tensor tomography
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2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jisoo Kim ◽  
Matias Kagias ◽  
Federica Marone ◽  
Zhitian Shi ◽  
Marco Stampanoni

AbstractMicrostructural information over an entire sample is important to understand the macroscopic behaviour of materials. X-ray scattering tensor tomography facilitates the investigation of the microstructural organisation in statistically large sample volumes. However, established acquisition protocols based on scanning small-angle X-ray scattering and X-ray grating interferometry inherently require long scan times even with highly brilliant X-ray sources. Recent developments in X-ray diffractive optics towards circular pattern arrays enable fast single-shot acquisition of the sample scattering properties with 2D omnidirectional sensitivity. X-ray scattering tensor tomography with the use of this circular grating array has been demonstrated. We propose here simple yet inherently rapid acquisition protocols for X-ray scattering tensor tomography leveraging on these new optical elements. Results from both simulation and experimental data, supported by a null space analysis, suggest that the proposed acquisition protocols are not only rapid but also corroborate that sufficient information for the accurate volumetric reconstruction of the scattering properties is provided. The proposed acquisition protocols will build the basis for rapid inspection and/or time-resolved tensor tomography of the microstructural organisation over an extended field of view.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jonas Graetz

AbstractTensor tomography is fundamentally based on the assumption of a both anisotropic and linear contrast mechanism. While the X-ray or neutron dark-field contrast obtained with Talbot(-Lau) interferometers features the required anisotropy, a preceding detailed study of dark-field signal origination however found its specific orientation dependence to be a non-linear function of the underlying anisotropic mass distribution and its orientation, especially challenging the common assumption that dark-field signals are describable by a function over the unit sphere. Here, two approximative linear tensor models with reduced orientation dependence are investigated in a simulation study with regard to their applicability to grating based X-ray or neutron dark-field tensor tomography. By systematically simulating and reconstructing a large sample of isolated volume elements covering the full range of feasible anisotropies and orientations, direct correspondences are drawn between the respective tensors characterizing the physically based dark-field model used for signal synthesization and the mathematically motivated simplified models used for reconstruction. The anisotropy of freely rotating volume elements is thereby confirmed to be, for practical reconstruction purposes, approximable both as a function of the optical axis’ orientation or as a function of the interferometer’s grating orientation. The eigenvalues of the surrogate models’ tensors are found to exhibit fuzzy, yet almost linear relations to those of the synthesization model. Dominant orientations are found to be recoverable with a margin of error on the order of magnitude of 1$$^{\circ }$$ ∘ . Although the input data must adequately address the full orientation dependence of dark-field anisotropy, the present results clearly support the general feasibility of quantitative X-ray dark-field tensor tomography within an inherent yet acceptable statistical margin of uncertainty.


IUCrJ ◽  
2021 ◽  
Vol 8 (5) ◽  
Author(s):  
Fredrik K. Mürer ◽  
Aldritt Scaria Madathiparambil ◽  
Kim Robert Tekseth ◽  
Marco Di Michiel ◽  
Pierre Cerasi ◽  
...  

Shales have a complex mineralogy with structural features spanning several length scales, making them notoriously difficult to fully understand. Conventional attenuation-based X-ray computed tomography (CT) measures density differences, which, owing to the heterogeneity and sub-resolution features in shales, makes reliable interpretation of shale images a challenging task. CT based on X-ray diffraction (XRD-CT), rather than intensity attenuation, is becoming a well established technique for non-destructive 3D imaging, and is especially suited for heterogeneous and hierarchical materials. XRD patterns contain information about the mineral crystal structure, and crucially also crystallite orientation. Here, we report on the use of orientational imaging using XRD-CT to study crystallite-orientation distributions in a sample of Pierre shale. Diffraction-contrast CT data for a shale sample measured with its bedding-plane normal aligned parallel to a single tomographic axis perpendicular to the incoming X-ray beam are discussed, and the spatial density and orientation distribution of clay minerals in the sample are described. Finally, the scattering properties of highly attenuating inclusions in the shale bulk are studied, which are identified to contain pyrite and clinochlore. A path forward is then outlined for systematically improving the structural description of shales.


Author(s):  
Marianne Liebi ◽  
Viviane Lutz-Bueno ◽  
Manuel Guizar-Sicairos ◽  
Bernd M. Schönbauer ◽  
Johannes Eichler ◽  
...  

