Using coherent X-ray ptychography to probe medium-range order.

Characterization of microscopic structural order and in particular medium range order (MRO) in amorphous materials is challenging. A new technique is demonstrated that allows analysis of MRO using X-rays. Diffraction data were collected from a sample consisting of densely packed polystyrene-latex micro-spheres. Ptychography is used to reconstruct the sample transmission function and fluctuation microscopy applied to characterize structural order producing a detailed `fluctuation map' allowing analysis of the sample at two distinct length scales. Independent verification is provided via X-ray diffractometry. Simulations of dense random packing of spheres have also been used to explore the origin of the structural order measured.

Nanoscale Fresnel coherent diffraction imaging tomography using ptychography.

We demonstrate Fresnel Coherent Diffractive Imaging (FCDI) tomography in the X-ray regime. The method uses an incident X-ray illumination with known curvature in combination with ptychography to overcome existing problems in diffraction imaging. The resulting tomographic reconstruction represents a 3D map of the specimen's complex refractive index at nano-scale resolution. We use this technique to image a lithographically fabricated glass capillary, in which features down to 70nm are clearly resolved.

Simultaneous X-ray fluorescence and ptychographic microscopy of Cyclotella meneghiniana.

Scanning X-ray fluorescence microscopy (XFM) is a particularly useful method for studying the spatial distribution of trace metals in biological samples. Here we demonstrate the utility of combining coherent diffractive imaging (CDI) with XFM for imaging biological samples to simultaneously produce high-resolution and high-contrast transmission images and quantitative elemental maps. The reconstructed transmission function yields morphological details which contextualise the elemental maps. We report enhancement of the spatial resolution in both the transmission and fluorescence images beyond that of the X-ray optics. The freshwater diatom Cyclotella meneghiniana was imaged to demonstrate the benefits of combining these techniques that have complementary contrast mechanisms.

Quantitative nanoscale imaging of lattice distortions in epitaxial semiconductor heterostructures using nanofocused X-ray Bragg projection ptychography.

We imaged nanoscale lattice strain in a multilayer semiconductor device prototype with a new X-ray technique, nanofocused Bragg projection ptychography. Applying this technique to the epitaxial stressor layer of a SiGe-on-SOI structure, we measured the internal lattice behavior in a targeted region of a single device and demonstrated that its internal strain profile consisted of two competing lattice distortions. These results provide the strongest nondestructive test to date of continuum modeling predictions of nanoscale strain distributions.

An in-vacuum x-ray diffraction microscope for use in the 0.7-2.9 keV range.

A dedicated in-vacuum coherent x-ray diffraction microscope was installed at the 2-ID-B beamline of the Advanced Photon Source for use with 0.7-2.9 keV x-rays. The instrument can accommodate three common implementations of diffractive imaging; plane wave illumination; defocused-probe (Fresnel diffractive imaging) and scanning (ptychography) using either a pinhole, focused or defocused probe. The microscope design includes active feedback to limit motion of the optics with respect to the sample. Upper bounds on the relative optics-to-sample displacement have been measured to be 5.8 nm(v) and 4.4 nm(h) rms/h using capacitance micrometry and 27 nm/h using x-ray point projection imaging. The stability of the measurement platform and in-vacuum operation allows for long exposure times, high signal-to-noise and large dynamic range two-dimensional intensity measurements to be acquired. Finally, we illustrate the microscope's stability with a recent experimental result.

Fresnel coherent diffraction tomography.

Tomographic coherent imaging requires the reconstruction of a series of two-dimensional projections of the object. We show that using the solution for the image of one projection as the starting point for the reconstruction of the next projection offers a reliable and rapid approach to the image reconstruction. The method is demonstrated on simulated and experimental data. This technique also simplifies reconstructions using data with curved incident wavefronts.

Use of a complex constraint in coherent diffractive imaging.

We demonstrate use of a complex constraint based on the interaction of x-rays with matter for reconstructing images from coherent X-ray diffraction. We show the complementary information provided by the phase and magnitude of the reconstructed wavefield greatly improves the quality of the resulting estimate of the transmission function of an object without the need for a priori information about the object composition.

