Five Seidel aberrations

Aberrations are departures of the path of electron beams from the path of the ideal (Gaussian or paraxial) imaging. The term, "(five) Seidel aberrations," is the generic name of the third-order aberrations (third order with respect to the product of α (angle between the electron beam and optical axis) and r (distance of the electron beam from the optical axis)), which occurs for a monochromatic but non-paraxial electron beam. The five aberrations are (1) spherical aberration (proportional to α³), (2) (off-axial) coma aberration (proportional to rα²), (3) off-axial astigmatism (proportional to r²α), (4) curvature of image field (proportional to r²α), and (5) distortion (proportional to r³). In the case of an electron microscope, since the specimen area magnified by the objective lens, the first-stage lens, is very small (r ～0), it is enough to consider the beams passing through the optical axis. Thus, the spherical aberration is most important for the objective lens. The (off-axial) coma aberration is next most important theoretically. Although an example of coma correction has been reported, the effect of coma aberration is small for high magnification images. Since the magnified images or the objects for the intermediate and projector lenses are not small, the aberrations produced by the beams passing through the positions distant from the optical axis give definite contributions. That is, off-axial astigmatism, curvature of image field and distortion are more important for the lenses at successive stages. In recent years, the spherical aberration has been successfully corrected.

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