Introduction

Geometrical charged-particle optics describes the motion of charged particles in macroscopic electromagnetic fields by employing the well-established nota tions and concepts of light optics. Macroscopic fields are produced by macro scopic elements, such as solenoids, magnetic multipoles, or by voltages applied to conducting devices, e.g., cylinders or apertures. We define the atomic fields within solid or biological objects as microscopic fields. The propagation of the particles in these fields will not be considered within the frame of geometrical charged-particle optics.

The description of the particle motion from the point of view of light op tics is reasonable because the elementary particles have particle and wave properties. The similarity between the propagation of light and particles is documented by the equivalent mathematical treatments [29]. Moreover, the properties of particle-optical instruments and their constituent components are described most appropriately in light-optical terms, which have been es tablished at a time when charged particles were still unknown. The treatment of particle motion by means of optical concepts has been proven extremely useful for the design of beam-guiding systems, the electron microscope in par ticular. This microscope has developed over the years from an image-forming system to a sophisticated analytical instrument yielding structural and chem ical information about the object on an atomic scale.