Measurement of wavefront and Wigner distribution function for optics alignment and full beam characterization of FELs

Abstract

Free-electron lasers deliver EUV and soft x-ray pulses with the highest brilliance available and high spatial coherence. Users of such facilities have high demands on the coherence properties of the beam, for instance when working with coherent di ractive imaging (CDI). Experimentally, we are recovering the phase distribition with an EUV Hartmann wavefront sensor. This allows for online adjustment of focusing optics such as ellipsoidal or Kirkpatrick-Baez mirrors minimizing the aberrations in the focused beam. To gain highly resolved spatial coherence information, we have performed a caustic scan at beamline BL2 of the free-electron laser FLASH using the ellipsoidal focusing mirror and a movable EUV sensitized CCD detector. This measurement allows for retrieving the Wigner distribution function, being the two-dimensional Fourier transform of the mutual intensity of the beam. Computing the reconstruction on a four-dimensional grid, this yields the entire Wigner distribution which describes the beam propagation completely. Hence, we are able to provide comprehensive information about spatial coherence properties of the FLASH beam including the global degree of coherence. Additionally, we derive the beam propagation parameters such as Rayleigh length, waist diameter and M².