The University of Southampton
University of Southampton Institutional Repository

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

Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements
Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements
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 Liebi et 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 transfer q range. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges of q. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.The mathematical framework and reconstruction algorithm for small-angle scattering tensor tomography are introduced in detail, as well as strategies which help to reduce the amount of data and therewith the measurement time required. Experimental validation is provided for the application to trabecular bone.
2053-2733
12-24
Liebi, Marianne
c459262b-49ce-4c21-bd5b-09c3282e8202
Georgiadis, Marios
2f89e800-1a6f-4a74-b60b-578aa254a6af
Kohlbrecher, Joachim
e5179dde-90c8-4a8c-af5c-299e9fe32eee
Holler, Mirko
6630bc04-e001-49dc-b144-bea5e9804ab3
Raabe, Jörg
f5fa8121-65b3-441a-a013-c090dbf552af
Usov, Ivan
30deb592-12e2-4963-b05e-36d58e41822e
Menzel, Andreas
82ceca70-40ae-40f2-81c4-07c3f485bc15
Schneider, Philipp
a810f925-4808-44e4-8a4a-a51586f9d7ad
Bunk, Oliver
9833fa0b-2541-49c4-8e4b-9770064d2806
Guizar-Sicairos, Manuel
95872578-0eda-497e-9778-4147bf4b97d9
Liebi, Marianne
c459262b-49ce-4c21-bd5b-09c3282e8202
Georgiadis, Marios
2f89e800-1a6f-4a74-b60b-578aa254a6af
Kohlbrecher, Joachim
e5179dde-90c8-4a8c-af5c-299e9fe32eee
Holler, Mirko
6630bc04-e001-49dc-b144-bea5e9804ab3
Raabe, Jörg
f5fa8121-65b3-441a-a013-c090dbf552af
Usov, Ivan
30deb592-12e2-4963-b05e-36d58e41822e
Menzel, Andreas
82ceca70-40ae-40f2-81c4-07c3f485bc15
Schneider, Philipp
a810f925-4808-44e4-8a4a-a51586f9d7ad
Bunk, Oliver
9833fa0b-2541-49c4-8e4b-9770064d2806
Guizar-Sicairos, Manuel
95872578-0eda-497e-9778-4147bf4b97d9

Liebi, Marianne, Georgiadis, Marios, Kohlbrecher, Joachim, Holler, Mirko, Raabe, Jörg, Usov, Ivan, Menzel, Andreas, Schneider, Philipp, Bunk, Oliver and Guizar-Sicairos, Manuel (2018) Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements. Acta Crystallographica Section A: Foundations and Advances, A74 (1), 12-24. (doi:10.1107/S205327331701614X).

Record type: Article

Abstract

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 Liebi et 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 transfer q range. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges of q. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.The mathematical framework and reconstruction algorithm for small-angle scattering tensor tomography are introduced in detail, as well as strategies which help to reduce the amount of data and therewith the measurement time required. Experimental validation is provided for the application to trabecular bone.

Text vk5021_rev - Accepted Manuscript
Download (1MB)
Text vk5021 - Version of Record
Available under License Creative Commons Attribution.
Download (1MB)

More information

Accepted/In Press date: 8 November 2017
e-pub ahead of print date: 1 January 2018
Published date: January 2018

Identifiers

Local EPrints ID: 415968
URI: https://eprints.soton.ac.uk/id/eprint/415968
ISSN: 2053-2733
PURE UUID: 442600e6-1396-49aa-9c6f-9eacdde37c8a
ORCID for Philipp Schneider: ORCID iD orcid.org/0000-0001-7499-3576

Catalogue record

Date deposited: 29 Nov 2017 17:30
Last modified: 06 Jun 2018 12:23

Export record

Altmetrics

Contributors

Author: Marianne Liebi
Author: Marios Georgiadis
Author: Joachim Kohlbrecher
Author: Mirko Holler
Author: Jörg Raabe
Author: Ivan Usov
Author: Andreas Menzel
Author: Oliver Bunk
Author: Manuel Guizar-Sicairos

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×