Reconstruction of grain boundaries in polycrystals by filtered back-projection of diffraction spots

2003 ◽  
Vol 36 (2) ◽  
pp. 319-325 ◽  
Author(s):  
Henning Friis Poulsen ◽  
Soeren Schmidt
Keyword(s):  
Grain Boundaries ◽  
Three Dimensional ◽  
Projection Algorithm ◽  
Reconstruction Method ◽  
X Rays ◽  
Back Projection ◽  
Filtered Back Projection ◽  
Mosaic Spread

A reconstruction method is presented for the generation of three-dimensional maps of the grain boundaries within powders or polycrystals. The grains are assumed to have a mosaic spread below 1°. They are mapped non-destructively by diffraction with hard X-rays, using a uniform mm2-sized beam. First the diffraction spots are sorted with respect to grain of origin by the indexing programGRAINDEX. Next, for each grain the reconstruction is performed by a variant of the filtered back-projection algorithm. The reconstruction method is verified by a simulation over ten grains. Using 64 reflections for each grain, sub-pixel accuracy is obtained. The potential of the method is outlined.

Generation of grain maps by an algebraic reconstruction technique

2003 ◽  
Vol 36 (4) ◽  
pp. 1062-1068 ◽  
Author(s):  
H. F. Poulsen ◽  
Xiaowei Fu
Keyword(s):  
Grain Boundaries ◽  
Three Dimensional ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Layer By Layer ◽  
X Rays ◽  
Algebraic Reconstruction Technique ◽  
Mosaic Spread ◽  
Average Size ◽  
Non Destructive

A reconstruction method is presented for the generation of three-dimensional maps of the grain boundaries within powders or polycrystals. The grains are assumed to have a mosaic spread below 1°. They are mapped layer by layer in a non-destructive way by diffraction with hard X-rays. First the diffraction spots are sorted with respect to grain of origin by the indexing programGRAINDEX. Next for each grain the reconstruction is performed byART– an iterative algebraic algorithm. The method is optimized by simulations. It is verified by a 50 keV study on one embedded layer in an aluminium specimen. The layer comprises ∼50 grain sections of an average size of 100 µm. Based on the use of five reflections per grain, a resolution of ∼5 µm is inferred.

An algebraic algorithm for generation of three-dimensional grain maps based on diffraction with a wide beam of hard X-rays

2004 ◽  
Vol 37 (1) ◽  
pp. 96-102 ◽  
Author(s):  
T. Markussen ◽  
Xiaowei Fu ◽  
L. Margulies ◽  
E. M. Lauridsen ◽  
S. F. Nielsen ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Projection Algorithm ◽  
Reconstruction Method ◽  
Layer By Layer ◽  
X Rays ◽  
Spatial Accuracy ◽  
Wide Beam ◽  
Absorption Contrast ◽  
Better Than

A reconstruction method is presented for generation of three-dimensional maps of the grain boundaries within powders or polycrystals. The grains are assumed to have a mosaic spread below 1°. They are mapped by diffraction with a wide beam of hard X-rays, using a setup similar to that of parallel-beam absorption contrast tomography. First the diffraction spots are sorted with respect to grain of origin. Next, for each grain the reconstruction is performed by an algebraic algorithm known as three-dimensional ART. From simulations it is found that reconstructions with a spatial accuracy better than the pixel size of the detector can be obtained from as few as five diffraction spots. The results are superior to three-dimensional reconstructions based on the same data using a variant of the filtered back-projection algorithm. In comparison with layer-by-layer type reconstructions based on the two-dimensional ART algorithm, as introduced by Poulsen & Fu [J. Appl. Cryst.(2003),36, 1062–1068], the quality of the maps is found to be similar, provided that five to ten spots are available for analysis, while data acquisition with the three-dimensional method is much faster. The three-dimensional ART methodology is validated on experimental data. With state-of-the-art detectors, the spatial accuracy is estimated to be 5 µm.

scholarly journals Novel nonlinear reconstruction method with grey-level quantisation units for electron tomography

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Norio Baba ◽  
Kenji Kaneko ◽  
Misuzu Baba
Keyword(s):  
Cross Section ◽  
Electron Tomography ◽  
Three Dimensional ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Back Projection ◽  
Grey Level ◽  
Discrete Processing ◽  
Structural Image ◽  
Tomography Reconstruction

AbstractWe report a new computed tomography reconstruction method, named quantisation units reconstruction technique (QURT), applicable to electron and other fields of tomography. Conventional electron tomography methods such as filtered back projection, weighted back projection, simultaneous iterative reconstructed technique, etc. suffer from the ‘missing wedge’ problem due to the limited tilt-angle range. QURT demonstrates improvements to solve this problem by recovering a structural image blurred due to the missing wedge and substantially reconstructs the structure even if the number of projection images is small. QURT reconstructs a cross-section image by arranging grey-level quantisation units (QU pieces) in three-dimensional image space via unique discrete processing. Its viability is confirmed by model simulations and experimental results. An important difference from recently developed methods such as discrete algebraic reconstruction technique (DART), total variation regularisation—DART, and compressed sensing is that prior knowledge of the conditions regarding the specimen or the expected cross-section image is not necessary.

Parallelization of filtered back-projection algorithm for computed tomography

2015 ◽  
Vol 7 (3) ◽  
pp. 197-205 ◽  
Author(s):  
Akram Boukhamla ◽  
Hayet Farida Merouani ◽  
Hocine Sissaoui
Keyword(s):  
Computed Tomography ◽  
Projection Algorithm ◽  
Back Projection ◽  
Filtered Back Projection
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