Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Department of Electronic Science and Technology, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China.
Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Department of Electronic Science and Technology, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China.
Ultramicroscopy. 2018 Dec;195:21-24. doi: 10.1016/j.ultramic.2018.08.017. Epub 2018 Aug 27.
A Differential algebraic method is of an effective technique in computer numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of electron lenses with quadrupole and octupole corrector whose electric/magnetic fields are in the forms of discrete arrays, for example, the files computed by FEM or FDM method. The quadrupole and octupole electro-magnetic fields of arbitrary point are obtained by local analytic expressions, and then field potentials are transformed into new forms which can be operated in the DA calculation. The program has been developed and tested as well. The geometric and chromatic aberrations coefficients up to fifth order of electron lenses with quadrupole and octupole corrector are calculated by the developed program.
微分代数方法是计算机数值分析中一种有效的技术。它基于非标准分析，方便地实现了任意高阶的微分。本文采用微分代数（DA）方法计算了具有四极和八极校正器的电子透镜的高次像差，其电/磁场采用离散数组的形式，例如由有限元或有限差分方法计算得到的文件。通过局部解析表达式得到任意点的四极和八极电磁场所需的场势，然后将其转换为可在 DA 计算中进行运算的新形式。该程序已经得到了开发和测试。利用开发的程序计算了带有四极和八极校正器的电子透镜的几何和色差的五阶像差系数。
