两电极静电同心球系统的近轴电子光学及其空间-时间像差

将从近轴解出发研究两电极静电同心球系统的空-时轨迹及其像差.由近轴轨迹方程和近轴运动方程出发,先求解两电极静电同心球系统中自光阴极逸出的运动电子的近轴空间-时间轨迹,然后讨论此系统的静动态电子光学及其空间-时间像差,揭示近轴光学系统成像的一般规律.文中定义和推导了各级近轴空间像差和近轴时间像差,得到了与关于近轴空间-时间像差同样的结论,表明完全可以直接由近轴轨迹方程和近轴运动方程出发来研究理想成像及其空间-时间像差.     

直接积分法研究电子光学成像系统的时间像差理论

提出了计算动态电子光学成像系统时间像差系数的新方法——直接积分法.以阴极面逸出的轴向电子初能为ε_z1（0≤ε_z1≤ε_0max）的近轴电子 轨迹为比较 基准,给出了时间像差的定义,详细叙述了直接积分法并给出求解动态电子光学成像系统时 间像差系数的积分表达式.τ变分法求得的二级几何时间像差系数必须求解微分方程, 而直接积分法求得的二级几何时间像差系数全部以积分形式表示,仅需进行积分运算,更适 用于成像系统的实际计算与设计. 关键词： 电子光学成像系统 阴极透镜 动态电子光学 时间像差理论     

复合电磁同心球系统的成像电子光学.B章:近轴像差

由复合电磁同心球系统的近轴方程两个特解出发,通过展开理想成像位置处图像转角表达式的途径,探讨了复合电磁同心球系统的近轴纵向像差和近轴横向像差。主要贡献是求得了近轴方程的两个特解在理想像面位置处的解析表达式,由此证明决定极限空间分辨率的二级近轴色球差能以Recknagel-Artimovich公式描述。导出了近轴横向像差的表达式,该像差由近轴色球差、近轴放大率色差和近轴各向异性色差等组成。     

静电聚焦同心球系统的成像电子光学 B章：近轴横向色差与几何横向球差

在A章基础上,进一步研究两电极静电聚焦同心球系统的轴上点电子光学横向像差。研究表明,对于成像电子光学系统,由光阴极发射的电子所形成的图像弥散,其轴上点的图像弥散由近轴横向色差与几何横向球差两部分组成,这证明了在静电聚焦同心球系统中,阴极透镜的二级近轴横向色差即Recknagel-Apцимович公式普遍成立。研究了宽电子束与细电子束之间轴上点横向像差之差异,最后讨论了两电极同心球系统向近贴聚焦系统过渡的特例。     

静电聚焦同心球系统验证电子光学成像系统的时间像差理论

关于动态电子光学成像系统的时间像差理论,计算时间像差系数有两种方法——τ变分法和直接积分法.它们的差别在于：τ变分法计算二级几何时间像差系数必须求解微分方程,而直接积分法仅需进行积分运算.采用静电同心球系统的理想模型对这两种方法的正确 性进行了检验.结果表明：这两种方法求解电子光学成像系统的时间像差系数的结果完全一致,所求得的时间色差系数与理想模型的解析解完全相同,从而证明两种方法是等价并且正确的.通过验证表明,直接积分法的计算更为简便,适于实际系统的计算与设计. 关键词： 阴极透镜 电子光学成像系统 动态电子光学 时间像差理论     

静电聚焦同心球系统的成像电子光学 C章：多电极同心球系统的电子光学

鉴于两电极静电聚焦同心球系统成像的定焦性质,当该系统的几何尺寸相对关系给定后,像面位置与放大率也就随之确定,改变系统的电参量引起的像面位置和放大率的变动是极其微小的。研究在由光阴极与栅状阳极组成的两电极同心球系统中插入任意多个栅极后,该系统的电子光学成像特性及其横向像差的变化规律。再次证实了在多电极静电聚焦同心球系统中,成像电子光学系统的二级近轴横向色差即Recknagel-Apцимович公式依然成立。着重讨论了三电极静电聚焦同心球系统的电子光学成像特性。     

静电聚焦同心球系统的成像电子光学 A章：电子轨迹方程

在成像电子光学中,静电聚焦同心球系统具有一系列宝贵的性质,其电位分布与电子轨迹能以解析形式表示,可以定量地研究系统的电子光学成像特性与横向像差。尽管前人已有不少研究,但都限于零级近似成像的认识,且其中存在着不少谬误。本系列文章将全面研究静电聚焦两电极与多电极同心球系统中电子的运动轨迹、电子光学成像特性与横向像差,探讨电子束在成像段形成的图像弥散,得出一些新的结论和认识,纠正文献中存在的一些谬误,建立自己的理论体系。本系列文章的第一篇主要探讨电子在两电极同心球系统中在静电场作用下的运动轨迹,导出了两电极静电聚焦同心球系统中自阴极面逸出的电子轨迹在极坐标系下的表示式ρ=f(φ)与圆柱坐标系下新的轨迹方程的表示式r=r(z),给出了自光阴极逸出的电子在成像段的行进轨迹的交轴位置及其斜率的近似和精确表示式。本文为全面研究静电聚焦同心球系统的电子光学性质及其像差奠定基础。     

