On-line monitoring of the spatial properties of hard X-ray free-electron lasers based on a grating splitter.

X-ray free-electron lasers (XFELs) play an increasingly important role in addressing the new scientific challenges relating to their high brightness, high coherence and femtosecond time structure. As a result of pulse-by-pulse fluctuations, the pulses of an XFEL beam may demonstrate subtle differences in intensity, energy spectrum, coherence, wavefront, etc., and thus on-line monitoring and diagnosis of a single pulse are required for many XFEL experiments. Here a new method is presented, based on a grating splitter and bending-crystal analyser, for single-pulse on-line monitoring of the spatial characteristics including the intensity profile, coherence and wavefront, which was suggested and applied experimentally to the temporal diagnosis of an XFEL single pulse. This simulation testifies that the intensity distribution, coherence and wavefront of the first-order diffracted beam of a grating preserve the properties of the incident beam, by using the coherent mode decomposition of the Gaussian-Schell model and Fourier optics. Indicatively, the first-order diffraction of appropriate gratings can be used as an alternative for on-line monitoring of the spatial properties of a single pulse without any characteristic deformation of the principal diffracted beam. However, an interesting simulation result suggests that the surface roughness of gratings will degrade the spatial characteristics in the case of a partially coherent incident beam. So, there exists a suitable roughness value for non-destructive monitoring of the spatial properties of the downstream beam, which depends on the specific optical path. Here, experiments based on synchrotron radiation X-rays are carried out in order to verify this method in principle. The experimental results are consistent with the theoretical calculations.