Reconstructing elastic strain fields from its Longitudinal Ray Transform.

RESUMEN: In the problem of Bragg-edge elastic strain tomography, measurements are obtained from energy resolved neutron transmission imaging, which provides information about the Longitudinal Ray Transform (LRT) of the elastic strain field. The goal is to recover the elastic strain field by inverting its LRT. The inversion of the ray transform for tensor fields is a well studied problem [1]. It is known that only the solenoidal part of symmetric tensor fields can be recovered from their LRT, there are inversion formulas available  that reconstruct such solenoidal component and there are stability estimates for such reconstruction. Nonetheless, by taking into  account that elastic strain fields additionally satisfy an equilibrium equation, it is possible to also recover the potential part of the elastic strain, for simply connected object [3], or under some extra requirements [2]. In this talk I will present the problem of inverting the LRT  for elastic strain tomography that arises from energy resolved neutron transmission imaging,  I will recall the classic results about the  inversion of the ray transform for tensor fields, and I will present the contributions of [2,3] dealing with the reconstruction of the potential  part of the elastic strain field using the equilibrium equation that is satisfied.

Posted on Nov 4, 2024 in Seminario IPCT, Seminars