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

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## Abstract

The main metrological performance of two full-field measurement techniques, namely local digital image correlation (DIC) and grid method (GM), are compared in this paper. The fundamentals of these techniques are first briefly recalled. The formal link which exists between them is then given (the details of the calculation are in Appendix 1). Under mild assumptions, it is shown that GM theoretically gives the same result as DIC, since the formula providing the displacement with GM is the solution of the minimization of the cost function used in DIC in the particular case of a regular marking. In practice however, the way the solution is found being totally different from one technique to another, they feature different metrological performance. Some of the metrological characteristics of DIC and GM are studied in this paper. Since neither guideline nor precise standard is available to perform a fair comparison between them, a methodology must first be defined. It is proposed here to rely on three metrological parameters, namely the displacement resolution, the bias and the spatial resolution, to assess the metrological performance of each technique. These three parameters are thoroughly defined in the paper. Some of these quantities depend on external parameters such as the pattern of the surface of interest, so the same set of grid images is processed with both techniques. Only the contribution of the camera sensor noise to the displacement resolution is considered in this study. The displacement resolution, the bias and the spatial resolution are not independent but linked. These links are therefore studied in depth for DIC and GM and compared. In particular, it is shown that the product between the displacement resolution and the spatial resolution can be considered as a metric to perform this comparison. The extension to speckled patterns of the lessons drawn from grids is finally addressed in the last part of the paper. As a general conclusion, it can be said that for the value of the bias fixed in this study, the additional cost due to grid depositing offers GM to feature a better compromise than subset-based local DIC between displacement resolution and spatial resolution.

### Keywords

Digital image correlation Displacement Full-field measurement Grid method Metrology Strain## Notes

### Acknowledgments

The GDR CNRS ISIS is gratefully acknowledged for its partial financial support of this study (TIMEX project).

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