Optimization of phase contrast imaging with a nano-focus x-ray tube

Propagation-based phase contrast imaging with a laboratory x-ray source is a valuable tool for studying samples that show only low absorption contrast, either because of low density, elemental composition, or small feature size. If a propagation distance between sample and detector is introduced and the illumination is sufficiently coherent, the phase shift in the sample will cause additional contrast around interfaces, known as edge enhancement fringes. The strength of this effect depends not only on sample parameters and energy but also on the experimental geometry, which can be optimized accordingly. Recently, x-ray lab sources using transmission targets have become available, which provide very small source sizes in the few hundred nanometer range. This allows the use of a high-magnification geometry with a very short source-sample distance, while still achieving sufficient spatial coherence at the sample position. Moreover, the high geometrical magnification makes it possible to use detectors with a larger pixel size without reducing the image resolution. Here, we explore the influence of magnification on the edge enhancement fringes in such a geometry. We find experimentally and theoretically that the fringes become maximal at a magnification that is independent of the total source-detector distance. This optimal magnification only depends on the source size, the steepness of the sample feature, and the detector resolution. A stronger influence of the sample feature on the optimal magnification compared to low-magnification geometries is observed.