Diffraction tomography of strain

We consider whether it is possible to recover the three dimensional strain field tomographically from neutron and x-ray diffraction data for polycrystalline materials. We show that the distribution of strain transverse to a ray cannot be deduced from one diffraction pattern accumulated along that pa...

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Bibliographic Details
Published in:Inverse problems 2015-04, Vol.31 (4), p.45005-45021
Main Authors: Lionheart, W R B, Withers, P J
Format: Article
Language:English
Subjects:
computed tomography (CT)
Diffraction
Materials information
Mathematical analysis
Pascal's theorem
Strain
Tensors
Three dimensional
Tomography
Transforms
transverse ray transform
x-ray diffraction
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Summary:We consider whether it is possible to recover the three dimensional strain field tomographically from neutron and x-ray diffraction data for polycrystalline materials. We show that the distribution of strain transverse to a ray cannot be deduced from one diffraction pattern accumulated along that path, but that a certain moment of that data corresponds to the transverse ray transform of the strain tensor and so may be recovered by inverting that transform given sufficient data. We show that the whole strain tensor can be reconstructed from diffraction data measured using rotations about six directions that do not lie on a projective conic. In addition we give an inversion formula for complete data for the transverse ray transform. We also show that Bragg edge transmission data, which has been suggested for strain tomography with polychromatic data, cannot provide the strain distribution within the material but only the average along the ray path.
ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/31/4/045005