scholarly journals Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements

2018 ◽  
Vol 74 (1) ◽  
pp. 12-24 ◽  
Author(s):  
Marianne Liebi ◽  
Marios Georgiadis ◽  
Joachim Kohlbrecher ◽  
Mirko Holler ◽  
Jörg Raabe ◽  
...  
Keyword(s):  
Small Angle ◽  
Three Dimensional ◽  
Reconstruction Algorithm ◽  
Reciprocal Space ◽  
Mathematical Framework ◽  
X Ray ◽  
Tensor Tomography ◽  
X Ray Scattering ◽  
Degree Of Orientation ◽  
Ray Scattering

Small-angle X-ray scattering tensor tomography, which allows reconstruction of the local three-dimensional reciprocal-space map within a three-dimensional sample as introduced by Liebiet al.[Nature(2015),527, 349–352], is described in more detail with regard to the mathematical framework and the optimization algorithm. For the case of trabecular bone samples from vertebrae it is shown that the model of the three-dimensional reciprocal-space map using spherical harmonics can adequately describe the measured data. The method enables the determination of nanostructure orientation and degree of orientation as demonstrated previously in a single momentum transferqrange. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges ofq. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.

scholarly journals Validation study of small-angle X-ray scattering tensor tomography

2020 ◽  
Vol 27 (3) ◽  
pp. 779-787 ◽  
Author(s):  
Manuel Guizar-Sicairos ◽  
Marios Georgiadis ◽  
Marianne Liebi
Keyword(s):  
Small Angle ◽  
Structural Information ◽  
Anisotropic Scattering ◽  
Reciprocal Space ◽  
Separate Analysis ◽  
X Ray ◽  
Tensor Tomography ◽  
X Ray Scattering ◽  
Dot Product ◽  
Ray Scattering

Small-angle scattering tensor tomography (SASTT) is a recently developed technique able to tomographically reconstruct the 3D reciprocal space from voxels within a bulk volume. SASTT extends the concept of X-ray computed tomography, which typically reconstructs scalar values, by reconstructing a tensor per voxel, which represents the local nanostructure 3D organization. In this study, the nanostructure orientation in a human trabecular-bone sample obtained by SASTT was validated by sectioning the sample and using 3D scanning small-angle X-ray scattering (3D sSAXS) to measure and analyze the orientation from single voxels within each thin section. Besides the presence of cutting artefacts from the slicing process, the nanostructure orientations obtained with the two independent methods were in good agreement, as quantified with the absolute value of the dot product calculated between the nanostructure main orientations obtained in each voxel. The average dot product per voxel over the full sample containing over 10 000 voxels was 0.84, and in six slices, in which fewer cutting artefacts were observed, the dot product increased to 0.91. In addition, SAXS tensor tomography not only yields orientation information but can also reconstruct the full 3D reciprocal-space map. It is shown that the measured anisotropic scattering for individual voxels was reproduced from the SASTT reconstruction in each voxel of the 3D sample. The scattering curves along different 3D directions are validated with data from single voxels, demonstrating SASTT's potential for a separate analysis of nanostructure orientation and structural information from the angle-dependent intensity distribution.

X-ray imaging with ultra-small-angle X-ray scattering as a contrast mechanism

2004 ◽  
Vol 37 (5) ◽  
pp. 757-765 ◽  
Author(s):  
L. E. Levine ◽  
G. G. Long
Keyword(s):  
Small Angle ◽  
Imaging Technique ◽  
Three Dimensional ◽  
Sample Volume ◽  
Contrast Imaging ◽  
X Ray ◽  
X Ray Scattering ◽  
X Ray Imaging ◽  
Contrast Mechanism ◽  
Ray Scattering

A new transmission X-ray imaging technique using ultra-small-angle X-ray scattering (USAXS) as a contrast mechanism is described. USAXS imaging can sometimes provide contrast in cases where radiography and phase-contrast imaging are unsuccessful. Images produced at different scattering vectors highlight different microstructural features within the same sample volume. When used in conjunction with USAXS scans, USAXS imaging provides substantial quantitative and qualitative three-dimensional information on the sizes, shapes and spatial arrangements of the scattering objects. The imaging technique is demonstrated on metal and biological samples.

