Fourier-based interpolation bias prediction in digital image correlation

Abstract

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.

A Critical Comparison of Some Metrological Parameters Characterizing Local Digital Image Correlation and Grid Method

“…As far as images of grids of nominal pitch p are concerned, it is possible to further simplify Equation 52. The spectrum of grid images has been thoroughly studied in [45] by using the stationary phase method.…”

“…The nature of the function used to perform this interpolation strongly influences the amplitude of this phenomenon. This amplitude is therefore difficult to predict and a wide literature is available on this subject, see [50,51,52] for instance. Note that other strategies than back-deforming the current image in the reference coordinate system can be used while performing DIC (see the comprehensive review in [53]), but the presence of a systematic error is observed in all cases.…”

“…This is an unfavorable situation, which enhances the effect of Bias 1 for DIC, so the results presented here can be considered as an upper bound for DIC. There is a wide literature showing that better results are obtained with other types of interpolants [31,51,52], this bias being almost entirely cancelled out in certain cases. In Figure 1, we give for instance the result obtained with a cubic spline.…”

The Influence of Specimen Thickness on the Lüders Effect of a 5456 Al-Based Alloy: Experimental Observations

“…Direct images can be readily obtained using 3D-DIC. The accuracy of this method was determined through a coupling factor that takes into account the image noise, interpolation bias, and the calculation algorithm parameters [32]. Establishing the theoretical measurement resolution for high-gradient deformation conditions (e.g., within Lüders or the PLC band) is difficult.…”

Traceable technique for an in situ full field in-plane measurement validation of digital image correlation

“…While using digital screens as reference for DIC measurements has been done before, it has not been used for top-down quantification of the measurement error. 8 The method is fully described in European Patent Application EP 30 26 632 AP. 9 The core idea of the method is to make DIC measurements more acceptable in an industrial setting.…”