钟形磁场高阶球差的分析与计算

Analysis and Calculation of Higher Order Spheric Aberrations in Glaser′s Bell Shaped Magnetic Lens

根据电子光学正则理论，在旋转对称系统中，将哈密顿表象的光程函数进行广义积分变换，得出只含有位置而不存在动量的简正形式光程函数。从而成功地算出了３、５、７、９级球差系数的解析公式。对于Ｇｌａｓｅｒ钟形磁场的３、５、７、９级球差系数进行了数值计算。由此提出和证明了高阶球差定理，即“旋转对称钟形磁透镜中，３级和７级球差系数恒为正号，而５级和９级球差系数则可以变号。但是总的球差则恒为正值”。

Based on canonical aberration theory, a generalized integration transformation has been performed on Hamiltonian eikonals, electron optical aberrations has thus been derived for up to the ninth order approximation in rotationally symmetric magnetic and electrostatic lenses. For Glasser′s bell shaped magnetic lens, third , fifth , seventh , ninth order spheric aberrations have been analytically derived and numerically calculated. It has been shown that third and seventh order spheric aberration coefficients always have positive signs, while fifth and ninth order spheric aberration coefficients may be positive or negative. Nevertheless, the total spheric aberration is still positive. This theoretical conclusion may be useful for estimating effects of higher order spheric aberrations in rotationally symmetric magnetic lenses.