基于渐近解的成像电子光学近轴横向像差理论及其验证

On Theory and Verification for Paraxial Lateral Aberrations of Imaging Electrostatic Electron Optics Based on Asymptotic Solutions

在成像电子光学系统的横向像差中,近轴像差是整个像面普遍存在、且影响图像中心像质的主要像差,并决定了系统的极限分辨率.本文由电子光学近轴方程的渐近解推导了近轴横向像差的普遍表示式,并通过一两电极静电同心球系统,推导了近轴轨迹特解的渐近解和精确解的解析表示,给出了二级和三级近轴色球差以及三级近轴放大率色差的表达式,证明了基于渐近解求解成像电子光学系统的近轴横向像差的途径是可行的和足够精确的.文中给出的近轴横向像差的简明形式对于成像电子光学系统的像差研究和像管设计具有实际意义.

In lateral aberrations of an imaging electron optical system,the paraxial lateral aberrations exit widespread in the whole image plane and that is also the main aberrations which effect image quality of central image and determine limiting image resolution of system.In the present paper,the paraxial lateral aberrations expressed in general form have been derived emphatically by using asymptotic solutions of paraxial equation for imaging electron optics.By using a bi-electrode electrostatic concentric spherical system model,the analytical forms of two special solutions of paraxial rays expressed by asymptotic and accurate solutions have been deduced and tested.The paraxial sphero-chromatic aberrations of second and third order,as well as the paraxial chromatic aberration of magnification of third order,have been deduced.Result completely proves that the approach based on asymptotic solutions to solve the paraxial lateral aberrations is accurate enough and practicable.A simple and clear form for expressing paraxial lateral aberrations of imaging electron optical systems is suggested for practical use,which will have practical significance for study of aberrations of imaging electron optics and for design of image tubes.