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- X-ray refraction (7)
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X-ray refraction related interaction has received rising interest since about two decades in the field of imaging, beam shaping and analysis although being discovered a century ago. Due to refraction at interfaces in inhomogeneous media X-rays undergo natural focusing (or defocusing) of waves, revealing caustics. Such Kind of intensity patterns are well-known for visible light, but have been sparsely discussed for X-rays. The Variation of irradiation density may be predicted in case of known shapes. Analogously to light optics, the intensity distributions cover several orders of magnitude including complete extinction. The partly convergent (and divergent) caustic stripes originate from narrow zones of typical size of some 10−6 of the boundary curvature radius. For the deflection of plane wave synchrotron radiation (energy in the range of some keV to some ten keV) at rods and tubes of several μm diameter, we find good Agreement between experiments and modeling by ray tracing according to Snell’s law without additional diffraction contributions. Apart from Basic Research implications, caustics may influence the performance of irradiation technologies such as sterilization or molecular cross-linking.
In order to investigate their microcracking behaviour, the microstructures of several β-eucryptite ceramics, obtained from glass precursor and cerammed to yield different grain sizes and microcrack densities, were characterized by laboratory and synchrotron x-ray refraction and tomography. Results were compared with those obtained from scanning electron microscopy (SEM). In SEM images, the characterized materials appeared fully dense but computed tomography showed the presence of pore clusters. Uniaxial tensile testing was performed on specimens while strain maps were recorded and analyzed by Digital Image Correlation (DIC). X-ray refraction techniques were applied on specimens before and after tensile testing to measure the amount of the internal specific surface (i.e., area per unit volume). X-ray refraction revealed that (a) the small grain size (SGS) material contained a large specific surface, originating from the grain boundaries and the interfaces of TiO2 precipitates; (b) the medium (MGS) and large grain size (LGS) materials possessed higher amounts of specific surface compared to SGS material due to microcracks, which decreased after tensile loading; (c) the precursor glass had negligible internal surface. The unexpected decrease in the internal surface of MGS and LGS after tensile testing is explained by the presence of compressive regions in the DIC strain maps and further by theoretical arguments. It is suggested that while some microcracks merge via propagation, more close mechanically, thereby explaining the observed X-ray refraction results. The mechanisms proposed would allow the development of a strain hardening route in ceramics.
3D imaging techniques are very fashionable nowadays, and allow enormous progress in understanding ceramic microstructure, its evolution, and its link to mechanical, thermal, and transport properties. In this feature article, we report the use of a powerful, yet not so wide-spread, set of X-ray techniques based on refraction effects. X-ray refraction allows determining internal specific surface (surface per unit volume) in a non-destructive fashion, position and orientation sensitive, and with a nanometric detectability. While the techniques are limited by the X-ray absorption of the material under investigation, we demonstrate showcases of ceramics and composite materials, where understanding of process parameter influence or simply of microstructural parameters could be achieved in a way unrivalled even by high-resolution techniques such as electron microscopy or computed tomography.
The performance of grating interferometers coming up now for Imaging interfaces within materials depends on the efficiency (visibility) of their main component, namely the phase grating. Therefore, experiments with monochromatic synchrotron radiation and corresponding simulations are carried out. The visibility of a Phase grating is optimized by different photon energies, varying detector to grating distances and continuous rotation of the phase grating about the grid lines. Such kind of rotation changes the projected grating shapes, and thereby the distribution profiles of phase shifts. This yields higher visibilities than derived from ideal rectangular shapes. By continuous grating rotation and variation of the propagation distance, we achieve 2D visibility maps. Such maps provide the visibility for a certain combination of grating orientation and detector position. Optimum visibilities occur at considerably smaller distances than in the standard setup.
Talbot-Lau interferometry provides X-ray imaging techniques with significant enhancement of the radiographic contrast of weakly absorbing objects. The grating based technique allows separation of absorption, refraction and small angle scattering effects. The different efficiency of rectangular and triangular shaped phase gratings at varying detector distances is investigated. The interference patterns (Talbot carpets) are modeled for parallel monochromatic radiation and measured by synchrotron radiation. In comparison to rectangular shapes of phase gratings much higher visibility is obtained for triangular shapes which yield enhanced contrast of a glass capillary test specimen.
A strategy to mitigate typical reconstruction artefacts in missing wedge computed tomography is presented. These artefacts appear as elongations of reconstructed details along the mean direction (i.e. the symmetry centre of the projections). Although absent in standard computed tomography applications, they are most prominent in advanced electron tomography and also in special topics of X-ray and Neutron tomography under restricted geometric boundary conditions. We investigate the Performance of the DIRECTT (Direct Iterative Reconstruction of Computed Tomography Trajectories) algorithm to reduce the directional artefacts in standard procedures. In order to be sensitive to the anisotropic nature of missing wedge artefacts, we investigate isotropic substructures of metal foam as well as circular disc models. Comparison is drawn to filtered backprojection and algebraic techniques. Reference is made to reconstructions of complete data sets. For the purpose of assessing the reconstruction Quality, Fourier transforms are employed to visualize the missing wedge directly. Deficient reconstructions of disc models are evaluated by a length-weighted boundary orientations. The DIRECTT results are assessd at different signal-to-noise ratios by means of local and integral evaluation Parameters.
