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Extreme ultraviolet (EUV) photon beam characterization techniques, Hartmann wavefront sensing and single shot ablation imprinting, were compared along the caustic of a tightly focused free-electron laser (FEL) beam at beamline FL24 of FLASH2, the Free-electron LASer in Hamburg at DESY. The transverse coherence of the EUV FEL was determined by a Young's double pinhole experiment and used in a back-propagation algorithm which includes partial coherence to calculate the beam intensity profiles along the caustic from the wavefront measurements. A very good agreement of the profile structure and size is observed for different wavelengths between the back-propagated profiles, an indirect technique, and ablation imprints. As a result, the Hartmann wavefront sensor including its software MrBeam is a very useful, single shot pulse resolved and fast tool for non-invasive determination of focal spot size and shape and also for beam profiles along the caustic.

Methods of ablation imprints in solid targets are widely used to characterize focused X-ray laser beams due to a remarkable dynamic range and resolving power. A detailed description of intense beam profiles is especially important in high-energy-density physics aiming at nonlinear phenomena. Complex interaction experiments require an enormous number of imprints to be created under all desired conditions making the analysis demanding and requiring a huge amount of human work. Here, for the first time, we present ablation imprinting methods assisted by deep learning approaches. Employing a multi-layer convolutional neural network (U-Net) trained on thousands of manually annotated ablation imprints in poly(methyl methacrylate), we characterize a focused beam of beamline FL24/FLASH2 at the Free-electron laser in Hamburg. The performance of the neural network is subject to a thorough benchmark test and comparison with experienced human analysts. Methods presented in this Paper pave the way towards a virtual analyst automatically processing experimental data from start to end.

Ptychography, a scanning coherent diffraction imaging method, can produce a high-resolution reconstruction of a sample and, at the same time, of the illuminating beam. The emergence of vacuum ultraviolet and X-ray free electron lasers (FELs) has brought sources with unprecedented characteristics that enable X-ray ptychography with highly intense and ultra-fast short-wavelength pulses. However, the shot-to-shot pulse fluctuations typical for FEL pulses and particularly the partial spatial coherence of self-amplified spontaneous emission (SASE) FELs lead to numerical complexities in the ptychographic algorithms and ultimately restrict the application of ptychography at FELs. We present a general adaptive forward model for ptychography based on automatic differentiation, which is able to perform reconstructions even under these conditions. We applied this model to the first ptychography experiment at FLASH, the Free electron LASer in Hamburg, and obtained a high-resolution reconstruction of the sample as well as the complex wavefronts of individual FLASH pulses together with their coherence properties. This is not possible with more common ptychography algorithms.

Proper diagnostics of intense free-electron laser (FEL) X-ray pulses is indisputably important for experimental data analysis as well as for the protection of beamline optical elements. New challenges for beam diagnostic methods are introduced by modern FEL facilities capable of delivering powerful pulses at megahertz (MHz) repetition rates. In this paper, we report the first characterization of a defocused MHz 13.5-nm beam generated by the free-electron laser in Hamburg (FLASH) using the method of multi-pulse desorption imprints in poly(methyl methacrylate)(PMMA). The beam fluence profile is reconstructed in a novel and highly accurate way that takes into account the nonlinear response of material removal to total dose delivered by multiple pulses. The algorithm is applied to experimental data of single-shot ablation imprints and multi-shot desorption imprints at both low (10 Hz) and high (1 MHz) repetition rates. Reconstructed response functions show a great agreement with the theoretical desorption response function model.

Ruthenium is a perspective material to be used for XUV mirrors at free-electron laser facilities. Yet, it is still poorly studied in the context of ultrafast laser-matter interaction. In this work, we present single-shot damage studies of thin Ru films irradiated by femtosecond XUV free-electron laser pulses at FLASH. Ex-situ analysis of the damaged spots, performed by different types of microscopy, shows that the weakest detected damage is surface roughening. For higher fluences we observe ablation of Ru. Combined simulations using Monte-Carlo code XCASCADE(3D) and the two-temperature model reveal that the damage mechanism is photomechanical spallation, similar to the case of irradiating the target with optical lasers. The analogy with the optical damage studies enables us to explain the observed damage morphologies.

Determining fluctuations in focus properties is essential for many experiments at Self-Amplified-Spontaneous-Emission (SASE) based Free-Electron-Lasers (FELs), in particular for imaging single non-crystalline biological particles. We report on a diffractive imaging technique to fully characterize highly focused, single-shot pulses using an iterative phase retrieval algorithm, and benchmark it against an existing Hartmann wavefront sensor. The results, both theoretical and experimental, demonstrate the effectiveness of this technique to provide a comprehensive and convenient shot-to-shot measurement of focused-pulse wave fields and source-point positional variations without the need for manipulative optics between the focus and the detector.

The four-dimensional Wigner distribution function is determined from intensity profiles measured in the focused photon beam of FLASH (Free-electron laser in Hamburg) for a variety of photon beamline settings. The Wigner formalism results in comprehensive coherence information without the requirement of simplifying assumptions on the beam. The entire four-dimensional spatial mutual coherence function, horizontal and vertical coherence lengths and the global degree of coherence are derived and compared to Young's double pinhole measurements [Opt. Express 20, 17480 (2012)].