Beam characterization of FLASH from Hartmann data and measurement of the Wigner distribution function

Abstract

The wavefront as well as beam parameters of the free electron laser FLASH emitting in the EUV spectral range were determined from wavefront measurements using self supporting Hartmann sensors. The devices were applied for alignment of the ellipsoidal focusing mirror at Beamline 2 (BL2), reducing the rms wavefront aberrations by more than a factor of 3. Beam quality M² and other beam parameters were evaluated from wavefront and intensity data delivered by the Hartmann sensor. Furthermore, 100 two-dimensional single pulse intensity distributions were recorded at each of 32 axial positions, spaced app. ±2 Rayleigh lengths around the waist of the optimized FEL beam with a magnifying EUV sensitized CCD camera. From these beam profile data the Wigner distribution function was reconstructed on two dimensional orthogonal subspaces. For separable beams this yields the complete Wigner distribution and gives comprehensive and high-resolution information on the propagation characteristics, including wavefront, mode content and spatial coherence. The wavefront of the optimized beam evaluated at waist position was in the order of λ?4 peak valley, whereas a significant contribution of uncorrelated higher order Hermite-Gauss modes and a global degree of coherence of 0.12 can be detected, leading to a substantial increase of the M² factor, which was determined to ~ 4.2 and ~ 3 in the horizontal and vertical direction, respectively. The obtained results are compared to the Hartmann experiments.