High-resolution dark-field electron microscopy. I. Useful approximations

Simple expressions are derived for the form of the intensity distributions in high-resolution dark-field electron micrographs of thin specimens for which the phase-object approximation may be applied. For cases in which the phase change of the electron wave can be assumed to be small it is shown that there is an optimum defocus value which gives the best, interpretable resolution. For dark-field images obtained either with a central beam stop or with a tilted incident beam, the image intensity is shown to depend on the square of the deviation of the projected potential from an average value. The further complications resulting when the phase change cannot be assumed small are discussed and illustrated by means of a simple example.