Fourier-based interpolation bias prediction in digital image correlation

Based on the Fourier method, this paper deduces analytic formulae for interpolation bias in digital image correlation, explains the well-known sinusoidal-shaped curves of interpolation bias, and introduces the concept of interpolation bias kernel, which characterizes the frequency response of the interpolation bias and thus provides a measure of the subset matching quality of the interpolation algorithm. The interpolation bias kernel attributes the interpolation bias to aliasing effect of interpolation and indicates that high-frequency components are the major source of interpolation bias. Based on our theoretical results, a simple and effective interpolation bias prediction approach, which exploits the speckle spectrum and the interpolation transfer function, is proposed. Significant acceleration is attained, the effect of subset size is analyzed, and both numerical simulations and experimental results are found to agree with theoretical predictions. During the experiment, a novel experimental translation technique was developed that implements subpixel translation of a captured image through integer pixel translation on a computer screen. Owing to this remarkable technique, the influences of mechanical error and out-of-plane motion are eliminated, and complete interpolation bias curves as accurate as 0.01 pixel are attained by subpixel translation experiments. (C) 2015 Optical Society of America