Crystal-based absolute photon energy calibration methods for hard x-ray free-electron lasers

Bragg diffraction from crystals is widely used to select a very narrow spectral range of x-ray pulses. The diffracted signal can be used to calibrate the photon energy, a fact that can be exploited very effectively at x-ray free-electron lasers (XFELs). This work describes three crystal-based methods used to this goal at a major x-ray FEL facility, the European XFEL. These methods, which have a wide applicability, have been developed in relation to the hard x-ray self-seeding setup installed at the SASE2 undulator. They are fast and straightforward to implement since they are based on techniques for extracting and identifying crystal reflections from standard diagnostic raw data while still delivering few electronvolts resolution.

Figure 1

Crystal setup and diagnostic devices used at the European XFEL SASE2 undulator and crystal rotation conventions. The schematic also shows the diagnostic devices in the photon beamline and experimental hutch, which were used in the copper K-edge scan in Sec. 3.

Figure 2

(a) An intersection of reflections at 9 keV measured using a spectrometer, as a function of the pitch angle ${\theta }_p$ for fixed values of the roll and yaw angles and (b) the fitted model.

Figure 3

Schematic technique of the spectrometer reflection classifier method proposed in this work.

Figure 4

(a) Raw data from single-shot spectrometer, (b) processed version (binarization, dilation, erosion), and (c) detected lines (Hough transform).

Figure 5

A confusion matrix showing the total predicted reflections versus the actual reflection classification.

Figure 6

Notch detected by a spectrometer for the C*(004) reflection at a pitch angle of 50°. The photon energy axis is calibrated postmeasurement using the model. The blue line is an average over multiple single-shots spectra.

Figure 7

Spectral notch measured at 8 keV: (a) the correlation between the measured photon energy and the pitch angle, (b) the calibrated photon energy ($+1\mathrm{eV}$), and the calculated C*(1-1-3) reflection plotted overlaying the scan.

Figure 8

Three shots from a pitch scan through reflection C*(1-1-3) as the crystal is rotated from 53.5° to 55°. A plot shows the variation of the intensity as the pitch angle was changed, as well as a Gaussian fit over the measured points.

Figure 9

Localization of reflections categorized by the reflection identifier.

Figure 10

Energy calibrations carried out with scintillator imager data and the surrogate model. The red cross indicates the calibrated photon energy at the peak measured pixel intensity. The inset shows the measured pixel intensities for the C*(113) reflection scan.

Figure 11

(a) The measured spectral intensity plotted against the calibrated photon energy with the Cu foil inserted (red), no Cu foil (blue), and the theoretical absorption signal (green). (b) The correlation of the crystal pitch along the C*(004) reflection without the copper foil inserted in front of the spectrometer. (c) The correlation of the crystal pitch angle and calibrated seeding energy along the C*(004) reflection with the copper foil inserted in front of the spectrometer. The image shows the full range measured and a close-up version with a compressed color scale.