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

Liebi, Marianne LU ; Georgiadis, Marios; Kohlbrecher, Joachim; Holler, Mirko; Raabe, Jörg; Usov, Ivan; Menzel, Andreas; Schneider, Philipp; Bunk, Oliver and Guizar-Sicairos, Manuel (2018) In Acta Crystallographica Section A: Foundations and Advances 74(1). p.12-24
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... (More)

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.

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organization
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Contribution to journal
publication status
published
subject
keywords
bone, small-angle X-ray scattering, spherical harmonics, tensor tomography
in
Acta Crystallographica Section A: Foundations and Advances
volume
74
issue
1
pages
13 pages
external identifiers
  • scopus:85039040527
DOI
10.1107/S205327331701614X
language
English
LU publication?
yes
id
160b8fba-7ab9-42f4-ba6d-27415f70aaea
date added to LUP
2018-01-05 10:21:02
date last changed
2018-01-06 03:00:02
@article{160b8fba-7ab9-42f4-ba6d-27415f70aaea,
  abstract     = {<p>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.</p>},
  author       = {Liebi, Marianne and Georgiadis, Marios and Kohlbrecher, Joachim and Holler, Mirko and Raabe, Jörg and Usov, Ivan and Menzel, Andreas and Schneider, Philipp and Bunk, Oliver and Guizar-Sicairos, Manuel},
  keyword      = {bone,small-angle X-ray scattering,spherical harmonics,tensor tomography},
  language     = {eng},
  month        = {01},
  number       = {1},
  pages        = {12--24},
  series       = {Acta Crystallographica Section A: Foundations and Advances},
  title        = {Small-angle X-ray scattering tensor tomography : Model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements},
  url          = {http://dx.doi.org/10.1107/S205327331701614X},
  volume       = {74},
  year         = {2018},
}