A stochastic algorithm for reconstruction of grain maps of moderately deformed specimens based on X-ray diffraction

In a recent paper [Alpers, Poulsen, Knudsen & Herman (2006). J. Appl. Cryst. 39, 582-588] a stochastic algorithm was presented for reconstruction of grain maps of undeformed polycrystals based on X-ray diffraction data. Here the formalism is extended to moderately deformed specimens. Each two-dimensional section of the specimen is reconstructed independently. Using a dual assignment of a grain label and an orientation to each pixel in a section and a prior model based on methods of discrete tomography, our stochastic algorithm converges in a few minutes for a 64 x 64 map. Simulations with higher than typical levels of noise in the data collection for three typical moderately deformed microstructures resulted in grain maps with the fraction of erroneously assigned pixels being 1.7% or much less.