Coherent X-ray beam expander based on a multilens interferometer.

A coherent X-ray beam expander based on a multilens interferometer is proposed in this paper. The multilens interferometer allows efficient generation of a highly diverging coherent beam up to several milliradians in the hard X-ray energy range. The optical properties of the interferometer were experimentally demonstrated at the ESRF ID13 undulator beamline (Grenoble, France), using 12.4 keV X-rays. The beam expander allowed us to control the angular size and photon flux density of the formed beam and enabled operation in both coherent and incoherent modes. The experimental results were fully consistent with the theoretical concepts and appropriate computer simulations. Future design improvements and related applications are also discussed.

X-ray phase-sensitive imaging using a bilens interferometer based on refractive optics.

The phase-sensitive X-ray imaging technique based on the bilens interferometer is developed. The essence of the method consists of scanning a sample, which is set upstream of the bilens across the beam of one lens of the interferometer by recording changes in the interference pattern using a high-resolution image detector. The proposed approach allows acquiring the absolute value of a phase shift profile of the sample with a fairly high phase and spatial resolution. The possibilities of the imaging technique were studied theoretically and experimentally using fibres with different sizes as the test samples at the ESRF ID06 beamline with 12 keV X-rays. The corresponding phase shift profile reconstructions and computer simulations were performed. The experimental results are fully consistent with theoretical concepts and appropriate numerical calculations. Applications of the interferometric imaging technique are discussed, as well as future improvements.

X-ray reflecto-interferometer based on compound refractive lenses.

An X-ray amplitude-splitting interferometer based on compound refractive lenses, which operates in the reflection mode, is proposed and realized. The idea of a reflecto-interferometer is to use a very simplified experimental setup where a focused X-ray beam reflected from parallel flat surfaces creates an interference pattern in a wide angular range. The functional capabilities of the interferometer were experimentally tested at the European Synchrotron Radiation Facility (ESRF) ID06 beamline in the X-ray energy range from 10 keV to 15 keV. The main features of the proposed approach, high spatial and temporal resolution, were demonstrated experimentally. The reflections from free-standing Si3N4 membranes, gold and resist layers were studied. Experimentally recorded interferograms are in good agreement with our simulations. The main advantages and future possible applications of the reflecto-interferometer are discussed.

Polymer X-ray refractive nano-lenses fabricated by additive technology.

The present work demonstrates the potential applicability of additive manufacturing to X-Ray refractive nano-lenses. A compound refractive lens with a radius of 5 µm was produced by the two-photon polymerization induced lithography. It was successfully tested at the X-ray microfocus laboratory source and a focal spot of 5 µm was measured. An amorphous nature of polymer material combined with the potential of additive technologies may result in a significantly enhanced focusing performance compared to the best examples of modern X-ray compound refractive lenses.

Hard x-ray single crystal bi-mirror.

We report a novel hard x-ray interferometer consisting of two parallel channels manufactured in a single Si crystal by means of microfabrication technology. The sidewall surfaces of the channels, similar to mirrors, scatter at very small incident angles, acting equivalently to narrow micrometer size slits as in the Young double-slit interferometer. Experimental tests of the interferometer were performed at the ESRF ID06 beamline in the energy range from 12 to 16 keV. The interference patterns at different grazing incidence angles were recorded in the near- and far-field. Evaluation of the influence of the channel surface roughness on the visibility of interference fringes was performed. The proposed interferometer design allows the arrangement of mirrors at different split distances.

Substantial Difference in Ordering of 10, 15, and 20 nm Iron Oxide Nanoparticles on a Water Surface: In Situ Characterization by the Grazing Incidence X-ray Scattering.

In the present study, for the first time, a unique combination of in situ grazing incidence small-angle X-ray scattering and X-ray reflectivity, accompanied by the pressure-area isotherm analysis, Brewster angle microscopy, and ex situ scanning electron microscopy, was applied for investigation of two-dimensional superlattices of magnetic nanoparticles as they form on a water surface in a Langmuir trough. Iron oxide particles of different sizes stabilized with a single layer of oleic acid were used. It is demonstrated that monodisperse 10 nm particles on a water surface reproducibly form identical highly ordered monolayers in a wide range of experimental conditions, while monodisperse 20 nm particles always form compact three-dimensional clusters and never the monolayers. Monodisperse particles of an intermediate size, 15 nm in diameter, build a metastable monolayer, which shows a tendency for spontaneous transformation to bi-, tri-, and multilayer islands. The importance to use both grazing incidence small-angle X-ray scattering and X-ray reflectivity together with the complementary techniques, to avoid misinterpretation of separate experimental data sets, is underlined.

