Near-field ptychography using lateral and longitudinal shifts

Image reconstruction of in-line holography depends crucially on the probing wave front used to illuminate an object. Aberrations inherent to the illumination can mix with the features imposed by the object. Conventional raw data processing methods rely on the division of the measured hologram by the intensity profile of the probe and are not able to fully eliminate artifacts caused by the illumination. Here we present a generalized ptychography approach to simultaneously reconstruct object and probe in the optical near-field. Combining the ideas of ptychographic lateral shifts of the object with variations of the propagation distance by longitudinal shifts, simultaneous reconstruction of object and probe was achieved equally well for a highly aberrated and a mildly disturbed probe without the need for an additional wave front diffuser. The method overcomes the image deterioration by a non-ideal probe and at the same time any restrictions due to linearization of the object's transmission function or the Fresnel propagator. The method is demonstrated experimentally using visible light and hard x-rays, in both parallel beam and cone beam geometry, which is relevant for high resolution x-ray imaging. It also opens up a new approach to characterize extended wave fronts by phase retrieval.