Reciprocal-space up-sampling from real-space over sampling in x-ray ptychography

We retrieve x-ray phase images from ptychographical data which, according to the conventional coherent diffractive imaging (CDI) criterion, have been grossly undersampled. Ptychographical data are intrinsically oversampled in real space, as the illumination function of subsequent exposures overlap. By exploiting the real- space redundancy in ptychography, we are able to recover the conventional CDI reciprocal sampling, despite an increase in the solid angle of the detector pixels. As a result the current experimental geometrical constraints placed upon probe size, object to detector distance, and pixel size are all relaxed.