## 2 Experimental Implementation of DIC
### Speckle Choice and Characterization  
The image contrast, provided here by a speckle painting as the non-painted beam does not provide sufficiently pronounced gray level fluctuations, plays a central role in the DIC measurement accuracy. It is usually designed to be random, to avoid mismapping between patterns of similar shapes, even though a periodic pattern could also be considered by the CMV software (e.g., [19]). Periodic patterns are also easier to produce, and several methodologies are compared here. Indeed, as shown in several studies [14; 20; 21], the spot diameter directly affects the performance of the full-field measurements and the pattern size that can be used. Most of the speckles are made black on white. [PERSON] et al. [21] show four experimental speckles: two white on black and two black on white. The results show that the spots' size and distribution are more prominent than the colors of the spots and the background. In order to determine the quality of our speckle, three different ones were made on an aluminum piece: one with spray paint, which is the most-used technique [22], another with a black fine felt tip pen, and the last with a sponge. These three examples are visible in Figure 2a-c.  
To measure the error and the uncertainty of the measured in-plane displacements the procedure described in [16] is adapted to the present set-up. It consists in applying a slight magnification achieved by moving the camera, mounted on a linear translation stage with micrometer resolution, towards the target object. In this way the object seems to be bigger. Thus, the apparent transformation of the sample is homogeneous and the displacement measured at each point can be compared with the one expected. In this case the camera is translated 6 mm closer to the aluminum piece, so the homogeneous apparent deformation is about 0.5%, and the DIC is performed on a 350 px\({}^{2}\) square area with 50 patterns in both directions. The distribution of the subpixel displacement is shown on Figure 3 in the pen case. Here, the subpixel displacement is divided into ten parts. Figure 3 clearly indicates that the obtained distribution is quite homogeneous for each part. It is then possible to determine the systematic error (see Figure 4a-c) and the measurement uncertainty (see Figure 4d-f) [23] for the different speckles applied and for different pattern sizes (10, 15, 20, and 25 px\({}^{2}\)). The black horizontal line in Figure 4f represents the maximum value of the y-axis of Figure 4d,e. These figures represent, respectively, the means and the standard deviations of the error for each subpixel part. It can be concluded from Figure 4 that the speckle made using the pen is the most beneficial to our experimental configuration. Indeed, the systematic error is always less than 0.01 px in this case (Figure 4b), whereas it can be up to the order of 0.02 px for the speckles using spray paint and the sponge (Figure 4a,c respectively). The value of the measurement uncertainty is between 0.005 and 0.01 px for the speckle using a pen. As expected, the uncertainty decreases with the increase in the size of the patterns. The uncertainty obtained considering the spray paint speckle (Figure 4d) is slightly higher  
Figure 2: Experimental speckles on aluminum piece. and is much more important with the sponge speckle (Figure 4f). As the best results are obtained with the speckle realized with the pen, this technique was therefore chosen to be applied to the tested beam. We have also chosen patterns of 20 px\({}^{2}\) in order to, on the one hand, obtain a low uncertainty and, on the other hand, place several elements in the thickness of the beam. This leads to an accuracy of the DIC slightly lower than one hundredth of a pixel. As the ratio mm/pixel is equal to 0.125 in our images, a displacement measurement accuracy of 1.25 \(\upmu\)m is expected.