Spatial coherence of X-ray planar waveguide exiting radiation

In this paper the spatial coherence properties of quasi-monochromatic one-dimensional nanosized x-ray beams exiting from planar waveguides have been theoretically investigated both in Fresnel and Frhaunofer diffraction regimes. The evolution of the coherence properties of the x-ray radiation during wave propagation has been described within the Huyghens-Fresnel optical formalism by means of the mutual coherence function. An analytical expression of the mutual coherence function of the x-ray radiation exiting from real planar waveguides, when a standing wavefield is excited into it, has been derived in a paraxial approximation. It can be verified within the wave formalism that, in diffraction experiments on crystalline samples in the Fresnel regime, for nearly ideal standing-wave confinement conditions and planar-waveguide resonator thickness of the order of 100 nm, sub-micrometer lateral resolutions normal to the scattering plane can be achieved. Our model leads to an analytical formula useful to estimate the lateral resolution of the diffraction patterns as a function of the resonator-layer thickness and the waveguide-sample distance.