  A new method for estimation of intragranular strain fields in polycrystalline
materials based on scanning three-dimensional X-ray diffraction data
(scanning-3DXRD) is presented and evaluated. Given an apriori known anisotropic
compliance, the regression method enforces the balance of linear and angular
momentum in the linear elastic strain field reconstruction. By using a Gaussian
Process (GP), the presented method can yield a spatial estimate of the
uncertainty of the reconstructed strain field. Furthermore, constraints on
spatial smoothness can be optimised with respect to measurements through
hyperparameter estimation. These three features address weaknesses discussed
for previously existing scanning-3DXRD reconstruction methods and, thus, offers
a more robust strain field estimation. The method is twofold validated; firstly
by reconstruction from synthetic diffraction data and, secondly, by
reconstruction of previously studied tin (Sn) grain embedded in a
polycrystalline specimen. Comparison against reconstructions achieved by a
recently proposed algebraic inversion technique is also presented. It is found
that the GP regression consistently produces reconstructions with lower root
mean squared errors, mean absolute errors and maximum absolute errors across
all six components of strain.
