An analytical study on the low-pass filtering effect of digital image correlation caused by under-matched shape functions

The low-pass filtering effect, which stems from undermatching of shape function, sincerely affects the metrological performance of digital image correlation, especially for localized deformations. Here, we build a theoretical model characterizing the low-pass filtering effect, which explicitly expresses the measured displacement in terms of subset size, shape function order, and underlying deformation field. Based on the model, we derive formulae for transfer function of digital image correlation and study the attenuation of Gaussian displacement fields. These results provide a deep insight into shape function undermatching and open up new possibilities for compensating the low-pass filtering effect.