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This corrects the article DOI: 10.1103/PhysRevLett.111.034802.
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We present results of a coherent x-ray diffractive imaging experiment performed on a single colloidal crystal grain. The full three-dimensional (3D) reciprocal space map measured by an azimuthal rotational scan contained several orders of Bragg reflections together with the coherent interference signal between them. Applying the iterative phase retrieval approach, the 3D structure of the crystal grain was reconstructed and positions of individual colloidal particles were resolved. As a result, an exact stacking sequence of hexagonal close-packed layers including planar and linear defects were identified.
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Modern X-ray free-electron lasers (XFELs) operating at high repetition rates produce a tremendous amount of data. It is a great challenge to classify this information and reduce the initial data set to a manageable size for further analysis. Here an approach for classification of diffraction patterns measured in prototypical diffract-and-destroy single-particle imaging experiments at XFELs is presented. It is proposed that the data are classified on the basis of a set of parameters that take into account the underlying diffraction physics and specific relations between the real-space structure of a particle and its reciprocal-space intensity distribution. The approach is demonstrated by applying principal component analysis and support vector machine algorithms to the simulated and measured X-ray data sets.
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A method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern is presented. The technique is based on scattering from non-redundant arrays (NRAs) of slits and records the degree of spatial coherence at several relative separations from 1 to 15â µm, simultaneously. Using NRAs the spatial coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRAâ III synchrotron storage ring was measured as a function of different beam parameters. To verify the results obtained with the NRAs, additional Young's double-pinhole experiments were conducted and showed good agreement.
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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.
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We present measurements of second- and higher-order intensity correlation functions (so-called Hanbury Brown-Twiss experiment) performed at the free-electron laser (FEL) FLASH in the non-linear regime of its operation. We demonstrate the high transverse coherence properties of the FEL beam with a degree of transverse coherence of about 80% and degeneracy parameter of the order 10(9) that makes it similar to laser sources. Intensity correlation measurements in spatial and frequency domain gave an estimate of the FEL average pulse duration of 50 fs. Our measurements of the higher-order correlation functions indicate that FEL radiation obeys Gaussian statistics, which is characteristic to chaotic sources.
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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.
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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.
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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.
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We present an x-ray study of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition by means of angular x-ray cross-correlation analysis. By applying two-point angular-intensity cross-correlation functions to the measured series of diffraction patterns the parameters of bond-orientational (BO) order in hexatic phase were directly determined. The temperature dependence of the positional correlation lengths was analyzed as well. The obtained correlation lengths show larger values for the higher-order Fourier components of BO order. These findings indicate a strong coupling between BO and positional order.
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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.