Geometric aberrations in electrostatic lenses: II. Aberration coefficients and their interrelations

Abstract

For pt.I see ibid., vol.19, no.4, p.284-8 (1986). The computer model described in the previous part has been used to derive a simple linear relationship between meridional ray paths in object and image spaces which is valid even for large (>80%) filling factors. Using this relationship the authors have shown that all eight of the meridional third-order coefficients (mij) are simply related as are all twelve of the fifth-order coefficients (qij). All the third- and fifth-order geometric aberrations of meridional rays are consequently expressed by three parameters, m16, q16 and sigma where, to rather good approximation, sigma 4 is equal to the overall voltage ratio of the lens. A function of the spherical aberration coefficients Csi is defined which will be zero for any lens to which the relationships derived apply and it is shown that for many different lens geometries this function is indeed zero within the accuracies of published data. Analytic expressions are developed for the principal surfaces of a lens. As an aid to the choice of a suitable lens for a given application, expressions are given for figures of merit for lenses of any finite magnification.