Extension of Scherzer's Theorem

Abstract

A monochromatic, nonrelativistic system with electrostatic and/or magnetic quadrupole fields having common planes of optical symmetry is treated theoretically. It is proven that certain aperture aberration coefficients are positive definite when there is a real object and image in one or both of the optical symmetry planes. In a purely magnetic system which is doubly focusing and has a real object and image, all aperture aberration coefficients are positive definite. Conditions that imply nonzero aperture aberrations for systems with virtual objects and/or images are also given.