Electronic simulation of the effect of lens aberrations on electron beam cross sections

Abstract

The curve in which an electron beam intersects an arbitrary plane, after being focused in a non-rotationally symmetric field, can be represented by the sum of a series of sine and cosine terms. The frequencies, amplitudes and relative phases of these terms are determined by the position of the beam in the object and aperture planes, and also by the values taken by four parameters (positive and negative integers). These parameters are related on the one hand to the order of rotational symmetry of the field, and on the other hand to the order of the various aberrations. A table is given of the values taken by the parameters for the various aberrations of fields of different orders of symmetry. The aberration figure in any cross section of the imaging beam can be displayed on the screen of an oscilloscope if the voltages applied to its X and Y plates are proportional to the sum of the sine and cosine terms (respectively) which represent the assumed form of the field. By means of a defocusing control, the form of an aberration can be explored in any part of the `caustic'. Also it is possible to simulate the simultaneous presence of several aberrations. The necessary circuits for generating and mixing the component voltages are described and examples are given of the effect of combining particular aberrations. A procedure is outlined for reproducing the form of the aberrations when the aperture is not circular but can still be defined by circular ares. Finally, it is shown how expressions for the magnitudes of the various aberration coefficients can be obtained by a perturbation method due to Sturrock.