Propagation of an X-ray beam modified by a photonic crystal.

A method of calculating the transmission of hard X-ray radiation through a perfect and well oriented photonic crystal and the propagation of the X-ray beam modified by a photonic crystal in free space is developed. The method is based on the approximate solution of the paraxial equation at short distances, from which the recurrent formula for X-ray propagation at longer distances is derived. A computer program for numerical simulation of images of photonic crystals at distances just beyond the crystal up to several millimetres was created. Calculations were performed for Ni inverted photonic crystals with the [111] axis of the face-centred-cubic structure for distances up to 0.4 mm with a step size of 4 µm. Since the transverse periods of the X-ray wave modulation are of several hundred nanometres, the intensity distribution of such a wave is changed significantly over the distance of several micrometres. This effect is investigated for the first time.

X-ray multilens interferometer based on Si refractive lenses.

We report a multilens X-ray interferometer consisting of six parallel arrays of planar compound refractive lenses, each of which creates a diffraction limited beam under coherent illumination. Overlapping such coherent beams produces an interference pattern demonstrating substantially strong longitudinal functional dependence. The interference fringe pattern produced by multilens interferometer was described by Talbot imaging formalism. Theoretical analysis of the interference pattern formation was carried out and corresponding computer simulations were performed. The proposed multilens interferometer was experimentally tested at ID06 ESRF beamline in the X-ray energy range from 10 to 30 keV. The experimentally recorded fractional Talbot images are in a good agreement with computer simulations.

Experimental observation of fractionated crystallization in polydisperse platelike colloids.

We have discovered that the long-term aging of the hexagonal columnar liquid-crystal phase of polydisperse gibbsite platelets leads to fractionated crystallization, that is, to the formation of coexisting columnar crystals with different periods. This process was revealed by microradian X-ray diffraction demonstrating the splitting of the Bragg intercolumnar reflections into sequences of sharper reflections. The fractionated crystallization was observed in a number of samples of sterically stabilized as well as charge-stabilized polydisperse gibbsite platelets.

Spatial structure of a focused X-ray beam diffracted from crystals.

The spatial structure of a beam focused by a planar refractive lens and Bragg diffracted from perfect silicon crystals was experimentally studied at the focal plane using a knife-edge scan and a high-resolution CCD camera. The use of refractive lenses allowed for a detailed comparison with theory. It was shown that diffraction leads to broadening of the focused beam owing to the extinction effect and, for a sufficiently thin crystal, to the appearance of a second peak owing to reflection from the back surface. It was found that the spatial structure of the diffracted beam depends on whether the crystal diffracts strongly (dynamically) or weakly (kinematically). The results help to understand the physical origin of the diffracted intensity recorded in a typical microbeam diffraction experiment.

Colloidal silver nanoparticle gradient layer prepared by drying between two walls of different wettability.

A one-dimensional silver (Ag) nanoparticle gradient layer is prepared from an aqueous colloidal solution upon a polystyrene (PS) coated silicon (Si) substrate. For preparation two walls of different wettability are used. The 40 nm PS-layer exhibits a locally constant film thickness due to the strong roughness correlation with the underlying Si-substrate and is less wettable as compared to the glass plate placed above. The Ag nanoparticles have a triangular prism-like shape. The structural characterization of the obtained complex gradient formed by drying is performed with microbeam grazing incidence small-angle x-ray scattering based on compound refractive lenses. Due to the adsorption from aqueous solution in the selective geometry a double gradient type structure defined by two areas with characteristic lateral lengths and a cross-over regime between both is observed.

Dark-field X-ray microscopy for multiscale structural characterization.

Many physical and mechanical properties of crystalline materials depend strongly on their internal structure, which is typically organized into grains and domains on several length scales. Here we present dark-field X-ray microscopy; a non-destructive microscopy technique for the three-dimensional mapping of orientations and stresses on lengths scales from 100 nm to 1 mm within embedded sampling volumes. The technique, which allows 'zooming' in and out in both direct and angular space, is demonstrated by an annealing study of plastically deformed aluminium. Facilitating the direct study of the interactions between crystalline elements is a key step towards the formulation and validation of multiscale models that account for the entire heterogeneity of a material. Furthermore, dark-field X-ray microscopy is well suited to applied topics, where the structural evolution of internal nanoscale elements (for example, positioned at interfaces) is crucial to the performance and lifetime of macro-scale devices and components thereof.

