The 'well-known' theory of electron image formation

A recent paper by Kirkland on nonlinear electron image processing, referring to a relatively new textbook, highlights the persistence in the literature of calculations based on incomplete and/or incorrect models of electron imageing, notwithstanding the various papers which have recently pointed out the correct forms of the appropriate equations. Since at least part of the problem can be traced to underlying assumptions about the illumination coherence conditions, we attempt to clarify both the assumptions and the corresponding equations in this paper, illustrating the effects of an incorrect theory by means of images calculated in different ways.The first point to be made clear concerning the illumination coherence conditions is that (except for very thin specimens) it is insufficient simply to know the source profiles present, i.e. the ranges of different directions and energies (focus levels) present in the source; we must also know in general whether the various illumination components are coherent or incoherent with respect to one another.