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Point by point strain scanning is often used to map the residual stress(strain) in engineering materials and components. However, the gauge volume andhence spatial resolution is limited by the beam defining apertures and can beanisotropic for very low and high diffraction (scattering) angles.Alternatively, wavelength resolved neutron transmission imaging has a potentialto retrieve information tomographically about residual strain induced withinmaterials through measurement in transmission of Bragg edges - crystallographicfingerprints whose locations and shapes depend on microstructure and straindistribution. In such a case the spatial resolution is determined by thegeometrical blurring of the measurement setup and the detector point spreadfunction. Mathematically, reconstruction of strain tensor field is described bythe longitudinal ray transform; this transform has a non-trivial null-space,making direct inversion impossible. A combination of the longitudinal raytransform with physical constraints was used to reconstruct strain tensorfields in convex objects. To relax physical constraints and generalisereconstruction, a recently introduced concept of histogram tomography can beemployed. Histogram tomography relies on our ability to resolve thedistribution of strain in the beam direction, as we discuss in the paper. Morespecifically, Bragg edge strain tomography requires extraction of the secondmoment (variance about zero) of the strain distribution which has not yet beendemonstrated in practice. In this paper we verify experimentally that thesecond moment can be reliably measured for a previously well characterisedaluminium ring and plug sample. We compare experimental measurements againstnumerical calculation and further support our conclusions by rigorousuncertainty quantification of the estimated mean and variance of the straindistribution.

Recovering the second moment of the strain distribution from neutron Bragg edge data