The Diffraction Theory of the Aberrations of Stigmatic Orthomorphic Optical or Electron Optical Systems Containing Toric Lenses or Quadrupoles

The diffraction theory of the aberrations of optical systems with an axis of rotational symmetry is now thoroughly established, and the extension to kindred electron optical systems is straightforward. In electron optics, however, certain types of systems containing quadrupoles are of importance, and such systems suffer from aberrations which affect only very oblique rays in axially symmetrical systems. The distortions of the wave surface which correspond to these new aberrations are listed in the present note, and Nijboer's expressions for the consequent disturbances in the image plane of a rotationally symmetrical system are supplemented accordingly. Only the special case—which is, nevertheless, an important one—of stigmatic systems, producing an image free of first-order distortion?, is considered. The analysis is applicable to electron optical orthogonal systems containing quadrupoles and optical systems containing parallel toric lenses alike.