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.     

Suppression of primary chromatic aberration by genetic algorithm in an advanced telephoto lens

This paper proposes a new method for finding a suitable glass combination set for an advanced telephoto lens via a genetic algorithm (GA). Normally, glass properties, inclusive of index and Abbe number, play a significant role in the elimination of primary chromatic aberration. So many optical glasses (over 300 different refractive types) have been developed hitherto that it is difficult to choose a state-of-the-art glass combination quickly. According to the newly developed GA operations in this paper, however, several suitable glass combinations can be found quickly through a unique sequence of function selection, crossover and mutation. An advanced telephoto lens design is employed in this research, which has the characteristic of being more sensitive to axial aberrations than lateral chromatic aberrations. The GA operations are described in the macro of the optical software program, CODE V. The simulation results in this research show that the primary chromatic aberration is efficiently eliminated after the application of GA. The main goal of this research is that during optimization, error function could be minimized only if primary aberrations are well under control in our first step; in a telephoto lens, the secondary spectrum of longitudinal chromatic aberration and lateral chromatic aberration caused by distortion play a role in chromatic aberration control as well; however, optimization with a combination of both primary chromatic aberration and secondary chromatic aberration will complicate the process with a lot of working variables. The GA method introduced in this paper might efficiently eliminate the primary chromatic aberration first by finding the best glass combination and its trend and then simplifying the following optimization process for all optical systems.     

阴极透镜象差的变分理论

本文运用变分原理研究了电磁复合聚焦阴极透镜的象差理论,导出了在任意象平面中象差系数的普遍公式。它们可以用Glaser导出的象差系数的线性组合来表示。这就表明了宽束与细束电子光学系统的象差都可以用统一的变分方法处理,并建立了两者之间的联系,本文采用矢量形式描写阴极透镜的近轴轨迹,并采用矩阵形式描写象差。本文所得的象差系数较之文献上已有结果形式更为简洁且适用于计算机计算。本文考虑了阴极面上磁场和横向电场不为零的情况,因而所得结果较为普遍。 关键词：     

宽束和细束电磁复合聚焦球面阴极透镜的象差理论

本文研究了对宽束和细束阴极透镜普遍适用的电磁复合聚焦球面阴极透镜的象差理论。在考虑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象差在内的全部三级横向象差矩阵公式。所得的结果较为完整、普遍。本文详细讨论了宽束和细束阴极透镜的关系,并用轨迹法和变分法严格证明了:当考虑阴极面逸出电子具有一定的初能量和初角度分布,并采用准规范化电位表示的近轴轨迹方程来讨论系统的理想成象时,宽束和细束两类阴极透镜从象差理论以至导出的三级横向象差、象差系数表示式都可以统一起来。本文采用矢量描写轨迹,运用矩阵表示象差,形式简洁,象差系数积分收敛,适合于计算机计算。 关键词：     

Chromatic aberrations of thin refractive variable-focus lens

We present an approach to an analysis of the third order chromatic aberrations of thin refractive fluid lenses with a variable focal length. A detailed theoretical analysis is performed for a simple fluidic variable-focus lens and formulas are derived for an optical design of such lenses. Aberration coefficients of the third order of the variable-focus lens can be completely characterized by three parameters which depend only on refractive indices of fluids forming the variable-focus lens. Formulas were derived for the change of the third-order aberration coefficients with the wavelength. Calculations are provided for Varioptic lens Arctic-416.     

The aberration theory of a combined electron focusing–deflection system with a rotating deflection field following the rotation of the electrons

A new type of combined magnetic focusing–electrostatic deflection systems whose orientation of deflection field is rotated synchronously with the beam electrons is proposed. This rotation deflection field can be formed by twistification of tube wall electrode (TWE) deflectors. Formulae are derived for the first-order optical properties, third-order geometrical aberrations and first-order chromatic aberrations of this system. A program was written in FORTRAN for numerical computation. An example is given; the computation results show that compared to the conventional systems, the proposed new system has lower deflection aberration coefficients.     