X-ray refraction is based on optical deflection of X-rays, similar to the well-known small angle X-ray scattering, but hundreds of times more intense, thus enabling shorter measurement time. We show that X-ray refraction techniques are suitable for the detection of pores, cracks, and in general defects. Indeed, the deflected X-ray intensity is directly proportional to the internal specific surface (i.e., surface per unit volume) of the objects. Although single defects cannot be imaged, the presence of populations of those defects can be detected even if the defects have sizes in the nanometer range.We present several applications of X-ray refraction techniques to composite materials:- To visualize macro and microcracks in Ti-SiC metal matrix composites (MMC);- To correlate fatigue damage (fibre de-bonding) of carbon fibre reinforced plastics (CFRP) to X-ray refraction intensity;- To quantify the impact damage by spatially resolved single fibre de-bonding fraction as a function of impact energy in CFRP laminates.An example of classic high-resolution computer tomography of an impact-damaged CFRP will also be presented, as a benchmark to the present state-of-the-art imaging capabilities. It will be shown that while (absorption) tomography can well visualize and quantify delamination, X-ray refraction techniques directly yield (spatially resolved) quantitative information about fibre de-bonding, inaccessible to absorption tomography.
The potentials of incoherent X-ray scattering (Compton) computed tomography (CT) are investigated. The imaging of materials of very different atomic number or density at once is generally a perpetual challenge for X-ray tomography or radiography. In a basic laboratory set-up for simultaneous perpendicular Compton scattering and direct beam attenuation tomography are conducted by single channel photon counting line scans. This results in asymmetric distortions of the projection profiles of the scattering CT data set. In a first approach, corrections of Compton scattering data by taking advantage of rotational symmetry yield tomograms without major geometric artefacts. A cylindrical sample composed of PE, PA, PVC, glass and wood demonstrates similar Compton contrast for all the substances, while the conventional absorption tomogram only reveals the two high order materials. Comparison to neutron tomography
reveals astonishing similarities except for the glass component (without hydrogen). Therefore, Compton CT offers the potential to replace neutron tomography, which requires much more efforts.
Typische 'Missing Wedge'(MW)-Artefakte in Rekonstruktionen der Computertomografie können mit dem iterativen DIRECTT-Algorithmus (Direkte iterative Rekonstruktion computertomografischer Trajektorien) unterdrückt werden. Die durch fehlende Projektionswinkel bedingten MW-Restriktionen betreffen bisher nur Sonderapplikationen der Röntgen- und Neutronentomografie, müssen in der Nanometer auflösenden Elektronentomografie jedoch als Standard akzeptiert werden. Die MW-Artefakte werden besonders effektiv mit einer spezifischen DIRECTT-Prozedur partiell diskreter Zwischenlösungen beseitigt. Für die Beurteilung der Abbildungsqualität werden Rekonstruktionen von vollständigen und unvollständigen Mess- und Modell-Datensätzen erzeugt und mit Ergebnissen anderer Algorithmen (gefilterte Rückprojektion (FBP) und ART-Methoden) verglichen. Die Fourier-Transformierten der Rekonstruktionen demonstrieren die erfolgreiche Ergänzung der fehlenden Information im MW-Bereich. Die quantitative Bewertung der lokalen Rekonstruktionsqualität mit Methoden der räumlichen Statistik ergibt auch für unterschiedliche Signal-Rausch-Verhältnisse signifikante Vorteile gegenüber FBP und ART.
Anhand von computertomografischen Messungen und Modellrechnungen werden DIRECTT-Rekonstruktionen im Vergleich mit gefilterten Rückprojektionen bewertet. Dazu wird die Rekonstruktionsqualität mittels einer zirkular erweiterten Modulations-Transfer-Funktion (MTF) und mit integralen Kenngrößen im Radon- und im Ortsraum verglichen. Zur Überprüfung der Rekonstruktionsgenauigkeit experimenteller Daten werden Mustermessungen einfacher Probengeometrien unter definierten physikalischen Bedingungen durchgeführt. Diese beinhalten die Monochromasie, die Unterdrückung von Kantenartefakten und die radiometrische Intensitätsbestimmung. Für die Qualität der Rekonstruktionen mittels DIRECTT erweisen sich sowohl unterschiedliche Rekonstruktionsfilter als auch der Verzicht auf jede Filterung als unerheblich, im Gegensatz zur gefilterten Rückprojektion.