We develop an improved 3D digital volume correlation (DVC) technique to measure displacement and strain fields throughout the interior of a material. Our eventual goal is to perform DVC with resolution comparable to that achieved in 2D DIC, with a correlation time that is commensurate with the image acquisition time. This would represent a significant improvement over the current state-of-the art available in the literature. Using an X-ray micro-CT scanner, we can resolve features at the 5 micron scale, generating 3D images with up to 8 billion voxels. We compute twelve degrees-of-freedom at each correlation point and utilize tricubic spline interpolation to achieve high accuracy. For DVC, the volume of data, number of correlation points and work to solve each correlation point grow cubically. We therefore employ parallel computing to handle this tremendous increase in computational and memory requirements. We demonstrate the application of DVC using an artificial deformation of actual PDMS samples with embedded particles forming an internal pattern.