Electrostatic Electron Lenses with a Minimum of Spherical Aberration

A method is suggested for the construction of electrostatic electron lenses by building equipotential surfaces whose position in space is calculated from an assumed axial potential. The calculations are carried through for examples of symmetrical and immersion lenses. The symmetrical lens chosen is the well-known one with minimum spherical aberration represented by an axial potential V(z) = V0+A exp (−Bz2) and it is shown that this lens can actually be constructed. An axial potential formed by a sum of two exponential terms is found, for suitable values of the constants, to reduce the spherical aberration to less than one-half that of the above symmetrical lens. An expression is proposed for the immersion lens with minimum spherical aberration. The aberration for this lens is approximately one-half that of the above symmetrical lens. It is shown that the usual formula for the focal length of a strong lens is merely the first term in an infinite series and that serious inaccuracies occur by not considering further terms.