布与低分辨率像素值之间的差别。在图像细节较丰富时,其差别较大。因此这种差别应视为优于直接计算的一种结果。本算法能够获得更加清晰的图像细节,灵活调整衍射面画幅尺寸,使得S-FFT算法在大衍射距离问题计算中能发挥其算法优势。     

Spline-Galerkin Solution of Dynamic Equations for Particle Comminution and Collection

The population balance equation is solved for particles undergoing a combination of growth, comminution, and collection. The approximation method is to use a weighted Galerkin technique with cubic B-splines and an implicit scheme for solving the system of ordinary differential equations. The cubic splines are defined on a graded mesh. The performance of the method is investigated by solving a model problem with simple but nonsmooth kernels. The weight function is chosen so that singularities in the equation can be easily treated. A self-similar solution for comminuted particles is shown to be a useful representation for the solution of the population balance equation provided that this equation is solved over a sufficiently long time interval. Stationary solutions of the equation are obtained for a model that describes both particle comminution and collection.     

Zur Theorie der diffusen Reflexion und Transmission beim Vorliegen elastischer Vielfachstreuung

In order to determine the diffuse reflectivity and transmittivity of multiply scattered particles, there is not necessarily the need of solving the complete differentiointegral equation of multiple scattering. It can be shown that the problem reduces to solving a set of two simultaneous differential equations of the first order, provided that the amount of sideward scattering may be neglected. The solutions of these equations furnish all data required, if the mechanism of single scattering is known.     

红外无损探测中多宗量多热源反演问题的研究

为研究红外无损探测稳态多热源反演逆问题, 建立不同形状的均质与非均质稳态热传导模型, 其中内热源个数、位置、强度、面积均为未知项. 基于数值算法中有限元算法对模型进行离散分析, 化简有限元矩阵方程, 最终转化为对Ax = b高度欠定方程的求解. 首次利用分段多项式谱截断奇异值分解法处理内热源逆问题, 并对算法进行改进, 有效改善了该算法在处理多热源反演时存在的严重的热源叠加效应. 根据反演出的内热源信息, 利用有限元算法计算重构出整个模型内所有节点的温度分布. 运用数值仿真Comsol软件和具体实物实验对算法进行有效性评估, 并验证算法在不同热传导模型中的表现. 结果表明, 算法能够准确反演出多热源各参量信息, 在非均质材料模型中仍能准确地反演出热源项, 并有效重构出模型内温度场. 该算法可应用于材料无损检测及人体红外医学成像等领域.     

求解光学CT图象重建问题的广义脉冲谱技术研究

间接法是目前实现医学诊断用近红外光三维成象(光CT)的最有潜力的手段之一.该方法基于以下假设,即给定分别对应于不同点激励源作用下成象组织体表面各点的传输光测量.在组织体内存在着与上述检测量相对应的、唯一的光学参数三维分布.由此,图象重建变成了特定光子传输模型的逆问题.本文提出采用广义脉冲谱技术(Generalized Pulse Spectrum Technique,GPST)进行光学CT图象重建逆问题的求解.给出了GPST在扩散方程光子传输模型逆问题求解中的具体实现,数值实验结果表明,通过选择合适的复频率点,采用GPST算法的图象重建结果优于其它现有算法,且响应时间合理.最后,本文还初步讨论了吸收和散射系数重建中复频率点选择的一些基本原则。     

Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm

A novel continuation method is presented for solving the inverse medium scattering problem of the Helmholtz equation, which is to reconstruct the shape of the inhomogeneous medium from boundary measurements of the scattered field. The boundary data is assumed to be available at multiple frequencies. Initial guesses are chosen from a direct imaging algorithm, multiple signal classification (MUSIC), along with a level set representation at a certain wavenumber, where the Born approximation may not be valid. Each update via recursive linearization on the wavenumbers is obtained by solving one forward and one adjoint problem of the Helmholtz equation.     

Self-consistent solution of Kohn-Sham equations for infinitely extended systems with inhomogeneous electron gas

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves iterations with alternate solving of the Poisson and Schrödinger equations. One of problems of such an approach is that the charge distribution renewed by means of the solution of the Schrödinger equation does not conform to boundary conditions of the Poisson equation for the Coulomb potential. The resulting instability or even divergence of iterations manifests itself most appreciably in the case of infinitely extended systems. The known attempts to deal with this problem are reduced in fact to abandoning the original iterative method and replacing it with some approximate calculation scheme, which is usually semi-empirical and does not permit to evaluate the extent of deviation from the exact solution. In this work, we realize the iterative scheme of solving the Kohn-Sham equations for extended systems with inhomogeneous electron gas, which is based on eliminating the long-range character of Coulomb interaction as the cause of tight coupling between charge distribution and boundary conditions. The suggested algorithm is employed to calculate energy the spectrum, self-consistent potential, and electrostatic capacitance of the semi-infinite degenerate electron gas bounded by an infinitely high barrier, as well as the work function and surface energy of simple metals in the model with homogeneous distribution of positive background. The difference between self-consistent Hartree solutions and those taking into account the exchange-correlation interaction is analyzed. The comparison with the results previously published in the literature is carried out. The case study of the metal-semiconductor tunnel contact shows this method as applied to an infinitely extended system where the steady-state current can flow.     

Electrostatic solution and rayleigh approximation for small nonspherical particles in a spheroidal basis

The electrostatic problem for the case of axially symmetric particles is analyzed in a spheroidal basis. In this case, the wavenumber is zero and Maxwell’s equations are reduced to the Laplace equation for scalar potentials. An alternative approach involves solving integral equations that are similar to those obtained within the framework of the extended boundary conditions method. The scalar potentials are represented as expansions in terms of eigenfunctions of the Laplace equation in a spheroidal frame of reference, and unknown expansion coefficients are determined from an infinite set of linear algebraic equations (the separation of variables method). These two approaches yield exact solutions of the problem in the case of axially symmetric particles, which coincide with known solutions in particular cases. Investigation of infinite systems allowed finding the boundaries where these algorithms are valid. Numerical calculations showed that, for spheroidal Chebyshev particles (i.e., perturbed spheroids), the Rayleigh approximation based on the electrostatic solution is applicable in a wide range of the problem parameters and is in fair agreement with the results obtained using the discrete dipole approximation.