The quicksands between wave and geometrical charged particle optics

Traditionally, the study of the optics of lenses, guns, energy analysers, spectrographs and accelerators is based on the solution of Laplaceʹs or Poissonʹs equation followed by the calculation of trajectories and hence of paraxial properties and aberration coefficients, emittances and the like. Instrumental optics especially for high-resolution microscopy requires other approaches since the point of departure is not a form of Newtonʹs equation but Schrödingerʹs equation. Thus highly perfected programs are available for calculating the propagation of waves through specimens, for example, and transfer theory and electron holography are expressed in the language of wavefunctions. ween these two extremes is a less well-explored territory. The study of brightness, partial coherence and the radiometric quantities is one example. The proper way of treating grossly under-sampled images is another; in the STEM, for example, a very interesting approach to the so-called “phase problem” (the problem of extracting the amplitude and phase of the electron wavefunction from an intensity record) involves recording the full far-field diffraction pattern from each object-pixel and manipulating the resulting template (image-valued image) in the computer. Such records will have very few electrons/pixel; what does this mean in practice? and the related problem of discrete formulation of the image-forming process are evoked.