Resolution limit of refractive lens and Fresnel lens in X-ray region

The limit of the spatial resolution of hard X-ray microscope has been calculated using Fermat's principle and diffraction theory. It is found that the theoretical spatial resolution limit of X-ray lenses is determined by the index of refraction. Refractive lenses and Fresnel lenses have essentially the same resolution limit as total-reflection-mirror optics and waveguides. Consequently, the spatial resolution limit of hard X-ray microscope with a single-element optics is considered to be approximately 10 nm.