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 el ectron laser FLASH emitting in the EUV spectral range were determined from wavefront measurements using self suppor ting Hartmann sensors. The devices were applied for align-ment of the ellipsoidal focusing mirror at Beamline 2 (BL2), reducing the rms wavefront aberrations by more than a fac-tor of 3. Beam quality M² and other beam parameters were evaluated from wavefront and intensity data delivered by the Hartmann sensor. Furthermore, 100 two-dime nsional single pulse intensity distributi ons were recorded at each of 32 ax-ial positions, spaced app. ±2 Rayleigh lengths around the wa ist of the optimized FEL beam with a magnifying EUV sen-sitized CCD camera. From these beam profile data the Wigner distribution function was reconstructed on two dimen-sional orthogonal subspaces. For separable beams this yields the complete Wigner distribution and gives comprehensive and high-resolution information on the propagation characteristic s, including wavefront, mode content and spatial coher-ence. The wavefront of the optimized beam eval uated at waist position was in the order of O /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 determin ed to ~ 4.2 and ~ 3 in the horizontal and vertical direction, respectively. The obtained re sults are compared to the Hartmann experiments. Keywords: Hartmann sensor, Wigner distribution, spatial coherence