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A simple coherent-imaging method due to Paganin et al. is widely employed forphase-amplitude reconstruction of samples using a single paraxial x-raypropagation-based phase-contrast image. The method assumes that thesample-to-detector distance is sufficiently small for the associated Fresnelnumber to be large compared to unity. The algorithm is particularly effectivewhen employed in a tomographic setting, using a single propagation-basedphase-contrast image for each projection. Here we develop a simple extension ofthe method, which improves the reconstructed contrast of very fine samplefeatures. This provides first-principles motivation for boosting fine spatialdetail associated with high Fourier frequencies, relative to the originalmethod, and was inspired by several recent works employing empirically-obtainedFourier filters to a similar end.

Boosting spatial resolution by incorporating periodic boundary conditions into single-distance hard-x-ray phase retrieval