Expected resolution limits of x-ray free-electron laser single-particle imaging for realistic source and detector properties.

The unprecedented intensity of x-ray free-electron laser sources has enabled single-particle x-ray diffraction imaging (SPI) of various biological specimens in both two-dimensional projection and three dimensions (3D). The potential of studying protein dynamics in their native conditions, without crystallization or chemical staining, has encouraged researchers to aim for increasingly higher resolutions with this technique. The currently achievable resolution of SPI is limited to the sub-10 nanometer range, mainly due to background effects, such as instrumental noise and parasitic scattering from the carrier gas used for sample delivery. Recent theoretical studies have quantified the effects of x-ray pulse parameters, as well as the required number of diffraction patterns to achieve a certain resolution, in a 3D reconstruction, although the effects of detector noise and the random particle orientation in each diffraction snapshot were not taken into account. In this work, we show these shortcomings and address limitations on achievable image resolution imposed by the adaptive gain integrating pixel detector noise.

Experimental 3D coherent diffractive imaging from photon-sparse random projections.

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.

On the characterization of a 1 m long, ultra-precise KB-focusing mirror pair for European XFEL by means of slope measuring deflectometry.

Recently, the European X-Ray Free Electron Laser (XFEL) has successfully produced its first X-ray photon pulse trains. This unique photon source will provide up to 27 000 photon pulses per second for experiments in different fields of science. In order to accomplish this, ultra-precise mirrors of dedicated shape are used to guide and focus these photons along beamlines of up to 930 m in length from the source in the undulator section to the desired focal point at an experimental station. We will report on a Kirkpatrick-Baez-mirror pair designed to focus hard-X-rays in the energy range from 3 to 16 keV to a 100 nm scale at the SPB/SFX instrument of the European XFEL. Both mirrors are elliptical cylinder-like shaped. The figure error of these 1 m long mirrors was specified to be better than 2 nm pv in terms of the height domain; this corresponds to a slope error of about 50 nrad rms (at least a best effort finishing is requested). This is essential to provide optimal experimental conditions including preservation of brilliance and wavefront. Such large and precise optics represents a challenge for the required deterministic surface polishing technology, elastic emission machining in this case, as well as for the metrology mandatory to enable a precise characterization of the topography on the mirror aperture. Besides the slope errors, the ellipse parameters are also of particular interest. The mirrors were under inspection by means of slope measuring deflectometry at the BESSY-NOM slope measuring profiler at the Helmholtz Zentrum Berlin. The NOM measurements have shown a slope error of 100 nrad rms on a aperture length of 950 mm corresponding to a residual figure deviation ≤20 nm pv for both mirrors. Additionally we found a strong impact of the mirror support conditions on the mirror shape finally measured. We will report on the measurement concept to characterize such mirrors as well as to discuss the achieved results.

A versatile liquid-jet setup for the European XFEL.

The SPB/SFX instrument of the European XFEL provides unique possibilities for high-throughput serial femtosecond crystallography. This publication presents the liquid-jet sample delivery setup of this instrument. The setup is compatible with state-of-the-art gas dynamic virtual nozzle systems as well as high-viscosity extruders and provides space and flexibility for other liquid injection devices and future upgrades. The liquid jets are confined in a differentially pumped catcher assembly and can be replaced within a couple of minutes through a load-lock. A two-microscope imaging system allows visual control of the jets from two perspectives.

Tomography of a Cryo-immobilized Yeast Cell Using Ptychographic Coherent X-Ray Diffractive Imaging.

The structural investigation of noncrystalline, soft biological matter using x-rays is of rapidly increasing interest. Large-scale x-ray sources, such as synchrotrons and x-ray free electron lasers, are becoming ever brighter and make the study of such weakly scattering materials more feasible. Variants of coherent diffractive imaging (CDI) are particularly attractive, as the absence of an objective lens between sample and detector ensures that no x-ray photons scattered by a sample are lost in a limited-efficiency imaging system. Furthermore, the reconstructed complex image contains quantitative density information, most directly accessible through its phase, which is proportional to the projected electron density of the sample. If applied in three dimensions, CDI can thus recover the sample's electron density distribution. As the extension to three dimensions is accompanied by a considerable dose applied to the sample, cryogenic cooling is necessary to optimize the structural preservation of a unique sample in the beam. This, however, imposes considerable technical challenges on the experimental realization. Here, we show a route toward the solution of these challenges using ptychographic CDI (PCDI), a scanning variant of coherent imaging. We present an experimental demonstration of the combination of three-dimensional structure determination through PCDI with a cryogenically cooled biological sample--a budding yeast cell (Saccharomyces cerevisiae)--using hard (7.9 keV) synchrotron x-rays. This proof-of-principle demonstration in particular illustrates the potential of PCDI for highly sensitive, quantitative three-dimensional density determination of cryogenically cooled, hydrated, and unstained biological matter and paves the way to future studies of unique, nonreproducible biological cells at higher resolution.

Single pulse coherence measurements in the water window at the free-electron laser FLASH.

The spatial coherence of free-electron laser radiation in the water window spectral range was studied, using the third harmonic (λ<(3rd) = 2.66 nm) of DESY's Free-electron LASer in Hamburg (FLASH). Coherent single pulse diffraction patterns of 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) multilamellar lipid stacks have been recorded. The intensity histogram of the speckle pattern around the first lamellar Bragg peak, corresponding to the d = 5 nm periodicity of the stack, reveals an average number of transverse modes of M¯ = 3.0 of the 3rd harmonic. Using the lipid stack as a 'monochromator', pulse-to-pulse fluctuations in the third harmonic λ(3rd) have been determined to be 0.033 nm.

