A MULTISLICE APPROACH TO THE SPHERICAL-ABERRATION THEORY IN ELECTRON OPTICS

A multislice, wave-optical approach to the spherical aberration theory in electron optics is presented for the case of magnetic lenses. It i s shown that, in order to remedy the inadequacy of a naive attempt car ried out by taking the standard multislice equations and simply adding the fourth order terms in the transverse coordinates in the phase bot h of the transmission function and of the propagation kernel, it is ne cessary to approximate the Schrodinger equation by a wide-angle differ ential equation of the parabolic type and to solve it by means of a ma rching type algorithm. It turns out that the solution can be separated into two parts, describing, as in the multislice method, the interact ion of the incoming spherically aberrated axial wavefunction with the field in a slice, and the propagation in a drift space. When the propa gation is evaluated by means of the stationary phase method, a differe ntial equation is obtained for the spherical aberration coefficient, w hose solution is identical to that obtained by Glaser in his particle approach based on the eikonal.