Direct measurement of transverse coherence length of hard X rays from interference fringes

We propose a simple interferometric technique for hard x-ray spatial coherence characterization, recording a Fresnel interference pattern produced by a round fiber or a slit. We have derived analytical formulas that give a direct relation between a visibility of interference fringes and either the source size or the transverse coherence length. The technique is well suited to third-generation synchrotron radiation sources and was experimentally applied to determine the spatial coherence length and the source size at the European Synchrotron Radiation Facility.

In-line holography and phase-contrast microtomography with high energy x-rays.

Holography with high energy x-rays is now feasible due to the coherence properties of third generation synchrotron sources. Simple in-line holographic techniques can be used to generate edge-enhanced images which for many samples can be interpreted without direct phase retrieval. The coherence properties of such sources and their exploitation for phase-contrast microimaging are demonstrated. The technique can easily be combined with computed microtomography (CMT) data collection and reconstruction strategies for three-dimensional imaging. A dramatically improved image contrast, as compared with absorption CMT, was obtained when imaging a wet human coronary artery specimen. In the tomograms, previously invisible detail could be visualized with absorbed doses below the level where radiation damage impedes the imaging. The results indicate the considerable potential of the in-line holographic CMT method in three-dimensional biomedical microscopy.

X-ray nanointerferometer based on si refractive bilenses.

We report a novel type of x-ray interferometer employing a bilens system consisting of two parallel compound refractive lenses, each of which creates a diffraction limited beam under coherent illumination. By closely overlapping such coherent beams, an interference field with a fringe spacing ranging from tens of nanometers to tens of micrometers is produced. In an experiment performed with 12 keV x rays, submicron fringes were observed by scanning and moiré imaging of the test grid. The far field interference pattern was used to characterize the x-ray coherence. Our technique opens up new opportunities for studying natural and man-made nanoscale materials.

Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary.

A two-step focusing set-up combining a Fresnel zone plate with an ellipsoidal capillary is presented. It is shown that, in addition to the anticipated gain in flux, the employment of the prefocusing micro-optic makes optimal use of the elliptical shape of the capillary by almost eliminating aberrations. A small cross section of the prefocused beam allows a tiny fraction of the capillary surface to be selected, thus reducing the influence of slope errors. An X-ray beam with a 15 keV energy was focused down to a spot size as small as 250 nm, demonstrating the best value that has been achieved up to now for single-bounce capillaries. The use of an ellipsoidal capillary as a micromirror under off-axis illumination by microfocusing optics may open up new opportunities in nanofocusing developments.

Submicrometer hard X-ray focusing using a single-bounce ellipsoidal capillary combined with a Fresnel zone plate.

A single-bounce capillary with an ellipsoidal shape has been used for two-step focusing in combination with a Fresnel zone plate (FZP). The FZP serves as a first microfocusing element and produces a demagnified micrometer image of the source, before the elliptical capillary makes a last final compression of the beam. With 15 keV X-rays from the European Synchrotron Radiation Facility BM5 bending magnet, the two-step demagnification system produced a focus of about 250 nm with a gain of more than 1000. The use of an ellipsoidal capillary as a micro-mirror under off-axis illumination using micro-prefocusing optics might open up new opportunities in nanofocusing developments.

Focusing high-energy x rays by compound refractive lenses.

Compound lenses made from low-Z materials (e.g., Be, B, C, and Al) set up as a linear array of refractive lenses are proposed for submicrometer focusing of high-energy x rays (>5 keV) in one or two dimensions. A theory of focusing based on Maxwell's equation and the Fresnel-Kirchhoff approach is presented. Compound refractive lenses were manufactured by drilling into an Al block a linear array of 200 closely spaced holes 0.5 mm in diameter for linear focusing and two crossed arrays of 100 holes each for point focusing. Focal spots of 3.7 mum and 8 mum x 18 mum were obtained at 30 keV for linear and two-dimensional lenses, respectively. Different technologies of manufacturing and possible applications of the proposed lenses are discussed.

Quantitative analysis of two-component samples using in-line hard X-ray images.

Methods for rapid quantitative phase-sensitive X-ray imaging of non-crystalline samples consisting of two distinct components are investigated. The transverse spatial distribution of the projected thickness of each component is reconstructed by computer processing of in-line images collected using synchrotron-generated hard X-rays and a position-sensitive detector with submicrometre spatial resolution. Different imaging techniques and associated image-processing algorithms are considered, with relative advantages and difficulties of each approach compared. A possible generalization of the method for the case of n-component samples is briefly discussed.