A systematic analysis of symmetric three-electrode electrostatic lenses

A thorough investigation of a class of axially symmetric three-electrode einzel lenses is given. The study is based on the analysis of axial potential distributions. Two different central/outer voltage ratios are examined. The spherical and chromatic aberration coefficients of a large class of lens models are calculated and plotted. For both voltage ratios general conclusions are drawn for the axial potential functions and electrode shapes that have small aberration coefficients. An electrostatic lens with small spherical aberration is given. General criteria are established for the design of symmetric three-electrode lenses.