Coaxial electron lenses

The resolving power of electron microscopes is limited chiefly by the fact that the spherical aberration of electron lenses of the conventional or "coreless" type can never be eliminated. In this paper a new type of electron lenses is investigated, called coaxial lenses. These contain a central cylindrical conductor, surrounded by a number of annular electrodes. The electrostatic fields in such lenses can be produced by super-imposing fields of a certain simple type, calculated and tabulated in this paper. This field corresponds to a "one-element" coaxial lens, containing an annular electrode in the form of a perforated disk with rounded edges, preceded and followed by cylindrical guard rings. At least two such elements are required to correct the aberrations of an ordinary electron microscope objective to the accuracy required, and a fully satisfactory system requires a three-element correcting lens. A two-element and a three-element system are calculated in detail and their theoretical performance is discussed.