Minimizing the total strain error in point-wise least squares using rotated gaussian weight strain filter (RGW-SF) in digital image correlation

The point-wise least squares (PLS) has been widely accepted as a simple and trustworthy strain computation method that smooths and differentiates the noisy displacement field calculated directly by digital image correlation (DIC). Smooth window size and kernel function need to be determined before using PLS. The selection of the proper smooth window size has long been a tricky issue for practitioners, which has an obvious impact on the final total strain error of complex deformation. A small smooth window may reduce the system/bias error but increase the random error, and vice versa. In this paper, a rotated Gaussian weight strain filter (RGW-SF) is proposed for heterogeneous strain field measurement. The motivation of RGW-SF is to adapt the weights of each point in tradition PLS smooth window to obtain lower total strain error, which is derived and then minimized to select an optimum strain filter with three weight parameters (i.e., sigma(x), sigma(y), theta). The effectiveness of the proposed RGW-SF is verified using simulated sinusoidal deformation images and the Star 6 image set from DIC-challenge 2.0. Experiments show that the RGW-SF can find a trade-offbetween the system error and the random error. The displacement and strain field accuracy, especially for the metrological efficiency indicator, by RGW-SF is much better than that of the PLS and the self-adaptive strain algorithm (SSA). The proposed RGW-SF is strongly suggested for unknown severely heterogeneous strain measurement.