Computer analysis of imaging energy filters

Computational methods and software have been developed for the analysis and design of magnetic imaging energy filters for transmission electron microscopes. The filters considered are of the omega and alpha types, in which the electron beam is steered through three or four bending magnets, to produce a stigmatic image with energy dispersion. An energy selection slit, located at a plane conjugate with the diffraction plane, then selects an image formed by electrons of a specific energy. After briefly reviewing the theory of such filters, the initial design procedure, using the analytic SCOFF (''sharp cut-off fringing field'') approximation, is described. The computer simulation of real imaging energy filters, with numerically computed fringing fields, is then described, for magnets with planar or curved polefaces. A damped-least-squares optimization procedure is used to adjust the strengths of the magnets and the positions, tilts and curvatures of the pole-faces in order to focus the beam and minimize the aberrations. External quadrupole and hexapole elements can also be introduced to improve the performance of the filter. The software can also compute the properties of filters employing conical polepieces, such as those used in the MANDOLINE filter. The computation procedure and features of the software are described and illustrated with typical examples.