TY - JOUR

T1 - Small-angle X-ray scattering tensor tomography

T2 - Model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements

AU - Liebi, Marianne

AU - Georgiadis, Marios

AU - Kohlbrecher, Joachim

AU - Holler, Mirko

AU - Raabe, Jörg

AU - Usov, Ivan

AU - Menzel, Andreas

AU - Schneider, Philipp

AU - Bunk, Oliver

AU - Guizar-Sicairos, Manuel

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - bone

KW - small-angle X-ray scattering

KW - spherical harmonics

KW - tensor tomography

U2 - 10.1107/S205327331701614X

DO - 10.1107/S205327331701614X

M3 - Article

C2 - 29269594

AN - SCOPUS:85039040527

SN - 2053-2733

VL - 74

SP - 12

EP - 24

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

IS - 1

ER -