Geometric aberrations in electrostatic lenses: I. A simple and accurate computer model

The authors have developed a computer model of the simple two-cylinder electrostatic lens using a variational method to describe the potential and a ray tracing procedure which involves all three second spatial derivatives of the potential and which contains routines to optimise the integration step size. Using this model they have calculated four third-order and two fifth-order aberration coefficients which describe rays which enter or leave the lens parallel to the axis. The third-order coefficients agree very well with previous results and the fifth-order coefficients have been calculated with significantly improved accuracy (20%) compared with earlier data.