Coherent x-ray scattering

This is a tutorial paper on the properties of partially coherent hard x-ray beams and their use in the structural analysis of condensed matter. The role of synchrotron radiation in the generation of coherent x-ray beams is highlighted and the requirements on the source properties are discussed. The technique of phase contrast imaging is briefly explained, as well as diffraction in the Fresnel and Fraunhofer regimes. The origin of speckle is elucidated and it is shown how oversampling of the diffraction pattern by at least a factor of two enables retrieval of the phases of the waves scattered from different parts of the object. This in turn allows for a direct reconstruction of the object's structure. One-dimensional objects, such as a fluid confined between two surfaces, cannot be unambiguously reconstructed by phase retrieval without additional assumptions. A trial-and-error method based on the analysis of waveguiding modes within the confined geometry is discussed