Correction of Electrostatic Lenses by Departure from Rotational Symmetry

Abstract

It is known that departures from rotational symmetry may offer correction possibilities for certain aberrations which limit the resolving power of present-day electron microscopes. The geometrical optics of such departures in electrostatic systems and the general correction conditions are investigated. The minimum number of design parameters is taken, in order to ensure a simple structure, and a theory is developed for the correction of third-order spherical aberration in the particular type of objective lens evolved. This theory is simple enough for computation, yet applies to lenses with four electrodes capable of a high magnification. An example shows a tolerance of 1/5 micron for the correcting electrode if the resolution limit is to be reduced to 10% of its rotationally symmetric value. A better example could probably bring this within engineering practice, but first-order astigmatic electrodes are also needed, and the tolerances of these are one or two factors of ten more exacting. It is therefore here that the difficulties will arise in the application of non-rotational symmetry.