Diffraction tomography of strain

We consider the tomographic recovery of strain from x-ray and neutron diffraction data of a polycrystalline material. We show that the distribu- tion of strain transverse to a ray cannot be deduced from one diffraction pattern accumulated along that path, but 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 give an example of sufficient data characterised by the data measured from rotations about six direction 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 a certain type of Bragg edge data which has been suggested for strain tomography with polychromatic data, can in fact only determine the change in the external dimension of a solid specimen and is otherwise unaffected by the distribution of strain along the ray.