Modeling the measurement accuracy of one-dimensional boundary subsets in digital image correlation

Abstract

Boundary subsets, which contain unwanted pixels from background image or other regions, generally occur at areas of vital mechanical importance. In this work, we establish a theoretical model characterizing the measurement accuracy of 1-dimensional boundary subsets, which explicitly expresses the retrieved displacement in terms of subset size, invalid pixels, shape function order, and underlying deformation field. Particularly, the transfer function of digital image correlation at boundary subsets is derived and verified, indicating possible amplification of amplitude and the existence of phase shift, which are quite different from standard full square subsets. Finally, the retrieved deformation near boundary is theoretically analyzed, and closed-form formulae are deduced for polynomial underlying displacements in consideration of the Weierstrass approximation theorem. To the author's knowledge, this is the first general mathematical model for boundary subsets, and paves the way for enhanced measurement accuracy.