Spatial and temporal coherence properties of single free-electron laser pulses.

The experimental characterization of the spatial and temporal coherence properties of the free-electron laser in Hamburg (FLASH) at a wavelength of 8.0 nm is presented. Double pinhole diffraction patterns of single femtosecond pulses focused to a size of about 10×10 µm(2) were measured. A transverse coherence length of 6.2 ± 0.9 µm in the horizontal and 8.7 ± 1.0 µm in the vertical direction was determined from the most coherent pulses. Using a split and delay unit the coherence time of the pulses produced in the same operation conditions of FLASH was measured to be 1.75 ± 0.01 fs. From our experiment we estimated the degeneracy parameter of the FLASH beam to be on the order of 10(10) to 10(11), which exceeds the values of this parameter at any other source in the same energy range by many orders of magnitude.

The soft x-ray instrument for materials studies at the linac coherent light source x-ray free-electron laser.

The soft x-ray materials science instrument is the second operational beamline at the linac coherent light source x-ray free electron laser. The instrument operates with a photon energy range of 480-2000 eV and features a grating monochromator as well as bendable refocusing mirrors. A broad range of experimental stations may be installed to study diverse scientific topics such as: ultrafast chemistry, surface science, highly correlated electron systems, matter under extreme conditions, and laboratory astrophysics. Preliminary commissioning results are presented including the first soft x-ray single-shot energy spectrum from a free electron laser.

Three-dimensional structure of a single colloidal crystal grain studied by coherent x-ray diffraction.

A coherent x-ray diffraction experiment was performed on an isolated colloidal crystal grain at the coherence beamline P10 at PETRA III. Using azimuthal rotation scans the three-dimensional (3D) scattered intensity from the sample in the far-field was measured. It includes several Bragg peaks as well as the coherent interference around these peaks. The analysis of the scattered intensity reveals the presence of plane defects in a single grain of the colloidal sample. We confirm these findings by model simulations. In these simulations we also analyze the experimental conditions required to phase the 3D diffraction pattern from a single colloidal grain. This approach has the potential to produce a high resolution image of the sample revealing its inner structure, with possible structural defects.

Coherence properties of individual femtosecond pulses of an x-ray free-electron laser.

Measurements of the spatial and temporal coherence of single, femtosecond x-ray pulses generated by the first hard x-ray free-electron laser, the Linac Coherent Light Source, are presented. Single-shot measurements were performed at 780 eV x-ray photon energy using apertures containing double pinholes in "diffract-and-destroy" mode. We determined a coherence length of 17 µm in the vertical direction, which is approximately the size of the focused Linac Coherent Light Source beam in the same direction. The analysis of the diffraction patterns produced by the pinholes with the largest separation yields an estimate of the temporal coherence time of 0.55 fs. We find that the total degree of transverse coherence is 56% and that the x-ray pulses are adequately described by two transverse coherent modes in each direction. This leads us to the conclusion that 78% of the total power is contained in the dominant mode.

X-ray holographic microscopy with zone plates applied to biological samples in the water window using 3rd harmonic radiation from the free-electron laser FLASH.

The imaging of hydrated biological samples - especially in the energy window of 284-540 eV, where water does not obscure the signal of soft organic matter and biologically relevant elements - is of tremendous interest for life sciences. Free-electron lasers can provide highly intense and coherent pulses, which allow single pulse imaging to overcome resolution limits set by radiation damage. One current challenge is to match both the desired energy and the intensity of the light source. We present the first images of dehydrated biological material acquired with 3rd harmonic radiation from FLASH by digital in-line zone plate holography as one step towards the vision of imaging hydrated biological material with photons in the water window. We also demonstrate the first application of ultrathin molecular sheets as suitable substrates for future free-electron laser experiments with biological samples in the form of a rat fibroblast cell and marine biofouling bacteria Cobetia marina.

Coherent diffractive imaging of biological samples at synchrotron and free electron laser facilities.

Coherent X-ray diffractive imaging (CXDI) is a new imaging technique that offers the potential to image non-crystalline materials to sub-nanometer resolutions. Here we review the progress in CXDI of biological samples at both synchrotron and free electron laser (FEL) sources. We outline the experimental design of a CXDI experiment and summarize the iterative phase retrieval techniques that are used to produce images from the measured diffraction patterns. We describe a selection of key experiments performed in bio-imaging with CXDI from synchrotron sources, and we discuss the proof-of-principle experiments performed at FLASH at DESY in Hamburg. Finally, we show through simulation that for realistic parameters of hard X-ray FELs a resolution of a few nanometers may be achieved for individual biological objects imaged with single pulses of FEL radiation. Furthermore, we revise how this resolution may be improved to the sub-nanometer range if we image multiple copies of samples with a reproducible structure.

Coherent-pulse 2D crystallography using a free-electron laser x-ray source.

Coherent diffractive imaging for the reconstruction of a two-dimensional (2D) finite crystal structure with a single pulse train of free-electron laser radiation at 7.97 nm wavelength is demonstrated. This measurement shows an advance on traditional coherent imaging techniques by applying it to a periodic structure. It is also significant that this approach paves the way for the imaging of the class of specimens which readily form 2D, but not three-dimensional crystals. We show that the structure is reconstructed to the detected resolution, given an adequate signal-to-noise ratio.

Unique phase recovery for nonperiodic objects.

It is well known that the loss of phase information at detection means that a diffraction pattern may be consistent with a multitude of physically different structures. This Letter shows that it is possible to perform unique structural determination in the absence of a priori information using x-ray fields with phase curvature. We argue that significant phase curvature is already available using modern x-ray optics and we demonstrate an algorithm that allows the phase to be recovered uniquely and reliably.