微分代数方法在静电电子透镜任意高阶像差分析中的应用

Differential Algebraic Method for Arbitrary High Order Aberration Analysis of Electrostatic Electron Lens Systems

微分代数是计算机数值分析领域中的一个非常有效的方法,它以非标准分析理论为基础,可以实现任意高阶微分的准确计算.本文根据微分代数方法的基本原理,将其引入到静电电子透镜的任意阶像差分析的计算中.通过计算例子,可以看出微分代数方法的计算结果非常精确,精度仅受限于机器精度和算法误差.同时结合微分代数方法可以很方便地计算到任意高阶像差的特性,给出了所研究的透镜全部五阶像差的分布图形.

Differential algebraic method is an effective technique in computer numerical analysis. It can exactly implement differentiation up to arbitrary high order based on the nonstandard analysis theory. The principle of differential algebraic method is applied to calculate arbitrary high order aberrations of electrostatic electron lens systems. An example is given to show that the numerical results have excellent accuracy, and the accuracy is limited only by the machine precision and the arithmetic errors. The arbitrary high order aberrations are conveniently calculated by differential algebra method and the fifth-order aberration diagrams are given.