Inline holography is a common phase-contrast imaging method which uses free-space propagation to encode the phase signal into measured intensities. However, quantitative retrieval of the sample's image remains challenging, imposing constraints on the nature of the sample or on the propagation distance. Here, we present a way of simultaneously retrieving the sample's complex-valued transmission function and the incident illumination function from near-field diffraction patterns. The procedure relies on the measurement diversity created by lateral translations of the sample with respect to a structured illumination. The reconstruction approach, in essence identical to that employed in ptychography, is applied to hard X-ray synchrotron measurements and to simulations. Compared to other inline holography techniques, we expect near-field ptychography to reduce reconstruction artefacts by factoring out wavefront imperfections and relaxing constraints on the sample's scattering properties, thus ultimately improving the robustness of propagation-based X-ray phase tomography.