Six-dimensional real and reciprocal space small-angle X-ray scattering tomography

Nature ◽  
2015 ◽  
Vol 527 (7578) ◽  
pp. 353-356 ◽  
Author(s):  
Florian Schaff ◽  
Martin Bech ◽  
Paul Zaslansky ◽  
Christoph Jud ◽  
Marianne Liebi ◽  
...  
Keyword(s):  
Small Angle ◽  
Reciprocal Space ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Simulation of small-angle X-ray scattering from thylakoid membranes

2009 ◽  
Vol 42 (4) ◽  
pp. 649-659 ◽  
Author(s):  
J. J. K. Kirkensgaard ◽  
J. K. Holm ◽  
J. K. Larsen ◽  
D. Posselt
Keyword(s):  
Experimental Data ◽  
Small Angle ◽  
Virtual Instrument ◽  
Three Dimensional ◽  
Thylakoid Membranes ◽  
Three Dimensional Model ◽  
General Applicability ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Small-angle X-ray scattering (SAXS) patterns are calculated from a three-dimensional model of photosynthetic thylakoid membranes. The intricate structure of the thylakoids is represented by sampling random `electron density points' on geometric surfaces. The simulation setup works as a virtual instrument, allowing direct comparison with experimental data. The simulations qualitatively reproduce experimental data and thus clarify the structural origin of the scattering features. This is used to explain recent SAXS measurements and as a guideline for new experiments and future quantitative modeling. The setup has general applicability for model testing purposes when modeling scattering from membrane systems of complex geometries.

scholarly journals Two practical Java software tools for small-angle X-ray scattering analysis of biomolecules

2014 ◽  
Vol 47 (2) ◽  
pp. 810-815 ◽  
Author(s):  
Andreas Hofmann ◽  
Andrew E. Whitten
Keyword(s):  
Small Angle ◽  
Three Dimensional ◽  
Small Angle Scattering ◽  
Ease Of Use ◽  
Scattering Data ◽  
X Ray ◽  
X Ray Scattering ◽  
Angle Scattering ◽  
Three Dimensional Models ◽  
Ray Scattering

Small-angle X-ray scattering has established itself as a common technique in structural biology research. Here, two novel Java applications to aid modelling of three-dimensional macromolecular structures based on small-angle scattering data are described.MolScatis an application that computes small-angle scattering intensities from user-provided three-dimensional models. The program can fit the theoretical scattering intensities to experimental X-ray scattering data.SAFIRis a program for interactive rigid-body modelling into low-resolution shapes restored from small-angle scattering data. The program has been designed with an emphasis on ease of use and intuitive handling. An embedded version ofMolScatis used to enable quick evaluation of the fit between the model and experimental scattering data.SAFIRalso provides options to refine macromolecular complexes with optional user-specified restraints against scattering data by means of a Monte Carlo approach.

Simulations of the transmission small angle x-ray scattering for three-dimensional architectures

2021 ◽  
Author(s):  
Tianjuan Yang ◽  
Jiahao Zhang ◽  
Jianyuan Ma ◽  
Shiyuan Liu ◽  
Xiuguo Chen
Keyword(s):  
Small Angle ◽  
Three Dimensional ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Determining the shape and periodicity of nanostructures using small-angle X-ray scattering

2015 ◽  
Vol 48 (5) ◽  
pp. 1355-1363 ◽  
Author(s):  
Daniel F. Sunday ◽  
Scott List ◽  
Jasmeet S. Chawla ◽  
R. Joseph Kline
Keyword(s):  
Small Angle ◽  
Semiconductor Industry ◽  
Three Dimensional ◽  
Critical Dimension ◽  
Dimensional Structure ◽  
Critical Dimensions ◽  
X Ray ◽  
Line Shapes ◽  
X Ray Scattering ◽  
Ray Scattering

The semiconductor industry is exploring new metrology techniques capable of meeting the future requirement to characterize three-dimensional structure where the critical dimensions are less than 10 nm. X-ray scattering techniques are one candidate owing to the sub-Å wavelengths which are sensitive to internal changes in electron density. Critical-dimension small-angle X-ray scattering (CDSAXS) has been shown to be capable of determining the average shape of a line grating. Here it is used to study a set of line gratings patternedviaa self-aligned multiple patterning process, which resulted in a set of mirrored lines, where the individual line shapes were asymmetric. The spacing between lines was systematically varied by sub-nm shifts. The model used to simulate the scattering was developed in stages of increasing complexity in order to justify the large number of parameters included. Comparisons between the models at different stages of development demonstrate that the measurement can determine differences in line shapes within the superlattice. The shape and spacing between lines within a given set were determined to sub-nm accuracy. This demonstrates the potential for CDSAXS as a high-resolution nanostructure metrology tool.

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