Properties of electrostatic correcting systems with annular apertures

Image formation in electron microscopes with circular hole and annular apertures is studied theoretically. The apertures-the circular hole aperture being negative with respect to the annular aperture-produce an additional electrostatic field that exerts a force on the electrons directed toward the optical axis. The resulting deflection angle decreases with increasing distance from the optical axis. This electrostatic field results in a correcting effect of the unavoidable spherical aberration of round electron lenses; the deflection toward the optical axis increases stronger than linearly with increasing distance from the optical axis. Analytical formulae are given for the correcting effect of circular hole and annular apertures. The expressions are based on the Davisson-Calbick formula, which is used to calculate focal length of a simple electrostatic lens.