Different algebraic method for computing the high-order aberrations of practical combined focusing-deflection systems

Differential algebraic (DA) method is an effective technique in computer numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. Some complicated nonlinear dynamics problem including high-order aberrations of electron optical systems can be solved effectively by mapping properties of DA quantities. However, the existing study applying DA method to the practical system is limited to simple electron lenses. In this paper, the application of DA method is extended to practical combined focusing-deflection systems, and the aberrations up to fifth order are calculated. The electric and magnetic fields of the electron lenses and deflectors, which are computed by finite element method (FEM) or finite difference method (FDM), are in the form of discrete arrays. Local analytical expressions for electric and magnetic field quantities are constructed from these arrays for arbitrary place where electron is traced in DA computation. Thus the developed DA method is applicable for engineering design and computing problem. Based on the study of the expressions and the structure of the aberration coefficients for the fifth-order aberrations of the combined focusing-deflection system and the local analytic expression of the practical electromagnetic field, correlative computer software was developed, whose interface is convenient to calculate the high-order aberrations of the practical systems. The new DA method and software are tested with a uniform magnetic field deflection having an analytic solution. And the results show that the accuracy is sufficiently high, only limited by machine precision. Finally, as an example, a practical combined magnetic focusing and magnetic deflection system is analyzed and discussed.     

细电子束像差与畸变参量非劣解中的最优解

以电子束偏转磁场的像差和畸变为目标,对参量进行非劣解中找出贴近理想的最优解。以SDS-3电子束曝光机的磁复合偏转系统为基础,分析了像差与电子束主轨迹的关系。并给出了磁聚焦和静电的偏转场相复合情况下竖轴的3级几何像差系数和1级色差系数公式。应用中表明,复合系统结构简单紧凑,像差小而可以不用动态校正。     

Electron mirror as a corrector of electron microscope objective aberrations

We describe a new optoelectronic system for correcting aberrations of the objective lens with the help of an electron mirror. The system is based on the implementation of a special focusing regime (so-called regime of superimposed images) in which two images of the object are formed in the plane passing through the center of the curvature of the mirror. One of these images is formed by the beams (with aberrations) emerging from the objective lens, and the other is formed by the beams (with cancelled aberrations) reflected from the mirror. The separation of the two superimposed images and visualization of the image with cancelled aberrations are performed by deflection of the electron beam in the axisymmetric magnetic field whose symmetry axis passes through the center of curvature of the electron mirror. The magnetic field distribution ensuring aberration-free deflection of the electron beam is calculated.     

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为EAST装置中性束注入器设计了一套用于将剩余离子在线电偏转的结构,并对系统各设备的核心参数进行了估算。在4.41kV偏转电压作用下,该电偏转系统可提供80keV氘离子束偏转所需的偏转电场。在偏转电场调制情况下,该电偏转系统可有效降低极板表面的热负荷,进而满足EAST中性束注入器稳态运行的需要。     

Multi-beam method to increase the stability of bridge deflection measurement

The main limitation to the accuracy of the detection of a bridge deflection using laser-based optical solutions is atmospheric turbulence because of the laser beam propagation in ground proximity. The multi-beam method is presented to increase the stability of bridge deflection measurement. It is based on the use of a four-beam optical system and a subpixel resolution algorithm for the measurement of the deflection of a laser beam that propagates through the system. To obtain accurate results, different algorithms for measuring the position of the deflected beam in different optical systems are tested and compared. Based on this comparison, the four-beam method based on the macropixels iteration centroid and four-beam optical system is selected, and an accuracy of 0.16 pixels is obtained by the determination of the beam position in our setup. The proposed method is adopted to detect the bridge deflection and an accuracy of 0.01 mm is gained when the scintillation index C_n² is 3×10⁻⁴ m^−2/3.     