复合电磁同心球系统的成像电子光学.A章:近轴光学

通过复合电磁同心球系统的理想模型,对成像电子光学近轴方程的轨迹求解进行探讨。首次推导了该系统的近轴电子轨迹的转角及近轴方程的两个特解的解析表达式,探讨了近轴成像性质,并将结果推广到两电极静电同心球系统、均匀平行复合电磁系统和静电近贴系统中。     

静电聚焦同心球系统的成像电子光学 D章：最小弥散圆与最佳像面位置的确定

由所导出的阴极透镜中普遍成立的二级近轴横向色差即著名的Recknagel-Apцимович表示式出发,研究电子束形成的最小弥散圆以及最佳成像面的位置的确定,考察由物面原点发射的电子束在栅状阳极上形成的散射圆以及整个阴极面发射所形成的交叉颈,描绘由物面原点逸出的电子射束在成像段所形成的电子射线的包络。该研究有助于读者理解电子光学像管中电子行进的轨迹以及成像段的电子轨迹的发散与会聚。     

多光束扫描成像系统的像差分析

根据几何光学理论,志出多光束扫描成 综合像差方程,分析了导致离轴扫描线像差的入射光线与成像系统光轴夹角、转镜面数等因素,并研究了各单项偈关工的权重因子。基于上述多光束扫描成像的综合像差方程,分析并给出了校正离轴扫描线像差的特殊透镜所应具备的预畸变因子。     

Static and dynamic imaging electron optics and spatial-temporal aberrations in a bi-electrode spherical concentric system with electrostatic focusing

In imaging electron optics, for a concentric spherical system composed of two spherical electrodes with electrostatic focusing, the electrostatic potential distribution and the spatial-temporal trajectory of electron motion can be expressed by analytical forms. It is naturally to take such system as an ideal model to investigate the imaging properties, as well as the spatial-temporal aberrations, to analyze its particularity and to find the clue of universalities and regularities. Research on this problem has important significance, which can afford theoretical foundation not only in studying static electron optics for the night vision devices, but also in studying dynamic electron optics for high-speed image converter tubes.In the present paper, based on the practical electron ray equation and electron motion equation for a bi-electrode concentric spherical system with electrostatic focusing, the spatial-temporal trajectories of moving electrons emitted from the photocathode have been solved, the exact and approximate formulae for image position and flight time of electrons, have been deduced. Start from solutions of spatial-temporal trajectories, the electron optical spatial-temporal properties of this system are then discussed. According to the definitions of spatial-temporal aberrations, the paraxial and geometrical lateral aberrations, as well as the paraxial and geometrical temporal aberrations, have been deduced, that are classified by the order of and .     

Paraxial imaging electron optics and its spatial-temporal aberrations for a bi-electrode concentric spherical system with electrostatic focusing

The paraxial solutions play an important role in studying electron optical imaging system and its spatial-temporal aberrations, as was discussed in previous paper [1], but investigation of a bi-electrode concentric spherical system with electrostatic focusing directly from paraxial electron ray equation and paraxial electron motion equation has not been done before. In this paper, we shall use the paraxial equations to study the spatial-temporal trajectories and their aberrations for a bi-electrode concentric spherical system with electrostatic focusing.In the present paper, start from the paraxial ray equation and paraxial motion equation, the paraxial spatial-temporal trajectory of moving electron emitted from the photocathode has been solved for a bi-electrode concentric spherical system with electrostatic focusing. The paraxial static and dynamic electron optics, as well as the paraxial spatial-temporal aberrations in this system are then discussed, the general regularity of imaging in paraxial optical system has been explored. The paraxial spatial aberrations, as well as the paraxial temporal aberrations with different orders, have been defined and deduced, that are classified by the order of (?_z/?_ac)^1/2 and (?_T/?_ac)^1/2. Thus we get same conclusions about paraxial spatial and temporal aberrations as we have given in the previous paper and it completely shows that the paraxial spatial-temporal aberrations can be investigated directly from the paraxial ray equation and paraxial motion equation.     

