静电聚焦双电极系统：静态与动态电子光学成像与时空像差分析

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"本文深入探讨了静电聚焦双电极球形同心系统在成像电子光学中的应用，重点关注静态和动态成像的特性以及时空像差。该系统由两个具有静电聚焦功能的球形电极组成，是研究电子光学理想模型的一个实例。作者Li-wei Zhou、Hui Gong、Zhi-quan Zhang和Yi-fei Zhang分别来自北京理工大学和装甲兵工程学院，他们在2009年8月提交，2010年1月接受，并最终在2011年的《Optik》期刊上发表这一研究成果。文章首先介绍了静电势在同心球形系统中的分布情况，以及电子运动的时空轨迹解析表达式。这些解析形式对于理解和模拟电子在该系统中的行为至关重要。接着，作者通过解决实际电子射线方程和电子运动方程，推导出了双电极同心球系统中电子的图像位置和飞行时间的精确和近似公式。进一步的讨论集中在系统的电子光学时空特性上，特别是对近轴和几何横向像差以及近轴和几何时间像差的分析。这些像差是评估成像质量的关键指标，它们直接影响到电子光学系统的成像精度。作者按照SQRT(Ε/√φ)和SQRT(Ε[R]/√φ)的顺序对这些像差进行了分类，其中Ε代表电势，φ代表电荷，R代表半径，这为理解和改进系统性能提供了理论依据。关键词包括静态电子光学、动态电子光学、近轴和几何横向像差、近轴和几何时间像差，以及带静电聚焦的双电极同心球系统。这些关键词突出了研究的核心内容，即在静态和动态条件下，如何理解和控制电子光学系统的成像质量和时间响应，这对于发展高分辨率、高速度的电子光学设备，如夜视装置和高速图像转换器管，具有重要意义。该研究提供了一个理论框架，用于分析和优化同心球形系统的成像性能，为电子光学领域的理论研究和实际应用提供了有价值的参考。"

Optik 122 (2011) 287–294

Contents lists available at ScienceDirect

Optik

journal homepage: www.elsevier.de/ijleo

Static and dynamic imaging electron optics and spatial–temporal aberrations in a

bi-electrode spherical concentric system with electrostatic focusing

Li-wei Zhou

a,∗

, Hui Gong

, Zhi-quan Zhang

, Yi-fei Zhang

Beijing Institute of Technology, Beijing 100081, PR China

Institute of Armored Force Engineering, Beijing 100072, PR China

article info

Article history:

Received 15 August 2009

Accepted 5 January 2010

Keywords:

Static electron optics

Dynamic electron optics

Paraxial and geometrical lateral aberrations

Paraxial and geometrical temporal

aberrations

A bi-electrode concentric spherical system

with electrostatic focusing

abstract

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 elec-

tron 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 partic-

ularity 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 trajecto-

ries 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 lat-

eral aberrations, as well as the paraxial and geometrical temporal aberrations, have been deduced, that

are classiﬁed by the order of

√





and

√





1. Introduction

For an electron optical imaging system, spatial-trajectory-spread and transit-time-spread produced by initial emission energy and

initial emission angle of photoelectrons are the fundamental problems of image tubes and high-speed image converter tubes. In the static

mode operation for these two tubes, the spatial-trajectory-spread of electron trajectories at the image plane determines limited spatial

resolution. In the streak mode operation for high-speed image converter tube, a point image of a photo event of very short duration is

imaged by the camera as a line because of transit-time-spread. The length of the line is proportional to the transit-time-spread. Obviously,

the shorter the length of the line, the better the time resolution of the camera.

It was proven that the spatial-trajectory-spread of an imaging system is mainly determined by the paraxial lateral aberration of second-

order, which is usually summarized as Recknagel–Artimovich formula [1,2]. Formula shows that the paraxial lateral aberration of second-

order does not depend on the concrete electrode structure and potential distributions, but depends on initial electron emission energy,

the strength of electric ﬁeld at the photocathode, the linear magniﬁcation of the system and the position of image plane.

Similarly, the transit-time-spread of an imaging system is mainly determined by the paraxial temporal aberration of ﬁrst-order, which

is expressed by Savoisky–Fanchenko formula [3]. Formula shows that the temporal aberration of ﬁrst-order depends only on the initial

emission energy, the strength of electric ﬁeld at the photocathode, but does not depend on the concrete electrode structure and potential

distribution. Besides, it does not depend on the linear magniﬁcation of the system and the position of image plane.

Thus, we may ﬁnd many similarities between Recknagel–Artimovich formula and Savoisky–Fanchenko formula, but the difference

exists. We can also ﬁnd the non-harmonious and non-symmetry between them if we think it over. Actually, either the spatial-trajectory-

spread or the transit-time-spread at an image plane, which are produced by spatial–temporal trajectories emitted from photocathode with

∗

Corresponding author at: Beijing Institute of Technology, School of Information Science and Technology, 5, Zhongguancun South Avenue, Haidian Zone, Beijing 100081,

PR China. Tel.: +86 10 68911748; fax: +86 10 68912550.

E-mail address: zhoulw@vip.sina.com (L.-w. Zhou).

doi:10.1016/j.ijleo.2010.01.003

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