中性束注入器电偏转系统的参数设计与估算研究

为EAST 装置中性束注入器设计了一套用于将剩余离子在线电偏转的结构,并对系统各设备的核心参数进行了估算。在4.41kV 偏转电压作用下,该电偏转系统可提供80keV 氘离子束偏转所需的偏转电场。在偏转电场调制情况下,该电偏转系统可有效降低极板表面的热负荷,进而满足EAST 中性束注入器稳态运行的需要。     

普遍的电偏转三级象差系数及其与光栅图的关系

本文将电偏转三级象差的工作推广,使适合于入射处就有电场的情况,导出一个能在任意平面上求三级偏转象差的公式,对分离式电偏转系统及叠合式偏转系统(Deflection Yoke)均适用。并经过数学处理,使公式简洁,换算方便,还将象差系数积分公式中的轴上场E₀(z)的一、二级微商全部消除,以提高计算精度。为了和我们的前一工作相对应,符号的命名和计算格式也与文献[1]相同,最后还描述了顶点在屏上的圆锥形细束在偏转后产生的光栅畸变、场曲、象散、彗差等图形与这套系数的对应关系。这种关系也完全适合于磁偏转三级象差的情况。 关键词：     

Large deflection of clamped circular plate and accuracy of its approximate analytical solutions

A different set of governing equations on the large deflection of plates are derived by the principle of virtual work(PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.     

Post-post-Newtonian deflection of light ray in multiple systems with PPN parameters

The post-Newtonian scheme in multiple systems with post-Newtonian parameters presented by Klioner and Soffel is extended to the post-post-Newtonian (PPN) order for light propagation problem in the solar system.Under considering the solar system experiment requirement,a new parameter ε is introduced.This extension does not change the virtue of the scheme on the linear partial differential equations of the potential and vector potential mentioned in previous work.Furthermore,this extension is based on the former work done by Richter and Matzner in one global system theory.As an application,we also consider the deflection of light ray in the global coordinates.And the deflection angle of light ray is obtained with post-Newtonian parameters.     

Analysis of the deflection system for a magnetic-field-immersedmagnicon amplifier

A linear analysis of the electron-beam deflection system in a magnicon amplifier is presented. The system consists of identical cavities, one driven and the remainder passive, separated by a drift space and immersed in an axial magnetic field. The cavities contain a rotating TM₁₁₀ mode. The length of each cavity is πν _z/ω, and that of the drift space is πν_z/ω_c, where ω is the RF frequency, ω_c is the relativistic gyrofrequency in the guide field, and ν_z is the mean axial velocity of the beam electrons. The linearized electron orbits are obtained for arbitrary initial axial velocity, radial coordinate, and magnetic field. The small-signal gain and the phase shift are determined. The special case where ω_c/ω=2 has unique features and is discussed in detail. For the NRL magnicon design, a power gain of 10 dB per passive cavity is feasible. Results from numerical modeling of a magnicon with two passive cavities are presented. Operation of the output cavity at the fundamental and higher harmonics of the input drive frequency is briefly discussed     

新型小型化牙科扫描仪探头的光学系统设计

为解决牙科扫描探头小型化问题,基于结构光三维重建算法,创新性地设计出一种投影与成像共孔径设置的小型化牙科三维扫描仪探头光学系统。系统采用分视场共孔径技术,部分视场用于实现投影功能,另一部分视场用于实现成像功能,投影区域和成像区域存在公共区域。仿真实验给出了在扫描范围为46×35mm2内的系统性能,借助LightTools软件做了照明分析仿真,证明了系统光路的可行性。     

关于声光效应光束偏转角的实验研究

对声光效应中光束偏转角进行了一系列实验研究.基于传统声光效应的基本原理,建立了光束偏转角理论模型并进行了相关计算.在此基础上进行声光效应的布拉格衍射实验.大量实验结果显示,所测量到的光束偏转角和理论值存在一定的差距.     

基于ybar-y图的光学结构计算方法研究

本文基于y_bar-y图, 建立了计算光学系统一阶结构的数学模型, 并利用粒子群优化算法对模型进行了求解, 可以自动优化出各种光学系统的一阶结构. 编写了一套含图形用户界面(GUI)的软件, 将光学系统的基本设计要求进行处理后导入GUI, 求解之后利用商用光学设计软件如ZEMAX等, 将一阶结构转换为实际透镜结构, 然后经过透镜优化, 就可以设计出满足要求的光学系统. 根据本文所提出的光学结构计算方法, 首先进行了1300万像素手机摄像物镜的设计, 该物镜使用了4片非球面, 各项性能指标能够满足设计要求. 然后设计出一套头盔显示光学系统的目镜, 使用了两片非球面透镜实现了90°的视场角, 其他的性能指标也都满足要求. 两类光学系统的设计实例验证了该方法是一种可靠的光学系统一阶结构获取方法.     

