We present a deterministic approach to the ptychographic retrieval of the wave at the exit surface of a specimen of condensed matter illuminated by X-rays. The method is based on the solution of an overdetermined set of linear equations, and is robust to measurement noise. The set of linear equations is efficiently solved using the conjugate gradient least-squares method implemented using fast Fourier transforms. The method is demonstrated using a data set obtained from a gold–chromium nanostructured test object. It is shown that the transmission function retrieved by this linear method is quantitatively comparable with established methods of ptychography, with a large decrease in computational time, and is thus a good candidate for real-time reconstruction.

We review the recently introduced technique of atomic-resolution chemical mapping in scanning transmission electron microscopy (STEM) based on energy-dispersive x-ray spectroscopy. Working at the atomic level is facilitated by ultrasensitive energy-dispersive x-ray detectors in combination with Cs-correction of the STEM probe. Details of the experimental implementation are discussed, and a theoretical framework within which the measured results can be understood is described. Three case studies are presented: the analysis of specimens of GaAs and SrTiO3, as well as examination of an interface between SrTiO3 and PbTiO3. Detailed theoretical simulations of the imaging process show that the projected positions of elements in atomic columns can be directly deduced from the chemical maps. For the core shells used, the effective ionization interaction is local and generally localized in the vicinity of the atoms being ionized. The local nature of the effective ionization potential means that this is an incoherent mode of imaging, akin to Z-contrast imaging but with additional chemical information.