Theory of temporal aberrations for electron optical imaging systems by direct integral method

A new approach to calculate the temporal aberration coefficients of dynamic electron optical imaging systems is put forward in this paper. A new definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0 ≤ ε_z1 ≤ ε_0max) as a criterion is considered. The new method for calculating the temporal aberration coefficients of dynamic electron optical imaging systems named 'direct integral method' is presented which gives new expressions of the temporary aberration coefficients expressed in integral form. The difference between 'direct integral method' and 'τ-variation method' is that the 'τ-variation method' needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the 'direct integral method' needs only to carry out the integral calculation of them, which is more convenient and suitable for computation in the practical design.