Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation

Many published research works regarding digital image correlation (DIC) have been focused on the improvements of the accuracy of displacement estimation. However, the original displacement fields calculated at discrete locations using DIC are unavoidably contaminated by noises. If the strain fields are directly computed by differentiating the original displacement fields, the noises will be amplified even at a higher level, and the resulting strain fields are untrustworthy. Based on the principle of local least-square fitting using two-dimensional (2D) polynomials, a 2D Savitzky-Golay (SG) digital differentiator is deduced and used to calculate strain fields from the original displacement fields obtained by DIC. The calculation process can be easily implemented by convolving the SG digital differentiator with the estimated displacement fields. Both homogeneous and inhomogeneous deformation images are employed to verify the proposed technique. The calculated strain fields clearly demonstrate that the proposed technique is simple and effective.