自动微分法求解粒子光学像差的精度分析  

Precision Analysis of Optical Aberration of Particles Calculated by Automatic Differentiation

作　　者：李文萍[1] 顾文琪[1] 

机构地区：[1]中国科学院电工研究所

出　　处：《微细加工技术》2007年第4期30-33,58,共5页Microfabrication Technology

摘　　要：将自动微分算法扩展到实际非解析场时会出现误差,从算法原理和具体实现的过程中分析了误差的来源及其相应的减小措施,提出用高稳定性的三次样条曲线插值将数值求解的场解析成任意节点处的场及其各阶导数,可以直接进行轨迹追踪。改进后,自动微分法处理实际场的最大相对误差为6.40146×10-3,计算结果和Munro软件设计的一致,并且消除了传统像差在计算过程中用高斯轨迹取代实际轨迹引入的误差,能够满足高性能粒子光学设计的实际需要。An error will appear when the automatic differentiation(AD) is applied in a practical non-analytic field.Form the principle of AD arithmetic and the process of its application,the origination of the error was analyzed to obtain the corresponding method of minimizing the calculation error.High stability cubic spline function is applied to interpolate field distribution and its derivatives at arbitrary point from field at mesh point.The improved method can trace the trajectory of charged particles directly and the largest relative error is 6.401 46×10-3.The final result is identical to that of Munro electron beam software and this method can eliminate the error from replacing the real trajectory by Guassian trajectory in the classic numerical approach.The improved method can meet for particles optics design with high performance.

关 键 词：自动微分 误差分析 有限元素法 样条函数 

分 类 号：TN305.7[电子电信—物理电子学]