静电聚焦同心球系统验证电子光学成像系统的时间像差理论

Test and verification of temporal aberration theory for electron optical imaging systems by an electrostatic concentric spherical system model

关于动态电子光学成像系统的时间像差理论,计算时间像差系数有两种方法———τ变分法和直接积分法.它们的差别在于:τ变分法计算二级几何时间像差系数必须求解微分方程,而直接积分法仅需进行积分运算.采用静电同心球系统的理想模型对这两种方法的正确性进行了检验.结果表明:这两种方法求解电子光学成像系统的时间像差系数的结果完全一致,所求得的时间色差系数与理想模型的解析解完全相同,从而证明两种方法是等价并且正确的.通过验证表明,直接积分法的计算更为简便,适于实际系统的计算与设计.

On theory of temporal aberration of dynamic electron optical imaging systems, we have put forward two methods: 'tau-variation method' and 'direct integral method' to calculate the temporal aberration coefficients. The difference between them is that the 'tau-variation method' needs to solve the differential equations for geometrical temporal aberration coefficients of second order, while the 'direct integral method' needs only to carry out the integral calculations. The aim of the present paper is to test and verify the correctness of the two methods using an electrostatic concentric. spherical system model. Results show that these two methods can obtain identical solutions and the solutions of temporal aberration coefficients of dynamic electron optical imaging systems are the same with the analytical solutions. Thus it can be concluded that these two methods are equivalent and correct, but the 'direct integral method' is more convenient for computation and it could be suggested to use in the practical design.