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Introducing Virtual DIC to Remove Interpolation Bias and Process Optimal Patterns

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Abstract

Background

Digital Image Correlation (DIC) is an image-based measurement technique routinely used in experimental mechanics, which provides displacement and strain maps of an observed surface/volume. The metrological performance of DIC has reached its limit which is directly determined by the texture of the imaged surface/volume.

Objective

This paper proposes a novel DIC strategy, which relies on a virtual image. This image, noiseless and of infinite resolution, is moreover optimized for providing measurements with the best metrological performance.

Methods

The so-called Virtual DIC retrieves the displacement fields by comparing this virtual image to the experimental images. No interpolation is required and processing optimal textures such as checkerboards is possible.

Results

Virtual DIC is first applied on synthetic images for comparison purposes with a usual DIC approach. Outstanding metrological performance is observed thanks to the possibility of processing checkerboard patterns.

Conclusions

The proposed Virtual DIC is twofold: (i) thanks to the use of a closed-form expression, built-in DIC operators are elaborated without recurring to noisy and poorly defined real images. Interpolation is therefore avoided; (ii) it makes possible it to process checkerboard patterns, which offers the best metrological performance.

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Acknowledgements

The authors acknowledge support from the ANR Grant ANR-18-CE08-0028-01. This work was also sponsored by the French government research program “Investissements d’Avenir” through the IDEX-ISITE initiative 16-IDEX-0001 (CAP 20-25), and from the AURA regional council.

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  1. Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, Clermont-Ferrand, F-63000, France

    Y. Shi, B. Blaysat, H. Chanal & M. Grédiac

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Correspondence to B. Blaysat.

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Appendix: Vocabulary and Definitions

Appendix: Vocabulary and Definitions

Three metrological parameters are discussed in this paper, namely the measurement resolution, the bias and the spatial resolution. Their definition, already given in [39, 52], are recalled below for the sake of complitness:

  • Measurement resolution: in Ref. [55], the measurement resolution is defined by the smallest change in a quantity being measured that causes a perceptible change in the corresponding indication. More precisely, it is proposed in [56] to define it as the change in quantity being measured that causes a change in the corresponding indication greater than one standard deviation of the measurement noise, which enables us to quantify the measurement resolution. This definition is quite arbitrary, any other (reasonable) multiple of the standard deviation being also potentially acceptable, but the idea is that the resolution quantifies the smallest change not likely to be caused by measurement noise [56].

  • Spatial resolution: the spatial resolution denoted by \(\ell _{\lambda }\) is defined here by the lowest period of a sinusoidal deformation that the technique is able to reproduce before losing a certain percentage \(\lambda\) of amplitude, this quantity being chosen a priori [57]. The advantage of this definition is that it is not based on an arbitrary value for the subset size in Local DIC or for the elements size in Global DIC. This makes it possible to compare the spatial resolution between these two techniques.

  • Bias:a systematic error generally occurs when a given technique returns actual details in displacement and strain maps. It is due to the fact that the amplitude of such apparent details is generally lower than the amplitude of the actual detail. This apparent “damping” is a bias, which can be quantified by considering a sinusoidal reference displacement field, and measuring the relative loss of amplitude exhibited by the displacement field returned by the technique under study, as suggested in Refs. [57,58,59,60]. Of course, the loss of amplitude depends on the frequency f of the sine function. This loss of amplitude is denoted here by l(f). In this context, the spatial resolution defined above is defined for a given bias \(\lambda\), the relation between \(\ell _{\lambda }\) and \(\lambda\) being that \(\ell _{\lambda }\) is the smallest value such that \(l(1/\ell _{\lambda })=\lambda\). We call here \(\lambda\) the bias of the method. This is a slight abuse of language since fixing \(\lambda\) does not mean that the damping of any displacement or strain field is actually equal to this \(\lambda\) value. Note finally that for DIC, the effect quantified here by \(\lambda\) is often referred to as the “matching bias”, because it occurs when there is a mismatch between the subset shape function used to describe the displacement within subsets on the one hand, and the degree of the actual displacement if the latter is described by a polynomial on the other hand.

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Shi, Y., Blaysat, B., Chanal, H. et al. Introducing Virtual DIC to Remove Interpolation Bias and Process Optimal Patterns. Exp Mech 63, 637–653 (2023). https://doi.org/10.1007/s11340-023-00941-2

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