Algorithm of reconstruction of a three-dimensional crystal structure from two-dimensional projections

Abstract

The article deals with a problem of three-dimensional crystal lattice reconstruction, which is an important stage in the X-ray structural analysis. The accuracy of parametric and structural identification of crystals directly depends on the quality of crystal lattice reconstruction. The proposed algorithm of reconstruction of a three-dimensional crystal lattice is based on minimizing the distances from each node to a line projected onto a specified plane. Three sets of two-dimensional node coordinates, obtained from three two-dimensional projections, are used as input data. We performed an analytical calculation of the reconstruction error, allowing the total reconstruction accuracy to be estimated. The results of computational experiments confirmed the high quality of the proposed reconstruction algorithms and its stability against the distortion of node coordinates. In addition, we revealed a problem of lattice system separability, with the identification accuracy for monoclinic, rhombic and tetragonal systems found to be 34%, 53% and 10%, respectively.

Keywords

• three-dimensional reconstruction
• two-dimensional projection
• crystal lattice
• unit cell
• image processing
• computed tomography
• structural identification
• Hausdorff metric