Image formation in the high-resolution transmission electron microscope

Materials scientists have come to rely on the fact that high-resolution transmission electron microscopes are able to produce micrographs that are images of atoms, or atom columns. Their confidence is justified. Any high-resolution TEM operated under well-established conditions (conditions that have been understood and utilized for decades) produces phase-contrast images in which intensity peaks correspond to the true column positions of the projected crystal lattice. In the high-resolution transmission electron microscope, structural information from the specimen is encoded in the spatial distribution of the phase of the scattered electron waves. Although the electron phase is not an observable (it is not gauge invariant), phase differences can be measured with interference experiments. A direct way is by electron holography, but the usual method is to image the specimen at the "optimum" or "extended" Scherzer defocus. At this focus, the objective lens shifts the phase of the scattered electron wave exiting the specimen such that interference causes the relative phase of the wave to form image peaks that map the atom positions at the resolution of the microscope. This result has been verified many times by theory, simulation, and countless experiments. It cannot be emphasized too strongly that high-resolution TEM images actually do show the positions of projected atom columns under the proper conditions. This is true whether we reconstruct the spatial fluctuations in the phase that carries the information on atom positions, or make them visible directly by interference. Improvement in the quality of atom position information in O Angstrom M images is due to the O Angstrom M's improved resolution, not to the fact that focal-series reconstruction is the method used to extract these positions from the phase of the electron wave