Subset Refinement for Digital Volume Correlation: Numerical and Experimental Applications

Digital image correlation (DIC) metrology has gained significant popularity over the past few decades because of its ease of use and reliable displacement measurement. Unlike other optical methods, such as for example interferometric techniques, which produce a fixed resolution depending on the particulars of the optical set-up used, key factors affecting accuracy and resolution of DIC include among others correlation point density (i.e., which pixels are selected as measurements points) and subset size (i.e., the area around the measurement pixel used in the correlation). Intuitively, following reasoning from experience with numerical techniques, a smaller correlation grid spacing and smaller subset size would be expected to produce more accurate results. However, this is not the case in DIC, thus implying that the overall accuracy of DIC metrology would benefit by selecting subset size and correlation point frequency depending on the strain field under observation. Such an adaptive parameter selection would be even more relevant when using DIC in three dimensions (termed Digital Volume Correlation, or DVC), where the computational cost is significantly increased over two-dimensional problems. Here we explore this idea of adaptive refinement by implementing a scheme for subset size selection and then applying it, first to a numerically defined test problem, and then to an actual experimental application. We investigate the relation between subset size and errors in DVC and propose an adaptivity parameter for subset refinement based on the norm of the gradient of the displacement gradient. This gradient parameter, which contains a significant amount of noise since it represents the second derivative of a discrete displacement field, is not used in a metrological sense, but only to determine areas where refinement is needed. In those areas, DVC is then re-computed with appropriately refined parameters and the results are merged with coarser analyses outside these areas. An application of the scheme to a compression experiment with a spherical inclusion in an elastic matrix is performed and shows increased result sensitivity in the region near the inclusion when parameter refinement is adaptively performed there.