The aberrations of a magnetically deflected electron beam are investigated in detail using an IBM 7094 computer. The computer programming is applicable to the case of one-dimensional deflection through small angles. The beam is treated as a group of electrons having no internal interactions, no energy spread, and producing no external fields. The field distributions that would produce minimum total aberration for a range of specified working distances, maximum deflection distances, coil widths, and coil openings are calculated. The aberrations produced by these ideal fields and by fields that deviate from the model are predicted. Typically, for a working distance of 3 in (7.62 cm), field coverage of 11 mm, and beam convergence angle of 3.54x1O-3rad, the maximum increase in spot diameter is of the order of 0.05 micron. Theoretical 1imitations on the minimum aberration of a specific deflection system are established. The aberration is expected to be further minimized if dynamic astigmatic correction, as described in this paper, is applied. Copyright © 1967 by The Institute of Electrical and Electronics Engineers, Inc.