*2.2. Digital Image Correlation*

Digital Image Correlation is a well-developed and popular tool for evaluation of surface deformations [7,8,10]. It can also be used as a non-destructive method for full-field measurements of displacements of a tested specimen surface. DIC was developed at the University of South Carolina in the early 80s [33,34].

DIC works by processing images taken during the deformation of an object. Then it tries to establish a mapping between the image coordinates of the reference (undeformed) object image and the image coordinates of the deformed object image by searching for the mapping which gives the highest correlation between the reference image and the current image. The mapping is then used for calculating full-field strains [35].

The images are stored as a 2D matrix of pixels and each image is correlated with the reference (undeformed) image. The points of the grid based on the specified image subsets are matched and identified as that associated with the highest value of the correlation coefficient. This coefficient is calculated between the reference subset "f" and the target subset "g", whose dimensions are equal and are M×N pixels using the zero-mean normalized cross-correlation criterion defined in Equation (1). Illustration of the basic principle of digital image correlation is shown in Figure 4.

**Figure 4.** Illustration of the basic principle of the digital image correlation method: sketch of the subset (**a,c**) and measurement points on the surface of a specimen (**b,d**) before (**a,b**) and after (**c,d**) deformation [36].

$$\text{CC}^{\text{ZMM}} = \frac{\sum\_{i=1}^{M} \sum\_{j=1}^{N} \left[ \left( f(i,j) - u\_f \right) \times \left( g(i,j) - u\_\mathcal{S} \right) \right]}{\sqrt{\sum\_{i=1}^{M} \sum\_{j=1}^{N} \left( f(i,j) - u\_f \right)^2 \times \sum\_{i=1}^{M} \sum\_{j=1}^{N} \left( g(i,j) - u\_\mathcal{S} \right)^2}}, \tag{1}$$

where *uf* is the intensity of the reference subset and *ug* is the intensity of the target subset form.
