Neutron transmission strain imaging, the longitudinal ray transform and PDEs

Abstract

I will discuss neutron transmission strain imaging which attempts to measure the residual strain field inside a polycrystalline object, such as a metal, by transmission of an energy resolved beam of neutrons. In this application, it is possible to reconstruct the longitudinal ray transform (LRT) of the strain field leading to an integral geometry problem for reconstruction. As is well known, from the LRT it is only possible to reconstruct the solenoidal part of a tensor, but by adding the physical equilibrium condition satisfied by the strain (a PDE) we can determine more. This talk is based on joint work with Chris Wensrich, Matias Courdurier, Bill Lionheart, Anna Polyakova, and Ivan Svetov which was begun during a programme at the Isaac Newton Institute.