Perfect Crystals in the Asymmetric Bragg Geometry as Optical Elements for Coherent X-ray Beams

Perfect crystals in the asymmetric Bragg geometry are evaluated as optical elements for manipulating coherent X-ray beams. Such optics can be used to modify the transverse coherence length of a synchrotron X-ray beam, with the intention of increasing the usable coherent flux. The wavelength range, angular divergence and flux of X-rays passing through a pinhole aperture are examined in detail, as functions of source and pinhole size, crystal-to-pinhole separation and the asymmetry factor. In developing this analysis, the behavior of asymmetrically cut crystals is explained in reciprocal space, with reference to the crystal truncation rod associated with the reflection. The results show that, for synchrotron beams that are collimated to a small fraction of the incident Darwin width, the wavelength range accepted by the crystal is typically dispersed into an angular spread in the exit beam. This chromatic aberration greatly reduces the transverse coherence length in a manner that does not conserve the coherent flux. The calculations are in agreement with measurements of the divergence and flux through a micrometer-sized pinhole using a synchrotron wiggler X-ray source.