In-line holography with hard x-rays at sub-15  nm resolution

X-ray in-line holography is well suited for three-dimensional imaging, since it covers a large field of view without the necessity of scanning. However, its resolution does not extend to the range covered by coherent diffractive imaging or ptychography. In this work, we show full-field holographic x-ray imaging based on cone-beam illumination, beyond the resolution limit given by the cone-beam numerical aperture. Image information encoded in far-field diffraction and in holographic self-interference is treated in a common reconstruction scheme, without the usual empty beam correction step of in-line holography. An illumination profile tailored by waveguide optics and exactly known by prior probe retrieval is shown to be sufficient for solving the phase problem. The approach paves the way toward high-resolution and dose-efficient x-ray tomography, well suited for the current upgrades of synchrotron radiation sources to diffraction-limited storage rings.