Discrete Tomographic Reconstruction of 2D Polycrystal Orientation Maps From X-ray Diffraction Projections Using Gibbs Priors

The determination of crystalline structures is a demanding and fundamental task of crystallography. This paper offers a new approach for rendering a 2D grain map of a polycrystal based on an orientation map reconstructed from X-ray diffraction patterns. The orientation map is produced by a Bayesian discrete tomographic algorithm, applying image-modelling Gibbs priors and a homogeneity condition. The optimization of the objective function is accomplished via the Gibbs Sampler in conjunction with simulated annealing. In order to express the structure of the orientation map, the similarity of orientations is defined by means of quaternions.