Ultimate limitations in the performance of kinoform lenses for hard x-ray focusing

Diffractive x-ray lenses suffer from limited focusing efficiency, which can be improved by replacing the binary nanostructures of the lenses with kinoforms. Here we present the first example of kinoform lenses for x rays and compare their efficiency with those of binary Fresnel zone plates (FZPs), realized through gray-scale-focused Xe ion beam lithography. Unexpectedly, experimental results indicate lower focusing efficiencies of kinoform lenses compared to binary FZPs between 5–7 keV. Simulations that include absorption reveal that kinoform lenses can only provide a limited boost in the diffraction efficiency in multi-keV x-ray energies and for impractical lens thicknesses. Combined with significant challenges in kinoform lens fabrication, the modest gains of this approach may suggest that it is not the path to increasing focusing efficiency