Theoretical estimation of interpolation bias error in digital image correlation

The popularity of digital image correlation technique have pointed out the urgent need to establish standard assessment criterion of speckle pattern quality, namely, the development of standard procedure to assess the metrological performance of various digital speckle patterns. The magnitude of digital image correlation calculation error due to sub-pixel interpolation (interpolation bias error) is an important parameter to evaluate the quality of speckle. However, there is no available method to estimate interpolation bias efficiently at present. In this paper, frequency method is employed to obtain the analytical expression of interpolation bias error. Band-limited and sinusoidal approximation forms are attained when sampling theorem is satisfied. The sinusoidal variation of interpretation bias error with respect to sub-pixel shift is explained. Based on sinusoidal approximation form of interpolation bias, this work introduces the concept of interpolation bias kernel. Interpolation bias kernel, which characterizes frequency bias response of specific speckle frequency, is exploited to decide the merits of the interpolation algorithm for correlation matching algorithm. Based on these theoretical results, this paper presents a method to estimate the interpolation bias error by speckle spectrum and interpolation bias kernel. This simple and effective algorithm has obvious speed advantage compared to traditional translation methods, and the simulation is conducted to verify this method. This work explains the inherent nature of interpolation bias and solves the problem of efficient interpolation bias estimation. This work could be used in interpolation optimization and filter size selection and contribute to the establishment of speckle quality assessment criterion as well. © 2016, Editorial Office of Chinese Journal of Theoretical and Applied Mechanics. All right reserved.