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

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.

Automated summary

This study introduces a novel method for measuring the position of single-sized spheres in 3D from a single, divergent, radiographic projection. By utilizing Fourier transform and minimizing projection residual, the method can determine the particle centers of equal-sized particles. The technique is validated on synthetic data and real radiographs, with the measurement uncertainty evaluated.