Diffractive imaging using partially coherent x rays.

The measured spatial coherence characteristics of the illumination used in a diffractive imaging experiment are incorporated in an algorithm that reconstructs the complex transmission function of an object from experimental x-ray diffraction data using 1.4 keV x rays. Conventional coherent diffractive imaging, which assumes full spatial coherence, is a limiting case of our approach. Even in cases in which the deviation from full spatial coherence is small, we demonstrate a significant improvement in the quality of wave field reconstructions. Our formulation is applicable to x-ray and electron diffraction imaging techniques provided that the spatial coherence properties of the illumination are known or can be measured.

Quantitative phase imaging with a scanning transmission x-ray microscope.

We obtain quantitative phase reconstructions from differential phase contrast images obtained with a scanning transmission x-ray microscope and 2.5 keV x rays. The theoretical basis of the technique is presented along with measurements and their interpretation.

Coherent X-ray scattering and lensless imaging at the European XFEL Facility.

Coherent X-ray diffraction imaging is a rapidly advancing form of lensless microscopy. The phase information of the diffraction pattern is embedded in a sufficiently sampled coherent diffraction pattern. Using advanced computational methods, this diffraction pattern can be inverted to produce an image of a sample with diffraction-limited resolution. It is attractive to use high-power coherent X-ray beams produced by future X-ray free-electron lasers for imaging nanoscale condensed matter, materials and biological samples. Here, the scientific case, requirements and the possible realisation of the coherent X-ray diffraction imaging beamlines at the European XFEL Facility are presented.

Fluctuation X-ray microscopy: a novel approach for the structural study of disordered materials.

Measuring medium-range order is a challenging and important problem in the structural study of disordered materials. We have developed a new technique, fluctuation x-ray microscopy, that offers quantitative insight into medium-range correlations in disordered materials at nanometre and larger length scales. In this technique, which requires a spatially coherent x-ray beam, a series of speckle patterns are measured at a large number of locations in a sample using various illumination sizes. Examination of the speckle variance as a function of the illumination spot size allows the structural correlation length to be measured. To demonstrate this technique we have studied polystyrene latex spheres, which serve as a model for a dense random-packed glass, and for the first time have measured the correlation length in a disordered system by fluctuation X-ray microscopy. We discuss data analysis and procedures to correct for shot noise and detector noise. This approach could be used to explore medium-range order and subtle spatial structural changes in a wide range of disordered materials, from soft matter to nanowire arrays, semiconductor quantum dot arrays and magnetic materials.

Structure and dynamics of a nanocolloidal silica gel dispersion.

We studied the structure and the dynamics of a nanocolloidal silica gel dispersed in an organic solvent [octylcyanobiphenyl (8CB)] as a function of the silica density by x-ray intensity fluctuation spectroscopy (XIFS). The silica density of the dispersed aerosil gel samples ranged from 0.03 to 0.20 g cm-3 and the autocorrelation of the silica scattering was probed over the q range from 0.03 to 0.15 nm-1 (corresponding to length scales from 42 to 209 nm) at a constant room temperature at which 8CB is in the smectic-A phase. The gel structure has a fractal dimension in this density range of df approximately 2.15. The time autocorrelation functions of the gels show clear density-dependent and complex dynamics. The gel relaxation times are very long and become bimodal with nonergodic character for densities from 0.10 to 0.16 g cm-3. In this same density range, the fluctuation contrast (strength) is a minimum while the relaxation time becomes independent of wave vector. Together, these results indicate that there is a narrow silica density range for these gels in which the dynamics changes dramatically. This suggests a complex phase diagram for the dynamics of aerosil gels as a function of densification.

Synchrotron beam coherence: a spatially resolved measurement.

We report a precise and spatially resolved measurement of the complex degree of coherence of a one-dimensional 1.5-keV beam produced by a third-generation synchrotron source. The method of phase-space tomography is used, which requires only measurements of the x-ray intensity. We find that the field is statistically stationary to within experimental error, the correlations are very well approximated by a Gaussian distribution, and the measured coherence length is in excellent agreement with expectations.

