A split and delay unit for the European XFEL

For the European XFEL [1] an x ray split and delay unit SDU is built covering photon energies from 5 keV up to 20 keV [2]. This SDU will enable time resolved x ray pump x ray probe experiments as well as sequential diffractive imaging [3] on a femtosecond to picosecond time scale. Further, direct measurements of the temporal coherence properties will be possible by making use of a linear autocorrelation. The set up is based on geometric wavefront beam splitting, which has successfully been implemented at an autocorrelator at FLASH [4]. The x ray FEL pulses will be split by a sharp edge of a silicon mirror coated with Mo B4C multi layers. Both partial beams will then pass variable delay lines. For different wavelengths the angle of incidence onto the multilayer mirrors will be adjusted in order to match the Bragg condition. For a photon energy of h 20 keV a grazing angle of 0.57 has to be set, which results in a footprint of the beam on the mirror of l 120 mm. At this photon energy the reflectance of a Mo B4 C multi layer coating with a multi layer period of d 3.2 nm and N 200 layers amounts to R 0.92. In order to enhance the maximum transmission for photon energies of h 8 keV and below, a Ni B4C multilayer coating can be applied beside the Mo B4C coating for this spectral region. Because of the different incidence angles, the path lengths of the beams will differ as a function of wavelength. Hence, maximum delays between 2.5 ps at h 20 keV and up to 23 ps at h 5 keV will be possibl

Resolution of a bent‐crystal spectrometer for X‐ray free‐electron laser pulses: diamond versus silicon

The resolution function of a spectrometer based on a strongly bent single crystal (bending radius of 10 cm or less) is evaluated. It is shown that the resolution is controlled by two parameters: (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, distance to a detector, and anisotropic elastic constants of the chosen crystal. The results allow the optimization of the parameters of bent‐crystal spectrometers for the hard X‐ray free‐electron laser sources.The resolution function of a bent‐crystal spectrometer for pulses of an X‐ray free‐electron laser is evaluated. Under appropriate conditions, the energy resolution reaches the ratio of the lattice spacing to the crystal thickness. imag

X-ray diffraction from strongly bent crystals and spectroscopy of X-ray free-electron laser pulses

The use of strongly bent crystals in spectrometers for pulses of a hard X-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated kinematically when the bending radius is small compared with the critical radius given by the ratio of the Bragg-case extinction length for the actual reflection to the Darwin width of this reflection. As a result, the spectral resolution is limited by the crystal thickness, rather than the extinction length, and can become better than the resolution of a planar dynamically diffracting crystal. As an example, it is demonstrated that spectra of the 12 keV pulses can be resolved in the 440 reflection from a 20 µm-thick diamond crystal bent to a radius of 10 cm

WavePropaGatorWavePropaGator: interactive framework for X-ray free-electron laser optics design and simulations

The $WavePropaGator$ (WPG) package is a new interactive cross-platform open-source software framework for modeling of coherent and partially coherent X-ray wavefront propagation. The WPG addresses the needs of beamline scientists and user groups to facilitate the design, optimization and improvement of X-ray optics to meet their experimental requirements. The paper presents a general description of the package and gives some recent application examples

Design of the mirror optical systems for coherent diffractive imaging at the SPB/SFX instrument of the European XFEL

The high degree of spatial coherence and extreme pulse energies available at x-ray free electron laser (XFEL) sources naturally support coherent diffractive imaging applications. In order to optimally exploit these unique properties, the optical systems at XFELs must be highly transmissive, focus to appropriate sizes matched to the scale of samples to be investigated and must minimally perturb the wavefront of the XFEL beam. We present the design and simulated performance of two state-of-the-art Kirkpatrik–Baez mirror systems that form the primary foci of the single particles, clusters and biomolecules and serial femtosecond crystallography (SPB/SFX) instrument of the European XFEL. The two systems, presently under construction, will produce 1 μm and 100 nm scale foci across a 3–16 keV photon energy range. Targeted applications include coherent imaging of weakly scattering, often biological, specimens

Specification of X-ray Mirrors in Terms of System Performance: new Twist to an old Plot

In the early 1990s, Church and Takacs pointed out that the specification of surface figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. We demonstrate the limitations of specification, characterization, and performance evaluation based on conventional statistical approaches, including root-mean-square roughness and residual slope variation, evaluated over spatial frequency bandwidths that are system specific, and a more refined description of the surface morphology based on the power spectral density distribution. We show that these limitations are fatal, especially in the case of highly collimated coherent x-ray beams, like beams from x-ray free electron lasers (XFELs). The limitations arise due to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the problem, we treat a method, suggested by Yashchuk and Yashchuk in 2012, based on an autoregressive moving average modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example specific to the x-ray optical systems under design at the European XFEL

Specification of x-ray mirrors in terms of system performance: new twist to an old plot

In the early 1990s, Church and Takacs pointed out that the specification of surface figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. We demonstrate the limitations of specification, characterization, and performance evaluation based on conventional statistical approaches, including root-mean-square roughness and residual slope variation, evaluated over spatial frequency bandwidths that are system specific, and a more refined description of the surface morphology based on the power spectral density distribution. We show that these limitations are fatal, especially in the case of highly collimated coherent x-ray beams, like beams from x-ray free electron lasers (XFELs). The limitations arise due to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the problem, we treat a method, suggested by Yashchuk and Yashchuk in 2012, based on an autoregressive moving average modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example specific to the x-ray optical systems under design at the European XFEL