磁浸没透镜的宽束曲轴像差分析的微分代数方法研究

Study on Differential Algebraic Method of Curvilinear-Axis Aberration Analysis with Wide Beam for Magnetic Immersion Lenses

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 ,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 ,将其引入到磁浸没透镜的宽束曲轴像差的分析计算中 ,得到了任意阶曲轴像差的微分代数表达式 .文中针对轴上磁场具有某种解析表达式的一个实际的磁浸没透镜系统 ,利用微分代数的曲轴像差分析方法 ,计算了它的曲轴像差 ,并给出了全部二阶和三阶几何像差的分布图形 .

Differential algebraic method is an effective technique in computer numerical analysis.It can exactly implement differentiation up to arbitrary high order.The principle of differential algebraic method is applied to calculate curvilinear-axis aberrations with wide beam for magnetic immersion lenses,and the differential algebraic expressions of arbitrary order aberrations are obtained.An illustrative magnetic immersion lens which has an analytic axial field distribution has been studied by using differential algebraic method of curvilinear-axis aberration analysis.All the second order and the third order geometric aberration diagrams are given.