The theorem due to Scherzer which states, in essence, that a conventional axially symmetric, magnetic or electrostatic lens can never be free from third order spherical aberration is well known. Attempts to circumvent this limitation have been carried out over the past thirty years with little result, but meanwhile the ill effects have been minimized by using magnetic lenses of very short focal length.The most studied alternative is the use of doubly symmetric strong focusing lenses. The first order imaging is performed with three or more quadrupoles, and the third order aberrations corrected with three octopoles. The design by Deltrap for example has no first order effect other than to invert the image, and has a third order spherical aberration coefficient which exactly cancels out that of the magnetic objective lens with which it us used. To avoid chromatic aberration this magnetic objective lens must have a very short focal length (2 mm for 100 kv operation with a resolution of 1 Å), and the overall system then has so much coma that the field of view is limited to 50 Å diameter.
Third order effect of postionization population redistribution in strong field
