  Diffraction of high-energy X-rays produced at synchrotron sources can provide
rapid strain measurements, with high spatial resolution, and good penetrating
power. With an uncollimated diffracted beam, through thickness averages of
strain can be measured using this technique, which poses an associated rich
tomography problem. This paper proposes a Gaussian process (GP) model for
three-dimensional strain fields satisfying static equilibrium and an
accompanying algorithm for tomographic reconstruction of strain fields from
high-energy X-ray diffraction. We present numerical evidence that this method
can achieve triaxial strain tomography in three-dimensions using only a single
axis of rotation. The method builds upon recent work where the GP approach was
used to reconstruct two-dimensional strain fields from neutron based
measurements. A demonstration is provided from simulated data, showing the
method is capable of rejecting realistic levels of Gaussian noise.
