Both high resolution and high precision are required to quantitatively determine the atomic structure of complex nanostructured materials. However, for conventional imaging methods in scanning transmission electron microscopy (STEM), atomic resolution with picometer precision cannot usually be achieved for weakly-scattering samples or radiation-sensitive materials, such as 2D materials. Here, we demonstrate low-dose, sub-angstrom resolution imaging with picometer precision using mixed-state electron ptychography. We show that correctly accounting for the partial coherence of the electron beam is a prerequisite for highquality structural reconstructions due to the intrinsic partial coherence of the electron beam. The mixed-state reconstruction gains importance especially when simultaneously pursuing high resolution, high precision and large field-of-view imaging. Compared with conventional atomic-resolution STEM imaging techniques, the mixed-state ptychographic approach simultaneously provides a four-times-faster acquisition, with double the information limit at the same dose, or up to a fifty-fold reduction in dose at the same resolution.

Reaching the full potential of X-ray nanotomography, in particular for biological samples, is limited by many factors, of which one of the most serious is radiation damage. Although sample deformation caused by radiation damage can be partly mitigated by cryogenic protection, it is still present in these conditions and, as we exemplify here using a specimen extracted from scales of the Cyphochilus beetle, it will pose a limit to the achievable imaging resolution. We demonstrate a generalized tomographic model, which optimally follows the sample morphological changes and attempts to recover the original sample structure close to the ideal, damage-free reconstruction. Whereas our demonstration was performed using ptychographic X-ray tomography, the method can be adopted for any tomographic imaging modality. Our application demonstrates improved reconstruction quality of radiation-sensitive samples, which will be of increasing relevance with the higher brightness of 4th generation synchrotron sources.

The performance of functional materials is either driven or limited by nanoscopic heterogeneities distributed throughout the material’s volume. To better our understanding of these materials, we need characterization tools that allow us to determine the nature and distribution of these heterogeneities in their native geometry in 3D. Here, we introduce a method based on x-ray near-edge spectroscopy, ptychographic x-ray computed nanotomography, and sparsity techniques. The method allows the acquisition of quantitative multimodal tomograms of representative sample volumes at sub–30 nm half-period spatial resolution within practical acquisition times, which enables local structure refinements in complex geometries. To demonstrate the method’s capabilities, we investigated the transformation of vanadium phosphorus oxide catalysts with industrial use. We observe changes from the micrometer to the atomic level and the formation of a location-specific defect so far only theorized. These results led to a reevaluation of these catalysts used in the production of plastics.