磁圆形透镜和磁六极透镜的复合系统的象差

近来磁六极透镜作为球差校正器引起了人们的注意。本文研究了磁圆形透镜和磁六极透镜的场分布叠加形成的复合系统的象差。我们在复数域中定义了内积,采用了复数的表象和微分算符,全面讨论了这种复合系统的高斯光学性质及二、三、四级象差,得出了各级象差所有的象差系数的公式。 关键词：     

激光靶心冲击波观测镜折反式光学系统设计

设计了一种激光靶心冲击波观测镜的光学系统.用反射式光学系统代替折射式光学系统,解决了普通玻璃在200 nm端透过率较低的问题.反射镜不引入色差,有利于系统在200~800 nm谱段消色差.为消系统轴外像差,反射系统选型为对称式.反射镜全部采用球面镜,为消反射镜以及平板玻璃窗带入的球差,引入校正镜(材料JGS1),在满足要求的条件下,控制折射镜的厚度,使系统色差满足瑞利判据的色差允差,得到了良好的成像质量.     

Optimization of 350× optical zoom lens with diffractive optical element

Through researching and validating, a set of optical designs using a diffractive optical element (DOE) and optimization process has been derived in this paper. We put forward a set of theories to solve the numerous quality issues in imaging and applied it to an optical design. For an optical design to be successful, it must comply with the standards of the optical system. Optical designers must also take into consideration imaging quality, wherein the most influential aspects are chromatic aberration and monochromatic aberration. We complied with systemic standards such as effective focal length and total system length. Diffractive Optical Element, based on the theory of wave phase difference, takes advantage of negative Abbe number, which might significantly eliminate chromatic aberrations of optics. Following the advanced technology applied to micro lens and etching process, precisely made micro DOE element now is possible to be manufactured in a large number. A 350× zoom lens with DOE is demonstrated in the proposal. The results show that regardless of whether chromatic aberration is axial or longitudinal, issues concerning the optical lens's chromatic aberration could be significantly reduced.     

梯度折射率棒透镜的色差模型

本文提出一个梯度折射率棒透镜(GRIN－RodLens)的色差模型,并运用本模型合理地解释了在色差测量过程发现的各类色差现象.     

On the chromatic aberration of magnetic lenses with a field distribution in the form of an inverse power low (B(z) ∝ z)

The chromatic aberration of magnetic lenses with the field distribution in the forms of inverse law have been studied by analytical and digital methods. These aberrations can be expressed in terms of Bessel function of fraction order. Analytical expressions for chromatic aberration coefficients of the spherical field model, which is useful for the study of single-pole magnetic lenses, are given.     

Aberration analysis of electron mirrors by a differential algebraic method

A differential algebraic (DA) method has been developed for the aberration analysis of electron mirrors. Since large ray slopes occur near the turning points in mirrors, the axial position is no longer suitable as the independent variable and the electron trajectory equation used in conventional lens theory is no longer feasible. A DA solution of the electron motion equation, wherein a single DA ray trace is performed on a non-standard extension of real number space called _nD_v, enables the aberrations of a mirror system to be obtained, in principle up to arbitrary order n, and with very high accuracy, due to the remarkable algebraic properties of _nD_v. With the DA method, the enormous effort to derive explicit formulae for the aberration coefficients of electron mirrors is avoided. A software package MIRROR_DA has been developed for the aberration analysis of electron mirrors, based on the DA method. Two examples of electron mirrors are presented. For the first example, for which the electrostatic and magnetic fields are represented by analytical models, the results computed with MIRROR_DA were shown to be in good agreement with those extracted by direct ray tracing, with relative deviations of less than 0.065% for all the primary aberration coefficients. The second example consists of a real magnetic lens and electrostatic mirror, with numerically computed fields, and from the results of MIRROR_DA, the spherical aberration coefficient C_s3 is almost cancelled out because of the correction effect of the mirror. The MIRROR_DA software is a novel, effective and precise tool for the aberration analysis of electron mirrors, capable of handling realistic and complicated systems of electron lenses and electron mirrors.     