Theory of paraxial lateral aberrations of electrostatic imaging electrostatic electron optics based on asymptotic solutions and its verification

In imaging electron optics, study of geometrical lateral aberrations of third order and paraxial lateral aberrations of second order has traditionally been paid more attention to, but the existence of paraxial chromatic aberrations of third order and paraxial chromatic aberrations of magnification of third order was almost ignored, and the general form of paraxial lateral aberration has not been studied theoretically.In the present paper, the paraxial lateral aberrations expressed in general form have been derived emphatically on the basis of asymptotic solutions of paraxial equation. The relationship between the coefficients of asymptotic solutions has been investigated, which proves that the coefficients of asymptotic solutions are related each other. Through a bi-electrode electrostatic spherical concentric system model, two special solutions expressed by asymptotic solutions and accurate solutions in a bi-electrode electrostatic spherical concentric system have been deduced, and the paraxial lateral aberrations have been verified and tested, in which the aberration coefficients are solved by asymptotic solutions of paraxial equation. Result completely proves that the approach based on asymptotic solutions to solve the paraxial lateral aberrations are practicable and accurate enough. The paraxial chromatic aberration of magnification of third order and the paraxial chromatic aberration of third order have been firstly derived, and the Recknagel-Artimovich formula of paraxial chromatic aberration of second order which possess an greatest part in the whole paraxial lateral aberrations has been deduced and confirmed. A simple and clear form for expressing paraxial lateral aberrations of imaging electron optics is suggested for practical use. Results of the present paper will have theoretical value for aberration theory of imaging electron optics and practical significance for the design of image tubes.     

电子束曝光机偏转系统及可动物镜分析

电子束大扫描场偏转系统设计中 ,像差的确定是一个必须解决的实际问题。以SDS 3电子束曝光机的磁复合偏转系统为基础 ,以双通道扫描原理进行扫描 ,分析了像差与电子束主轨迹的关系。给出了可动物镜的条件 ,并利用这一条件分析电子束最佳轨迹的结构和方法。并使用计算机辅助设计研究电子束曝光机聚焦偏转系统的结构。由该电子束曝光机试验结果表明 ,复合系统结构简单紧凑 ,像差小而可以不用动态校正。采用矢量描写电子轨迹 ,以积分式表示像差。以 0 .0 0 5rad半张角 ,5× 10 -5的高压纹波 ,5 0mm的像距 ,10mm× 10mm扫描场的边脚处 ,使动态校正前的总像差为 0 .0 3μm。     

On the theory of temporal aberrations for cathode lenses

A new approach to the theory of temporal aberration for cathode lenses is given in the present paper. A definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0ε_z1ε_0max) is considered. A new method to calculate the temporal aberration coefficients of cathode lenses named “direct integral method” is also presented. The “direct integral method” gives new expressions of the temporal aberration coefficients which are expressed in integral forms. The difference between “direct integral method” and “τ-variation method” is that the “τ-variation method” needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the “direct integral method” only needs to carry out the integral calculation for all of these temporal aberration coefficients of second order.All of the formulae of the temporal aberration coefficients deduced from “direct integral method” and “τ-variation method” have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solutions and the solutions of temporal aberration coefficients of the first and second order are the same as with the analytical solutions. Although some forms of the results seem different, but they can be transformed into the same form. Thus, it can be concluded these two methods given by us are equivalent and correct, but the “direct integral method” is related to solve integral equations, which is more convenient for computation and could be suggested for use in practical design.     

电磁复合聚焦—偏转球面阴极透镜的相对论象差理论

本文应用变分原理研究了电磁复合聚焦-偏转球面阴极透镜的相对论象差理论。在考虑阴极面逸出电子具有一定的初能量和初角度分布,物场和象场弯曲以及阴极面上磁场和横向电场不为零的情况下,导出了任意理想象面上的一级近轴横向象差和包括色球差在内的全部三级几何横向象差,以及各种特殊类型象差系数的明显表达式。本文导出的象差公式不仅普遍适用于宽束和细束阴极透镜,而且普遍适用于相对论或非相对论,阴极和屏为球面或平面时的各种情况。本文以复数描写轨迹,用矩阵表示象差,形式简洁,适合于计算机计算。 关键词：     

Spherical aberration from trajectories in real and hard-edge solenoid fields

For analytical, real and hard-edge solenoidal axial magnetic fields, the low-energy electron trajectories are obtained using the third-order paraxial ray equation. Using the particle trajectories, it is shown that the spherical aberration in the hard-edge model is high and it increases monotonously with hard edginess, although the focal length converges, in agreement with a recent field and spherical aberration model. The model paved the way for a hard-edge approximation that gives correct focal length and spherical aberration, which is verified here by the trajectory method. In essence, we show that exact hard-edge fields give infinite spherical aberrations.