## 2 Experimental Analyses Performed by DIC
The extrinsic parameters consist of the rotation matrix \(\mathbf{R}\) and translation vector \(\mathbf{t}\). The centre of the camera's coordinate system is located in its principal point, and the camera's image plane is defined by its coordinate system axes. Since the pinhole camera model does not consider lens distortion, to accurately estimate the 3D coordinates of the object surface points using a real camera, the radial \(\alpha_{\rm r}\) and tangential \(\alpha_{\rm t}\) lens distortion parameters must also be determined (Figure 4). These can then be used to modify the distorted image using relations:  
\[ \begin{split} x_{\rm d}&=x\Big{[}1+k_{1}\big{(}x^{ 2}+y^{2}\big{)}+k_{2}\big{(}x^{2}+y^{2}\big{)}^{2}+k_{3}\big{(}x^{2}+y^{2}\big{)} ^{3}\Big{]},\\ y_{\rm d}&=y\Big{[}1+k_{1}\big{(}x^{2}+y^{2}\big{)} +k_{2}\big{(}x^{2}+y^{2}\big{)}^{2}+k_{3}\big{(}x^{2}+y^{2}\big{)}^{3}\Big{]}, \end{split}  \tag{4}\]  
where \(k_{1}\), \(k_{2}\), \(k_{3}\) are the coefficients of lens radial distortion, or  
\[ \begin{split} x_{\rm d}&=x+\big{[}2p_{1}xy+p_{2} \big{(}3x^{2}+y^{2}\big{)}\big{]},\\ y_{\rm d}&=y+\big{[}p_{1}\big{(}x^{2}+3y^{2}\big{)} +2p_{2}xy\big{]},\end{split}  \tag{5}\]  
where \(p_{1}\), \(p_{2}\) are the coefficients of lens tangential distortion. In the case of Dantex Dynamics correlation systems calibration, only \(p_{1}\), \(p_{2}\) and \(k_{1}\), \(k_{2}\) coefficients are determined. The \(k_{3}\) coefficient is only used when severe curvatures arise, e.g., in the case of wide/angle lenses. The calibration of the cameras of the Q-400 Dantec Dynamics correlation system was realised by three different calibration targets with \(9\times 9\) checkerboard fields. In the first  
Figure 4: Effect of radial and tangential distortion on the position of the registered surface point. Figure 3: A transformation from the 3D world coordinates of the analysed object to the 2D pixel coordinates of the image. case, each array had an edge length of 1.5 mm (Figure 5a). In this case, the area of the target in the calibration mode, which is performed at the full resolution of the cameras (2452 \(\times\) 2056 px), covered approximately 12.5% of the field of view. In addition, the authors also performed calibration of the camera system using targets with edge lengths of 2.0 mm (Figure 5b) and 3.0 mm (Figure 5c). The middle of the targets covered approximately 22% of the field of view. The largest covered approximately 50% and almost perfectly copied the evaluated part of the sample. It should be mentioned that the targets with field sizes of 1.5 mm and 3.0 mm were supplied by the manufacturer. They are made by etching in ceramic material with very high precision, guaranteeing a nominal X/Y Standard Deviation of up to 1 \(\upmu\)m [45]. In contrast, a 2.0 mm field size target was prepared by authors, printing on a vinyl film applied to a glass plate with an expected standard precision (nominal X/Y standard deviation of up to 150 \(\upmu\)m) to analyse the measurement inaccuracies arising in such a case. During the calibrations of the cameras performed by three different targets, calibration files containing information about the cameras' intrinsic and extrinsic parameters and the distortion of their lenses, respectively, were sequentially acquired. The first stored file contained the information obtained by evaluating five positions of the calibration target, i.e., the number of positions after which the system estimates for the first time the calibration parameters of the cameras. The last file contained the calibration parameters estimated from 25 different calibration target positions, i.e., the maximum number allowed by the Istra4D V.4.3.0 software. Thus, 21 different calibration files were acquired for each calibration (63 in total) and subsequently used to evaluate the analyses performed.