Calculation of focussing quality of the electrostatic mirror objective free of the third-order spherical aberration

The formulas for the coefficients of spherical aberration of axisymmetrical electrostatic electron mirror have been obtained. The technique of excluding from the integrand of high-order derivatives of the potential axial distribution in mirror systems is given. The conditions of elimination of spherical aberration in a three-electrode axisymmetrical mirror consisting of coaxial cylinders of equal diameter are found. Using a method of direct numerical calculations of the exact equations of trajectories, the fifth-order spherical aberration coefficient of a mirror objective was calculated and its limiting resolution was estimated. The calculations show that the resolution of the electrostatic mirror objective under consideration is not worse than that of the best objectives with magnetic lenses. The schematic diagram of a transmission electron microscope with a dark-field image, the objective of which is an electrostatic electron mirror, is presented