Coherence Properties of Individual Femtosecond Pulses of an X-Ray Free-Electron Laser

Measurements of the spatial and temporal coherence of single, femtosecond x-ray pulses generated by the first hard x-ray free-electron laser, the Linac Coherent Light Source, are presented. Single-shot measurements were performed at 780 eV x-ray photon energy using apertures containing double pinholes in “diffract-and-destroy” mode. We determined a coherence length of $17\mu \mathrm{m}$ in the vertical direction, which is approximately the size of the focused Linac Coherent Light Source beam in the same direction. The analysis of the diffraction patterns produced by the pinholes with the largest separation yields an estimate of the temporal coherence time of 0.55 fs. We find that the total degree of transverse coherence is 56% and that the x-ray pulses are adequately described by two transverse coherent modes in each direction. This leads us to the conclusion that 78% of the total power is contained in the dominant mode.

Figure 1

A sketch of the experiment showing 13 undulator modules, a set of Kirkpatrick-Baez mirrors focusing the beam on a sample frame and the detector, protected from the direct beam by a beamstop. The inset shows scanning electron microscopy images of different apertures before (a) and after (b) the exposure of a single LCLS pulse. The inset (c) shows a case when the center of the beam missed the double pinhole (marked by the red circles).

Figure 2

Measured diffraction patterns. Left column: Interference fringes from pinholes separated by $2$ (a), 8 (d), and $15\mu \mathrm{m}$ (g), each exposed to a single shot of the LCLS beam as a function of the transverse momentum transfer $q_x$, $q_y$. The area used for the analysis of the transverse coherence is shown by the dashed black rectangle close to the center of the patterns. Middle column: Line scans of the interference fringes on the right edge of the marked region, experimental data (red dots), and results of the theoretical fit (black lines). Right column: Enlarged regions of the line scans shown in the middle column.

Figure 3

The modulus of the effective complex degree of coherence $|{\gamma }_{12}^{\mathrm{eff}}|$ as a function of pinhole separation. The experimental values determined from the fitting procedure are shown by red circles. The error bars show the standard deviation of these values. A Gaussian function (black line) has been fit to the best shot values (black squares) which gives a coherence length of $16.8\pm 1.7\mu \mathrm{m}$. The blue dashed line shows the decrease in the value of $|{\gamma }_{12}^{\mathrm{eff}}|$ due to the maximum measured offset between the position of the apertures and the incident beam. (Inset) The contribution of higher order modes to the modulus of the complex degree of coherence. The fully coherent case (single mode) is shown by the red dashed line. The two-mode contribution is shown by the black line.