【摘要】 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。更多还原

【Abstract】 High order combined geometric chromatic aberrations were calculated with Differential Algebra,a method which is capable of directly evaluating arbitrarily high order derivatives with accuracy up to the upper limit of the computer to be used.Arbitrary order transfer properties of the system can be expressed in term of Differential Algebra.The corresponding differential algebraic coefficients of the 1st to the 3rd order combined geometric chromatic aberrations were given.Specific demonstration of this new technique was shown in the calculation of an electrostatic electron lens,whose axial potential density can be analytically described.更多还原