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Abstract

Free-Electron-Lasers (FELs) have enabled tremendous possibilities in x-ray science due to their ultrashort, highly intense and coherent radiation. At present, FELs rely primarily on the Self Amplified Spontaneous Emission process, which is of a stochastic nature, and emit pulses which may fluctuate drastically from shot to shot. Since many of the novel experiments at FELs require a high degree of beam focusing, in particular for imaging single non-crystalline biological particles, it is imperative to characterize the specific properties of single-shot focused complex wave fields versus different states of the FEL machine. Therefore, a deterministic approach applicable to various FEL operation regimes is desirable to enable the investigation of photon beam properties. The statistical evaluation of the determined properties over different ensembles of pulses leads to an understanding of and potentially optimization of the radiation to be delivered. In this thesis, I have studied different realizations and methods of focused wave field determination at beamline BL2 at the Free electron Laser At Hamburg (FLASH) for various radiation regimes. An iterative diffraction imaging technique has been developed to study highly coherent pulses. The method comprises of a phase retrieval algorithm applied to single far-field diffraction patterns of highly focused pulses. Also, the Hartmann Wavefront Sensing method, as a classical approach, has been applied to measure photon beam properties in the same machine state. The comparison of results has built confidence in the validity of the imaging method. A transition to partially coherent radiation caused the algorithmic convergence of the iterative technique to fail. Therefore, a general iterative algorithm has been demonstrated based on Schell’s theorem to reconstruct single-shot complex wave fields, as well as estimating the spatial degree of coherence. The properties of measured pulses have been determined with the lowest level of available information compared to the conventional methods, as a single-shot 2D diffraction pattern measured in the far-field. These imaging methods are applicable across a very broad photon energy range since no absorptive optics are needed between the focusing optics and the detector. Additionally, the variation in longitudinal source position within the operating undulator segments has been determined precisely as feedback from both algorithms, providing further insight into how FEL machine parameters influence the optical properties of the photon beam.

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