Coherence in X-ray physics

Highly brilliant synchrotron radiation sources have opened up the possibility of using coherent X-rays in spectroscopy and imaging. Coherent X-rays are characterized by a large lateral coherence length. Speckle spectroscopy is extended to hard X-rays, improving the resolution to the nm range. It has become possible to image opaque objects in phase contrast with a sensitivity far superior to imaging in absorption contrast. All the currently available X-ray sources are chaotic sources. Their characterization in terms of coherence functions of the first and second order is introduced. The concept of coherence volume, defined in quantum optics terms, is generalized for scattering experiments. When the illuminated sample volume is smaller than the coherence volume, the individuality of the defect arrangement in a sample shows up as speckle in the scattered intensity. Otherwise, a configurational average washes out the speckle and only diffuse scattering and possibly Bragg reflections will survive. The loss of interference due to the finite detection time, to the finite detector pixel size and to uncontrolled degrees of freedom in the sample is discussed at length. A comparison between X-ray scattering, neutron scattering and mesoscopic electron transport is given. A few examples illustrate the possibilities of coherent X-rays for imaging and intensity correlation spectroscopy.