Optical design of electron microscope lenses and energy filters

Paraxial electron trajectory equations of round lenses and prisms are derived from the Newton-Lorentz equation. Objective lenses of TEM giving the minimum spherical and minimum axial chromatic aberration coefficients are discussed. A variety of magnetic lenses for SEM are shown schematically. Trajectory equations of three kinds of prisms (electro-static prism, magnetic prism and Wien filter) are described in a unified form. Optical properties of various prisms are summarized based on these equations. Two filters, the Wien filter and the omega filter, are reviewed in detail by taking examples of high-resolution electron energy loss spectroscopy (EELS) instrument and energy filtering transmission electron microscopy (EFTEM) instrument, respectively. The Wien condition is satisfied even at the fringing field regions by using an eight-pole filter. Effects of retarding field in the Wien filter are demonstrated. The dispersion of omega filter is estimated analytically in a simple omega filter. Not only the design of filter but also the magnification combination of pre- and post-filter lenses determines non-isochromaticity.