X-ray ptychography with highly-curved wavefront

Abstract

The recent development of scanning coherent x-ay diffraction microscopy (also known as ptychography) eliminates several constraints exerted by coherent imaging. In particular, an illuminating wave (the probe) can have an arbitrary shape, as a diffraction data redundancy due to multiple measurements at overlapping neighboring probe positions permits its independent reconstruction along with the scattering potential (the object wave). A priori knowledge, such as a finite sample support, is reduced to a recording of sequential probe positions and a plausible guess to be used as a starting estimate for iterative phase retrieval. Using a focusing probe, such as one produced by a zone plate, we investigate the effectiveness of the reconstruction algorithm and find that it is significantly less successful at reconstructing wavefronts with large curvature (extended phase variation) than the wavefronts with almost flat phase structure. Our simulations show that when the actual probe has large phase variation, the amount of overlap required for a successful reconstruction of both object and probe depends upon the phase difference between the actual probe and the probe used as a starting estimate for the reconstruction. We quantitatively define the circumstances for successful reconstruction of an object placed away from focus. We use an experimental dataset measured with a moderate amount of overlap to show that a successful reconstruction of the test sample can be done using a curved probe as an initial guess.