Abstract
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.
Highlights
A collection of spheres is the simplest form that a granular material can take, yet it exhibits most of the rich behaviour that makes granular mechanics such a fascinating and active field of research [e.g., 1, 2, 3]
Given the complexity of grain kinematics, imaging methods capable of identifying individual grains are extremely pertinent [5, 6] and there exist grain-based image analysis methods which are able to characterise a granular system from such measurements [7, 8]
It is important to mention a similar method for parallel projections of granular media, where boundary conditions are imposed to regularise the displacements in the x-ray direction [19]
Summary
A collection of spheres is the simplest form that a granular material can take, yet it exhibits most of the rich behaviour that makes granular mechanics such a fascinating and active field of research [e.g., 1, 2, 3]. Several recent works have used an initial tomography scan of a granular packing and updated particle positions only with a few radiographs of each subsequent imaged state [15], itself a discrete version of [16, 17].
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