2021 ◽  
Author(s):  
Jisoo Kim ◽  
Matias Kagias ◽  
Federica Marone ◽  
Zhitian Shi ◽  
Marco Stampanoni

Abstract Microstructural information over an entire sample is important to understand the macroscopic behavior of materials. X-ray scattering tensor tomography facilitates the investigation of the microstructural organisation in statistically large sample volumes. However, established acquisition protocols based on scanning small-angle X-ray scattering and X-ray grating interferometry inherently require long scan times even with highly brilliant X-ray sources. Recent developments in X-ray diffractive optics towards circular pattern arrays enable fast single-shot acquisition of the sample scattering properties with 2D omnidirectional sensitivity. Leveraging on these new optical elements, we propose here simple yet inherently rapid acquisition protocols forX-ray scattering tensor tomography. Results from both simulation and experimental data, supported by a null space analysis, suggest that the proposed acquisition protocols are not only rapid but also corroborate that sufficient information for the accurate volumetric reconstruction of the scattering properties is provided. The proposed acquisition protocols will build the basis for rapid inspection and/or time-resolved tensor tomography of the microstructural organisation over an extended field of view.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Marios Georgiadis ◽  
Aileen Schroeter ◽  
Zirui Gao ◽  
Manuel Guizar-Sicairos ◽  
Marianne Liebi ◽  
...  

AbstractMyelin insulates neuronal axons and enables fast signal transmission, constituting a key component of brain development, aging and disease. Yet, myelin-specific imaging of macroscopic samples remains a challenge. Here, we exploit myelin’s nanostructural periodicity, and use small-angle X-ray scattering tensor tomography (SAXS-TT) to simultaneously quantify myelin levels, nanostructural integrity and axon orientations in nervous tissue. Proof-of-principle is demonstrated in whole mouse brain, mouse spinal cord and human white and gray matter samples. Outcomes are validated by 2D/3D histology and compared to MRI measurements sensitive to myelin and axon orientations. Specificity to nanostructure is exemplified by concomitantly imaging different myelin types with distinct periodicities. Finally, we illustrate the method’s sensitivity towards myelin-related diseases by quantifying myelin alterations in dysmyelinated mouse brain. This non-destructive, stain-free molecular imaging approach enables quantitative studies of myelination within and across samples during development, aging, disease and treatment, and is applicable to other ordered biomolecules or nanostructures.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fredrik K. Mürer ◽  
Basab Chattopadhyay ◽  
Aldritt Scaria Madathiparambil ◽  
Kim Robert Tekseth ◽  
Marco Di Michiel ◽  
...  

AbstractWhile a detailed knowledge of the hierarchical structure and morphology of the extracellular matrix is considered crucial for understanding the physiological and mechanical properties of bone and cartilage, the orientation of collagen fibres and carbonated hydroxyapatite (HA) crystallites remains a debated topic. Conventional microscopy techniques for orientational imaging require destructive sample sectioning, which both precludes further studies of the intact sample and potentially changes the microstructure. In this work, we use X-ray diffraction tensor tomography to image non-destructively in 3D the HA orientation in a medial femoral condyle of a piglet. By exploiting the anisotropic HA diffraction signal, 3D maps showing systematic local variations of the HA crystallite orientation in the growing subchondral bone and in the adjacent mineralized growth cartilage are obtained. Orientation maps of HA crystallites over a large field of view (~ 3 × 3 × 3 mm3) close to the ossification (bone-growth) front are compared with high-resolution X-ray propagation phase-contrast computed tomography images. The HA crystallites are found to predominantly orient with their crystallite c-axis directed towards the ossification front. Distinct patterns of HA preferred orientation are found in the vicinity of cartilage canals protruding from the subchondral bone. The demonstrated ability of retrieving 3D orientation maps of bone-cartilage structures is expected to give a better understanding of the physiological properties of bones, including their propensity for bone-cartilage diseases.


Author(s):  
Gabriel P. Paternain ◽  
Mikko Salo

AbstractWe consider the geodesic X-ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and non-positive curvature. We establish a stability estimate of the form $$L^2\mapsto H^{1/2}_{T}$$ L 2 ↦ H T 1 / 2 , where the $$H^{1/2}_{T}$$ H T 1 / 2 -space is defined using the natural parametrization of geodesics as initial boundary points and incoming directions (fan-beam geometry); only tangential derivatives at the boundary are used. The proof is based on the Pestov identity with boundary term localized in frequency.


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