The routine atomic resolution structure determination of single particles is expected to have profound implications for probing structure–function relationships in systems ranging from energy-storage materials to biological molecules. Extremely bright ultrashort-pulse X-ray sources – X-ray free-electron lasers (XFELs) – provide X-rays that can be used to probe ensembles of nearly identical nanoscale particles. When combined with coherent diffractive imaging, these objects can be imaged; however, as the resolution of the images approaches the atomic scale, the measured data are increasingly difficult to obtain and, during an X-ray pulse, the number of photons incident on the 2D detector is much smaller than the number of pixels. This latter concern, the signal `sparsity', materially impedes the application of the method. An experimental analog using a conventional X-ray source is demonstrated and yields signal levels comparable with those expected from single biomolecules illuminated by focused XFEL pulses. The analog experiment provides an invaluable cross check on the fidelity of the reconstructed data that is not available during XFEL experiments. Using these experimental data, it is established that a sparsity of order 1.3 × 10−3 photons per pixel per frame can be overcome, lending vital insight to the solution of the atomic resolution XFEL single-particle imaging problem by experimentally demonstrating 3D coherent diffractive imaging from photon-sparse random projections.

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.

Wavefront analysis is a fast and reliable technique for the alignment and characterization of optics in the visible, but also in the extreme ultraviolet (EUV) and X-ray regions. However, the technique poses a number of challenges when used for optical systems with numerical apertures (NA) > 0.1. A high-numerical-aperture Hartmann wavefront sensor was employed at the free electron laser FLASH for the characterization of a Schwarzschild objective. These are widely used in EUV to achieve very small foci, particularly for photolithography. For this purpose, Schwarzschild objectives require highly precise alignment. The phase measurements acquired with the wavefront sensor were analyzed employing two different methods, namely, the classical calculation of centroid positions and Fourier demodulation. Results from both approaches agree in terms of wavefront maps with negligible degree of discrepancy.

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.

We measured the transverse coherence at FLASH2, a variable gap undulator line at the FLASH free-electron laser user facility at DESY in Hamburg. We demonstrate, theoretically and experimentally, a revised version of Young’s double pinhole approach to perform single-shot, repeatable and non-invasive transverse coherence measurements. At beamline FL24 of FLASH2, the transverse coherence of pulses was systematically characterized at wavelengths of 8, 13.5 and 18 nm for different FEL source settings. We determine degrees of coherence of 57% to 87% in the vertical and horizontal direction, respectively. These measurements can facilitate the planning of novel, coherence-based experiments at the FLASH facility.

Wavefront‐propagation simulations have been performed to complete the design of a monochromator beamline for FLASH2, the variable‐gap undulator line at the soft X‐ray free‐electron laser in Hamburg (FLASH). Prior to propagation through the beamline optical elements, the parameters of the photon source were generated using the GENESIS code which includes the free‐electron laser experimental data. Threshold tolerances for the misalignment of mirror angles are calculated and, since diffraction effects were included in the simulations, the minimum quality with respect to the slope errors required for the optics is determined.

Ptychograhy is a scanning coherent diffraction imaging technique capable of providing images of extended samples with diffraction-limited resolution. However, ptychography experiments are time-consuming due to their scanning nature which also prevents their use for imaging of dynamical processes. Recently, setups based on two con-focal lenses were proposed to perform single-shot ptychography in the visible regime by measuring the diffraction pattern produced by multiple overlapping beams in one shot. However, this approach cannot be extended straightforwardly to X-ray wavelengths due to the application of refractive optics. In this work, we demonstrate a novel and nascent single-shot ptychography setup utilizing the combination of X-ray focusing optics with a two-dimensional beam-splitting diffraction grating. It allows single-shot imaging of extended samples at X-ray wavelengths. As a proof of concept, we performed single-shot ptychography in the XUV range at the free-electron laser FLASH and obtained a high-resolution reconstruction of the sample.

The PERCIVAL detector is a CMOS imager designed for the soft X-ray regime at photon sources. Although still in its final development phase, it has recently seen its first user experiments: ptychography at a free-electron laser, holographic imaging at a storage ring and preliminary tests on X-ray photon correlation spectroscopy. The detector performed remarkably well in terms of spatial resolution achievable in the sample plane, owing to its small pixel size, large active area and very large dynamic range; but also in terms of its frame rate, which is significantly faster than traditional CCDs. In particular, it is the combination of these features which makes PERCIVAL an attractive option for soft X-ray science.