Optimized algebraic reconstruction technique for generation of grain maps based on three-dimensional x-ray diffraction (3DXRD)

Recently, an algebraic reconstruction method has been presented for generation of three-dimensional (3D) maps of the grain boundaries within polycrystals. The grains are mapped layer by layer in a nondestructive way by diffraction with hard x rays. We optimize the algorithm by means of simulations and discuss ways to automate the analysis. The use of generalized Kaiser-Bessel functions as basis functions is shown to be superior to a conventional discretization in terms of square pixels. The algorithm is reformulated as a block-iterative method in order to incorporate the instrumental point-spread function and, at the same time, to avoid the need to store the set of equations. The first reconstruction of a full layer and two neighboring 3D grains from experimental data are demonstrated.