X-ray lensless microscopy from undersampled diffraction intensities

X-ray coherent diffraction imaging including ptychography provides the nanoscale resolved three-dimensional description of matter. The combination of these approaches to the Bragg geometry case arouses a strong interest for its capability to provide information about strain state in crystals. Among the existing approaches, ptychography is particularly appealing because it allows the investigation of extended or weakly scattering samples. Coherent diffraction imaging approaches, based on redundancy in the collected diffraction intensity data set, are highly time consuming and rely on state-of-the-art mechanical setups, both being strong limitations for a general application. We show here that these can be overcome by regularization-based inversion algorithms introducing a priori structural knowledge. This method, which can be generalized to other wavelengths or beam sources, opens new possibilities for the imaging of radiation-sensitive specimens or very large samples.