American Institute of Mathematical Sciences

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February  2009, 3(1): 69-85. doi: 10.3934/ipi.2009.3.69

A greedy method for reconstructing polycrystals from three-dimensional X-ray diffraction data

Arun K. Kulshreshth 1, , Andreas Alpers 2, , Gabor T. Herman 1, , Erik Knudsen 2, , Lajos Rodek 1, and  Henning F. Poulsen 2,

1. 

Department of Computer Science, The Graduate Center, CUNY, NY 10016, United States, United States, United States
2. 

Center for Fundamental Research: ‘Metal Structures in Four Dimensions’, Risø DTU, Technical University of Denmark, DK-4000 Roskilde, Denmark, Denmark, Denmark

Received  April 2008 Revised  October 2008 Published  February 2009

An iterative search method is proposed for obtaining orientation maps inside polycrystals from three-dimensional X-ray diffraction (3DXRD) data. In each step, detector pixel intensities are calculated by a forward model based on the current estimate of the orientation map. The pixel at which the experimentally measured value most exceeds the simulated one is identified. This difference can only be reduced by changing the current estimate at a location from a relatively small subset of all possible locations in the estimate and, at each such location, an increase at the identified pixel can only be achieved by changing the orientation in only a few possible ways. The method selects the location/orientation pair indicated as best by a function that measures data consistency combined with prior information on orientation maps. The superiority of the method to a previously published forward projection Monte Carlo optimization is demonstrated on simulated data.
Keywords: 3DXRD, X-Ray Diffraction., Grain Map, Tomography, Reconstruction, Discrete Inverse Problem.
Mathematics Subject Classification: 94A08, 92F05, 74N15, 90C5.
Citation: Arun K. Kulshreshth, Andreas Alpers, Gabor T. Herman, Erik Knudsen, Lajos Rodek, Henning F. Poulsen. A greedy method for reconstructing polycrystals from three-dimensional X-ray diffraction data. Inverse Problems and Imaging, 2009, 3 (1) : 69-85. doi: 10.3934/ipi.2009.3.69
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