Characterization of temporal coherence of hard X-ray free-electron laser pulses with single-shot interferograms

Temporal coherence is one of the most fundamental characteristics of light, connecting to spectral information through the Fourier transform relationship between time and frequency. Interferometers with a variable path-length difference (PLD) between the two branches have widely been employed to characterize temporal coherence properties for broad spectral regimes. Hard X-ray interferometers reported previously, however, have strict limitations in their operational photon energies, due to the specific optical layouts utilized to satisfy the stringent requirement for extreme stability of the PLD at sub-ångström scales. The work presented here characterizes the temporal coherence of hard X-ray free-electron laser (XFEL) pulses by capturing single-shot interferograms. Since the stability requirement is drastically relieved with this approach, it was possible to build a versatile hard X-ray interferometer composed of six separate optical elements to cover a wide photon energy range from 6.5 to 11.5 keV while providing a large variable delay time of up to 47 ps at 10 keV. A high visibility of up to 0.55 was observed at a photon energy of 10 keV. The visibility measurement as a function of time delay reveals a mean coherence time of 5.9 ± 0.7 fs, which agrees with that expected from the single-shot spectral information. This is the first result of characterizing the temporal coherence of XFEL pulses in the hard X-ray regime and is an important milestone towards ultra-high energy resolutions at micro-electronvolt levels in time-domain X-ray spectroscopy, which will open up new opportunities for revealing dynamic properties in diverse systems on timescales from femto­seconds to nanoseconds, associated with fluctuations from ångström to nanometre spatial scales.