Single-projection reconstruction technique for positioning monodisperse spheres in 3D with a divergent x-ray beam

Edward Andò (1, 2) , Benjy Marks (3) , Stéphane Roux (4)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 3SR - Laboratoire sols, solides, structures - risques [Grenoble]
3 The University of Sydney
4 LMPS - Laboratoire de Mécanique Paris-Saclay

The measurement of the position of single-sized spheres in 3D from a single, divergent, radiographic projection is addressed in the present study with the development of a novel method. Generally speaking, the location of the shadow cast by a single sphere on a detector defines a source-detector ray; the position of the particle along this ray is identified by the strong prior knowledge of its radius and the size of the shadow. For a dense assembly of equal-sized particles whose projections overlap, a novel Fourier transform based technique is introduced to give a first 3D determination of the particle centres. The uncertainty of this measurement is calculated from synthetic data with a known noise distribution. A further refinement of this measurement is performed based on the minimisation of the projection residual. The combined approach is validated both on synthetic data, and on real radiographs of a glass bead packing. The effect of noise on the measurement uncertainty is evaluated. The technique is made available to the community in the open source python package radioSphere.

Domaines: Matériaux; Science des matériaux [cond-mat.mtrl-sci]; Mécanique statistique [cond-mat.stat-mech]; Mécanique des matériaux [physics.class-ph]; Mécanique des solides [physics.class-ph]

Edward Andò, Benjy Marks, Stéphane Roux. Single-projection reconstruction technique for positioning monodisperse spheres in 3D with a divergent x-ray beam. Measurement Science and Technology, 2021, 32 (9), ⟨10.1088/1361-6501/abfbfe⟩. ⟨hal-03210946⟩