On the theory of temporal aberrations for electron optical imaging systems by using "direct integral method"

A new approach to the theory of temporal aberration for the dynamic electron optical imaging systems is given in the present paper. A new definition of temporal aberrations is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0 ≤ ε_z1 ≤ ε_0max) is considered. A new method to calculate the temporal aberration coefficients of dynamic electron optical imaging system, which is named "Direct Integral Method", is also presented. All of the formulae of the temporal aberration coefficients deduced from "Direct Integral Method" and "τ-Variation Method" have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solution and the solutions of temporal aberration coefficients of first and second-order are the same with the analytical solutions. Thus it can be concluded these two methods given by us are equivalent and correct, but the "Direct Integral Method" is related to solve integral expressions, which is more convenient for computation and could be suggested to use in the practical design.