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Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction

Marianne Liebi1, Marios Georgiadis2, Joachim Kohlbrecher1

  • 1Paul Scherrer Institut, 5232 Villigen PSI, Switzerland.

Acta Crystallographica. Section A, Foundations and Advances
|December 23, 2017
PubMed
Summary

Small-angle X-ray scattering tensor tomography reconstructs 3D reciprocal-space maps in trabecular bone. This advanced technique determines nanostructure orientation and degree of orientation with improved data efficiency.

Keywords:
bonesmall-angle X-ray scatteringspherical harmonicstensor tomography

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Area of Science:

  • Materials Science
  • Biophysics
  • X-ray Physics

Background:

  • Small-angle X-ray scattering (SAXS) tensor tomography enables 3D reciprocal-space map reconstruction within samples.
  • Previous work demonstrated its capability for nanostructure orientation determination over a limited q-range.

Purpose of the Study:

  • To provide a detailed mathematical framework and optimization algorithm for SAXS tensor tomography.
  • To reconstruct the complete 3D reciprocal-space map of trabecular bone over extended momentum transfer (q) ranges.
  • To assess the efficacy of spherical harmonics for modeling bone nanostructure.

Main Methods:

  • Detailed mathematical framework and optimization algorithm development for SAXS tensor tomography.
  • Application to trabecular bone samples from vertebrae.
  • Modeling of the 3D reciprocal-space map using spherical harmonics.
  • Reconstruction over extended q-ranges with uniform angular sampling and advanced regularization.

Main Results:

  • The spherical harmonics model adequately describes the measured data for trabecular bone.
  • The complete reciprocal-space map of bone was reconstructed over extended q-ranges.
  • Uniform angular sampling and advanced regularization strategies were shown to reduce data requirements.
  • Nanostructure orientation and degree of orientation were determined.

Conclusions:

  • SAXS tensor tomography is a powerful method for characterizing 3D nanostructure in materials like bone.
  • The detailed mathematical framework and optimization improve reconstruction accuracy and efficiency.
  • Advanced data acquisition and processing strategies enhance the method's applicability.