Systematic errors in two-dimensional digital image correlation due to lens distortion

Lens distortion practically presents in a real optical imaging system causing non-uniform geometric distortion in the recorded images, and gives rise to additional errors in the displacement and strain results measured by two-dimensional digital image correlation (2D-DIC). In this work, the systematic errors in the displacement and strain results measured by 2D-DIC due to lens distortion are investigated theoretically using the radial lens distortion model and experimentally through easy-to-implement rigid body, in-plane translation tests. Theoretical analysis shows that the displacement and strain errors at an interrogated image point are not only in linear proportion to the distortion coefficient of the camera lens used, but also depend on its distance relative to distortion center and its magnitude of displacement. To eliminate the systematic errors caused by lens distortion, a simple linear least-squares algorithm is proposed to estimate the distortion coefficient from the distorted displacement results of rigid body, in-plane translation tests, which can be used to correct the distorted displacement fields to obtain unbiased displacement and strain fields. Experimental results verify the correctness of the theoretical derivation and the effectiveness of the proposed lens distortion correction method.