Tensor tomography of Strain

Bill Lionheart (University of Manchester)

Frank Adams Room 1, School of Mathematics, Alan Turing Building,

We have been working for many years on measuring stress and strain with polarized light which results in the inverse problem for the Truncated Transverse Ray Transform. Recently however we have been considering the measurement of strain using x-ray diffraction and this results in the Transverse Ray Transform. I will explain how this arises in the physical problem and how the explicit inverse might be used with limited data. The classical Pascal's theorem in projective geometry will make a guest appearance. I will go on to explain a filtered back projection inversion for the complete data Transverse Ray Transform, including a intriguing bit of abstract algebra. I will conclude with a proof that "Bragg Edge Tomography" cannot determine strain.

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