## 3 DIC Method for Deformation Measurement  
Measurement of deformations according to the DIC method is performed with the use of a stochastic contrast dot pattern, which must have been previously applied to the test area [10]. In general, the method includes tracking the relative position of each point during deformation. Thus, the authors in [10] note that the specific image can be represented as a matrix of natural numbers. Accordingly, the areas of white correspond to the number 0, and black to \(-100\). Taking into account that a single number will not be unique in the matrix, it is appropriate to consider a certain subset of adjacent numbers (area of dots or pixels). This area usually takes the form of a square with a side of 10-50 pixels, and due to the fact that it includes several points with different variations of the gray level, the set of different correlation areas is obtained. (see Figure 2). The center of each such subset is considered as the measuring (reference) point. For each subset, the position of the point is tracked, and the coordinates on the sequentially obtained images are determined. The fundamental principle used in the DIC method is to match the physical point on the reference image with its position on the images of the deformed surface [10; 60]. As shown in Figure 1, the area around a particular pixel can be indicated an area of arbitrary shape, within which the distribution of shades will be unique (the speckle). After that, according to an algorithm using the appropriate software, the plot with the same distribution of pixel shades is found. During the correlation process, subsets of numbers are shifted until the pattern on the deformed image best matches the reference image, which is determined by the total difference in the gray levels of each point [60]. Good pattern determines the possibility to make the correlation with high confidence and low noise level. In the DIC method, the determination of the parameters of the dot pattern (the speckle) is one of the main factors that can reduce the total measurement error and improve the overall result [61]. The main requirements that need to be met by the pattern applied to the surface are given in [62; 63] and include the following: high contrast of the pattern, the degree of filling of the surface with the pattern by 50-70%, isotropy and randomness. The optimal size of the points is determined for each case of the study, according to the method described in [63]. General pattern requirements are given on Figure 3.  
Figure 2: The principle of tracking the relative position of the subset with different variations of the gray level (I) in the DIC method. Among the parameters of the experimental setup are the following (see Figure 4): camera resolution (c \(\times\) r, pixels), width (w, mm) and height (h, mm) of the studied area, the focal length of the camera (f, mm) and the distance from the camera to the sample (d, mm). Focal length is a variable parameter that allows the researcher to adjust the distance to the image and increase the sharpness of the studied area display. The resolution (\(c\times r\)) is a technical characteristic of a digital camera and determines the dimension of the digital image (columns \(\times\) rows). Using the previously accepted values of \(c\times r\) and the size of the studied area (\(h\times w\)), the size of the physical surface, which is displayed by one pixel of the digital image could be obtained [63]:  
\[\xi_{w}=\frac{w}{c}, \tag{1}\]  
\[\xi_{h}=\frac{h}{r}. \tag{2}\]  
Values \(\xi_{w},\xi_{h}\) determine the width and height of the area of the physical surface that corresponds to one pixel of the digital image and are assumed as the equal (\(\xi_{w}=\xi_{h}=\xi\)). It is important to note, that in most modern digital cameras, the resolution of \(c\times r=4\times 3\) (\(3\times 2\)) is used. Therefore, the most effective use of pixel image is achieved if \(h/w=1.33\).