Measurement of the spatial coherence function of undulator radiation using a phase mask.

A measurement of the horizontal coherence function of 7.9 keV radiation from an undulator beam line at the Advanced Photon Source is reported. X-ray diffraction from a phase-shifting mask was used, and the coherence function was measured as a function of the width of beam-conditioning slits in the beam line. The coherence distribution is found to be best described by a Lorentzian function.

X-ray speckle contrast variation across absorption edges.

We measured static x-ray speckle contrast variation with the incident photon energy across a sample-specific absorption edge. In this paper, we present a theoretical description of this energy dependency consistent with our data. We found that the contrast depends mainly on the imaginary part of the complex index of refraction in the sample, as well as on the instrumental resolution. The speckle contrast decreases as the absorption cross section in the sample increases at the absorption edge. This result is not predicted by commonly used theory.

Illumination for coherent soft X-ray applications: the new X1A beamline at the NSLS.

The X1A soft X-ray undulator beamline at the NSLS has been rebuilt to serve two microscopy stations operating simultaneously. Separate spherical-grating monochromators provide the resolving power required for XANES spectroscopy at the C, N and O absorption edges. The exit slits are fixed and define the coherent source for the experiments. The optical design and the operational performance are described.

Small-angle X-ray scattering using coherent undulator radiation at the ESRF.

A simple approach for producing a high-coherent-flux X-ray beam for small-angle-scattering studies used at the Troika beamline of the European Synchrotron Radiation Facility is reported. For such small-angle studies it is permissible to reduce the longitudinal coherence .length of the beam, thus increasing the energy bandpass and intensity of the beam, because there is only a small optical path-length difference. By using mirrors and filters to cut unwanted energies from the undulator harmonic structure, a high-flux beam of >10(9) photons s(-1) through a 5 micron-diameter pinhole at 8.2 keV with a bandpass of 1.3% can be produced. The coherent properties of this beam have been measured by analyzing a static speckle pattern from an aerogel sample imaged by a directly illuminated CCD camera. The speckle size and contrast are compared with the expected values based on a statistical analysis of the intensity distribution of speckle patterns obtained using partially coherent conditions. The expected widths of the spatial autocorrelation are found, but there is an apparent incoherent fraction of the beam which reduces the measured contrast. The method presented is to be used as a tool to optimize conditions for diffraction experiments using coherent X-rays.

Soft x-ray instrumentation and its applications at the advanced photon source.

Knowledge of the intermediate energy range from 0.5-4 keV, bridging the "soft" and "hard" x-ray regions, is relatively underdeveloped. However, recent developments in the techniques of microscopy and magnetic circular dichroism have emphasized the need to operate in this energy range for microelectronic, biological, and materials science related experiments. The strong dipole-allowed 3d to 4f transitions in rare-earth magnetic materials fall in this region, as do the K-shells of many of the second and third row elements of the periodic table. Two beamlines to be constructed at the Advanced Photon Source (APS) have been designed to cover this energy region. The proposed undulator source, the beamline layout, and the experimental programs for these beamlines are described.

Ultrahigh-Resolution X-ray Tomography.

Ultrahigh-resolution three-dimensional images of a microscopic test object were made with soft x-rays collected with a scanning transmission x-ray microscope. The test object consisted of two different patterns of gold bars on silicon nitride windows that were separated by approximately 5 micrometers. Depth resolution comparable to the transverse resolution was achieved by recording nine two-dimensional images of the object at angles between -50 and +55 degrees with respect to the beam axis. The projections were then combined tomographically to form a three-dimensional image by means of an algorithm using an algebraic reconstruction technique. A transverse resolution of approximately 1000 angstroms was observed. Artifacts in the reconstruction limited the overall depth resolution to approximately 6000 angstroms; however, some features were clearly reconstructed with a depth resolution of approximately 1000 angstroms.