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微分代数是计算机数值计算领域中的一种强有力的新型数学方法 ,它为任意高阶微分的计算提供了一种可达到机器精度的极为简便的手段。本文根据微分代数的基本原理 ,研究了它在高阶复合几何像差 色像差分析计算中的应用 ,得到了系统的任意阶传递性质的微分代数表示 ,并具体给出了一至三阶复合几何像差 色像差所对应的微分代数系数。文中还以一个轴上电位分布具有解析表达式的静电电子透镜为例 ,计算了它的一至三阶复合几何像差 色像差系数 ,并给出了一阶色差分布图形。
Differential algebra is a powerful new mathematical method in the field of computer numerical computation. It provides a very simple and convenient method to calculate the precision of any high-order differential. Based on the basic principle of differential algebra, this paper studies the application of differential algebraic representation in high-order composite geometrical aberrations, obtains the differential algebraic representation of arbitrary order transfer property of the system, and gives the first to third order composite geometries Differential algebraic coefficient corresponding to aberration chromatic aberration. Taking an electrostatic lens with an analytic expression on the on-axis potential distribution as an example, the first to third order geometric chromatic aberration coefficients are calculated and the first-order color difference distribution graph is given.