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An imaging and aberration theory of electron- or ion-optical systems composed of arbitrary stationary electromagnetic fields without space charges and currents in the beam-occupied region is developed. It follows the theory of systems with a straight optical axis as formulated by H. Rose. The electromagnetic field is expanded into plane multipoles about the arbitrarily curved and twisted axis. In the expansion of the eikonal, all terms are given which are needed for the calculation of the image aberrations up to the third rank (rank = Seidelian order + power of disturbing potentials + power of the chromatic deviation). For the image aberrations of the second rank, an integral expression is given, from which the single aberration integrals may be derived. Systems with single-section symmetry are treated in more detail.

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Dreidimensional abbildende Elektronenmikroskope II. Theorie elektronenoptischer Systeme mit gekrümmter Achse / Three-dimensionally Imaging Electron Microscopes II. Theory of Electron-optical Systems with a Curved Axis