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Differential Phase Contrast (DPC) imaging, in which deviations in the bright field beam are in proportion to the electric field, has been extensively studied in the context of pure elastic scattering. Here we discuss differential phase contrast formed from core-loss scattered electrons, i.e. those that have caused inner shell ionization of atoms in the specimen, using a transition potential approach for which we study the number of final states needed for a converged calculation. In the phase object approximation, we show formally that differential phase contrast formed from core-loss scattered electrons is mainly a result of preservation of elastic contrast. Through simulation we demonstrate that whether the inelastic DPC images show element selective contrast depends on the spatial range of the ionization interaction, and specifically that when the energy loss is low the delocalisation can lead to contributions to the contrast from atoms other than that ionized. We further show that inelastic DPC images remain robustly interpretable to larger thicknesses than is the case for elastic DPC images, owing to the incoherence of the inelastic wavefields, though subtleties due to channelling remain. Lastly, we show that while a very high dose will be needed for sufficient counting statistics to discern differential phase contrast from core-loss scattered electrons, there is some enhancement of signal-to-noise ratio with thickness that makes inelastic DPC imaging more achievable for thicker samples.

The achievable instrumental performance of a scanning transmission electron microscope (STEM) is determined by the size and shape of the incident electron probe. The most important optical factor in achieving the optimum probe profile is the radius of the probe-forming aperture, which determines the convergence semi-angle of the illumination. What is often overlooked however is that small deviations from this optimum can degrade both the resolution and interpretability of image contrast. A 30% error in aperture radius can lead to a factor of 2 contrast reduction in typical lattice spacings, and a 5 {\AA} error in the thickness measurement of thin layers (such as gate oxides). Theoretical calculations of the optimum convergence angles, from a wave-optical consideration of the probe forming conditions, are explained and their consequences discussed. An experimental approach to the measurement and tuning of the convergence angle is then introduced. This is intended for uncorrected electron microscopes. For corrected instruments, Cs=0, and Cc usually determines the choice of aperture - see e.g. ULTRAMICROSCOPY 108, (2008) 1454-1466, Comment: 12 pages, 11 figures

The projected electrostatic potential of a thick crystal is reconstructed at atomic-resolution from experimental scanning transmission electron microscopy data recorded using a new generation fast- readout electron camera. This practical and deterministic inversion of the equations encapsulating multiple scattering that were written down by Bethe in 1928 removes the restriction of established methods to ultrathin ($\lesssim 50$ {\AA}) samples. Instruments already coming on-line can overcome the remaining resolution-limiting effects in this method due to finite probe-forming aperture size, spatial incoherence and residual lens aberrations., Comment: 6 pages, 3 figures