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NotationNew approximate formulae for the focal length and principal aberration coefficients of electrostatic and magnetic lenses have been suggested by Crewe. These are compared with earlier approximate expressions and similarities and diierences are indicated; they are also compared with calculated values for some real lenses. These comparisons confirm Crewe's findings and elucidate some unexplained features of these.

An analytical treatment of the electron’s motion in a magnetic monopole field results in useful expressions for both the lens action and the mirror action of the field. Using an appropriate definition of the magnetic moment of the electron, it is shown that there is an exact conservation of this parameter in the monopole field, implying that the motion is perfectly adiabatic. This property is important when the field is used for directing Auger electrons from a target to a detector; that is, when it is used as a parallelizer in a through-the-lens detection scheme. Regarding the monopole field as an electron lens, the image position and magnification are derived for an arbitrary object position. Expressions for both the axial aberrations (chromatic and spherical) and the image aberrations (coma, field curvature, astigmatism, distortion, and transverse chromatic) are derived for an arbitrary number of intermediate images between object and final image. The chromatic aberration turns out to be independent of the number of intermediate images and the spherical aberration decreases slightly with this number. This property is important when an electron beam must be focused to a small probe in a strong magnetic field. It is shown that if a certain combination of deflectors is used in conjunction with the monopole field, an ideal swinging objective lens is obtained: All image aberrations except field curvature disappear. Designs are presented in which the monopole field is used in the objective lenses of a transmission electron microscope and a scanning electron microscope.