电子束曝光机大物面强磁透镜的研究

以SDS-3电子束曝光机的聚焦透镜系统为基础,在0.005弧度半张角,3×10－5的高压纹波,50 mm的像距,30×30 mm扫描场的条件下,研究了电磁透镜成像的笛卡尔坐标系中的近轴轨迹方程,给出了相应的计算初值条件和实例.讨论了电子束曝光机聚焦透镜系统中的球差、彗差、像散、场曲和畸变等电子光学特性的确定以及系统像质评定的问题.     

面对称光学系统的初级波像差理论研究

非旋转轴对称光学系统波像差理论的建立有利于理解旋转 轴对称光学系统的装调误差和离轴三反射光学系统等非旋转轴对称光学系统的选型设计. 本文利用旋转轴对称球面光学系统的全口径初级波像差理论推导了子孔径面对称光学系统的初级波像差分布公式, 证明了面对称光学系统中的节点像差理论, 即除球差外的所有初级像差的零值节点偏离视场中心, 而不再是视场的旋转对称函数; 并首次阐述了多零值节点初级非对称像差产生的根源和变化特性. 该理论可以有效指导非对称光学系统初始结构的选择和优化设计过程. 关键词： 面对称 像差 几何光学     

Cumulative interaction in the deflection cavities of a high-powermagnicon amplifier

A major factor limiting the output power of a high-power magnicon is RF breakdown in its penultimate cavity. Utilization of the principal of angle summing allows us to achieve cumulative interaction between a beam and RF fields of the magnicon deflection system, and thus to decrease the maximum electric field in the penultimate cavity. In this paper, the problems of implementing a cumulative interaction in a magnicon deflecting system are discussed. A deflecting system with coupled cavities working according to the principal of angle summing, which has been tested with success experimentally, has a limitation caused by instabilities that can limit pulse duration at a power level higher than a few tens of milliwatts. The method described employs a set of uncoupled penultimate cavities to obtain cumulative interaction at high power without sacrifice of pulsewidth     

Active control of horseshoes chaos in a driven Rayleigh oscillator with fractional order deflection

The problem of suppressing chaos in the Rayleigh oscillator with fractional order deflection is considered. The explanation of Melnikov?s techniques shows that the dynamic performance and robustness of the system are highly dependent on the fractional order α. The feedback control system is considered as active control strategy. It is revealed with analytical results that periodic perturbation from the controller enhances the performance of the active control strategy. The proposed control strategy is more efficient for deflection order α∈[1.5,2.5] and under super resonant condition between the driven frequency and perturbation frequency. Numerical simulations demonstrate the effectiveness of Melnikov?s analysis.     

Effect of shear strain on the deflection of a clamped magnetostrictive film-substrate system

The effect of in-plane shear strain of a clamped bimorph on the deflection produced by magnetization of the film is investigated. The deflection is found by minimizing the Gibbs free energy with respect to four parameters, strains and curvatures along x and y directions at the interface, by assuming that the curvature in the y direction varies as a function of aspect ratio w/l along x. A set of standard linear equations of four parameters are obtained and the deflection is expressed in terms of the four parameters by solving the equations using Cramer rules. The inconsistencies pointed out by previous authors are also reviewed. For actuators made of thick and short clamped film-substrate system, the in-plane shear deformation should not be omitted. The present calculation model can give a relatively simple and accurate prediction of deflection for thick and short specimens of aspect ratio w/l<10, which supports the results obtained by finite element modeling.     

双目显微系统光路偏转与平行性检测

针对双目系统中各自光路的偏转和2条光路之间的不平行会增加轴外像差,降低成像质量,并造成双目视觉的不同一性,引起使用者的不适,提出一套激光检测和评价双目系统光路偏转和平行性的方法。将待测系统拆分成元件,先检测元件的光路偏转和平行性,然后逐步组合元件,实验测得待测双目系统光路存在0.5 mm以上的光路偏转距离,入射平行光出射系统后夹角达0.8左右。结果表明,该方法可以应用于显微镜工业生产和检测之中。     

Optical deflection tomography with the phase-shifting schlieren

We present a new optical deflection tomography method that takes advantage of the phase-shifting schlieren. The reconstruction algorithm is based on filtered backprojection. The instrument is well adapted for three-dimensional imaging of spatially sparse objects exhibiting large refractive index variations. It achieves a 35 μm resolution with a 3 mm depth of field. Its performance is illustrated with a bundle of fibers immersed in a matching index solution.