A novel method for indexing electron backscattered diffraction (EBSD) patterns is found to be significantly more accurate and faster than traditional indexing methods.

A Monte Carlo implementation of the expand–maximize–compress algorithm is presented and compared with the standard implementation.

In coherent-diffraction-imaging experiments, the symmetry of the particle may complicate and facilitate the solution of the orientation problem and the structure at the same time. For symmetric particles, the correlation-maximization method can find the relative orientations of the diffraction patterns and determine the symmetry of the particle.

A predicted model-aided reconstruction algorithm is proposed for orientation determination and phase retrieval in X-ray free-electron laser single-particle imaging. The predicted model-aided algorithm exhibits significant improvements in the success rate, accuracy and efficiency of the reconstruction process.

A predicted model-aided one-step classification–multireconstruction algorithm for X-ray free-electron laser single-particle imaging is proposed. The algorithm is capable of processing mixed diffraction patterns from multiple molecules, classifying diffraction patterns by different molecules, determining their orientations and reconstructing multiple 3D diffraction intensities, in one step.

A new pole figure inversion technique using the `cubochoric' and modified-Lambert projection methods together with total variation regularization is proposed.

An adaptive forward modeling orientation reconstruction algorithm is presented and illustrated. Combined with near-field high-energy X-ray diffraction microscopy measurements, the algorithm reconstructs maps of crystallographic orientations in polycrystals that include intra-granular orientation gradients, which arise in many applied materials.

The mathematical framework and reconstruction algorithm for small-angle scattering tensor tomography are introduced in detail, as well as strategies which help to reduce the amount of data and therewith the measurement time required. Experimental validation is provided for the application to trabecular bone.

An algorithm is described that calculates the most likely primitive unit cell given a set of randomly oriented electron-diffraction patterns with unknown angular relationships.

A description and evaluation are given of XGANDALF, extended gradient descent algorithm for lattice finding, an algorithm developed for fast and accurate indexing of snapshot diffraction patterns.