Achieving diffraction-limited resolution in soft-X-ray Fourier-transform holography

•Investigation of spatial-resolution limit of X-ray Fourier-transform holography in theory and experiment.•Design rules for the experimental geometry matching detector angular acceptance and divergence of reference wave.•Theoretical description and experimental demonstration of image artifacts in strongly reference-limited geometries.•Numerical post-processing methods to remove artifacts and recover image details up to the diffraction limit. The spatial resolution of microscopic images acquired via X-ray Fourier-transform holography is limited by the source size of the reference wave and by the numerical aperture of the detector. We analyze the interplay between both influences and show how they are matched in practice. We further identify, how high spatial frequencies translate to imaging artifacts in holographic reconstructions where mainly the reference beam limits the spatial resolution. As a solution, three methods are introduced based on numerical post-processing of the reconstruction. The methods comprise apodization of the hologram, refocusing via wave propagation, and deconvolution using the transfer function of the imaging system. In particular for the latter two, we demonstrate that image details smaller than the source size of the reference beam can be recovered up to the diffraction limit of the hologram. Our findings motivate the intentional application of a large reference-wave source enhancing the image contrast in applications with low photon numbers such as single-shot experiments at free-electron lasers or imaging at laboratory sources.