Computer aided analysis and design of non-rotationally symmetric electrostatic lens systems

Computer software has been developed to analyze an arbitrary electrostatic lens system containing geometric asymmetries such as those produced by tolerance variations and electrode misalignment, and predict the behavior of an electron beam in such a lens system. The method employed separates the type of asymmetry from the magnitude of the asymmetry in a particular lens system, thereby greatly reducing the bulk of calculations. The software produces a graphic display of electron trajectories through the actual symmetric lens system. Additionally, coefficients are calculated which describe electron beam deflection as well as departures from the cardinal lens properties of the ideal rotationally symmetric lens system produced by the geometric asymmetry. This software package allows the designer to determine the effect of tolerance variations and other asymmetries on lens performance, thereby enabling him to determine tolerance criteria for the lens. The types of asymmetries and tolerance variations dealt with are: ellipticity, enlargement, offset and tilting of electrodes with respect to the axis of the lens system. Results predicted by the software have been experimentally verified.