A simple quadrupole-octupole electromagnetic lens

Charged particle beam trajectories in a simple electromagnetic quadrupole-octupole lens are numerically calculated based on analytical expressions for the +potential distribution. Locations of the lens foci in the image space are determined over a wide range of initial conditions. Relationships between the electrostatic and magnetic lens components that provide correction for chromatic aberrations of off-axis beams, which are different from classical beams, are obtained. Phase contours at the lens exit are calculated for beams occupying the major part of the aperture, and conditions for transforming the phase contour with minimal distortions are found.     

Aberration analyses for liquid zooming lenses without moving parts

Liquid lenses with an adjustable focal length are of particular interest for their potential applications in compact imaging or zooming systems. We have analyzed the aberrations for liquid zooming lenses and compared them with those of traditional lenses. Based on the 3rd order aberration theory, possible structures for the liquid zooming lens without moving mechanism were determined. We showed that a two-group liquid lens system is the simplest one that contains no moving mechanical parts and has enough parameters to correct all chromatic aberrations for any focal length and most monochromatic aberrations for certain focal lengths.     

多级聚焦-偏转复合系统的相对论象差理论

本文在文献[1]的基础上,导出了聚焦-偏转复合系统的相对论一级色差及另一形式的相对论三级几何象差公式,得出了各种象差系数的明显公式,应用上述理论,本文讨论了多级电-磁的偏转复合系统中象差的叠加问题。 关键词：     

Differential algebraic method for time of flight property of electrostatic electron lenses

Differential algebraic method is a powerful technique in computer numerical analysis. It presents a straightforward method for computing arbitrary order derivatives of functions with extreme high accuracy limited only by the truncation error of the computer. When applied to nonlinear dynamical systems, the arbitrary high-order transfer properties of the systems can be computed directly with high precision. In this article, the time of flight (TOF) property of electrostatic electron lens systems is studied by differential algebraic method and their arbitrary order TOF transfer properties can be numerically calculated. As an example, Schiske's model electrostatic lens has been studied by the efficient differential algebraic TOF method.     

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。     

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：     

泛卡塞格林光学系统的色差研究

泛卡塞格林光学系统结构简单、像质优良,广泛应用于空间光学领域中。从对研制完成的谱段位于500～800nm的泛卡塞格林光学镜头的调制传递函数(MTF)的测量结果出发,结合泛卡塞格林光学系统的结构特点,分析表明光学设计的色差来源于其高次施密特非球面镜,提出了一种利用非球面镜的最小色差条件来改进光学系统的新方法。通过三级像差理论,分析了施密特非球面镜的面形方程,计算出最小色差条件及相应的中性带高度,进行光学设计的优化改进,取得了良好的效果。结果表明,改进后光学系统的色差由原来的31.4μm减少为4.25μm,且光学系统的MTF值达到0.6以上(40lp/mm),像质优良。该方法为类似光学系统的设计提供了一定的参考价值。     

A New Approach to the Design of Hybrid Lenses for Integrated Optics

The Fresnel lens is one of the most extensively studied components in both classical and integrated optics. This structure is free from axial spherical aberration, but is heavily affected by both off-axis and chromatic aberrations. The latter can be compensated by introducing a refractive component, whose chromatic behavior is the opposite of that of the diffractive lens. This hybrid refractive-diffractive structure, however, is not able to deal effectively with off-axis aberrations, namely, with coma. In this work, a novel methodology for the design of corrected hybrid lenses is proposed which allows for correction of both chromatism and coma. The design method is based on a ray-optics variational approach which provides a range of possible achromatic solutions. An optimization procedure is performed by means of a series of beam propagation method numerical calculations which make it possible to simulate the lens operation and thus to find the best solution.