## 2 Experimental Analyses Performed by DIC  
The analyses described in the paper were carried out on a specimen with a hole (Figure 1), made by water jet machining of PS-1 sheet (Vishay Measurements Group GmbH, Heilbronn, Germany) with 3 mm thickness, the material of which has a modulus of elasticity \(E=2500\) MPa and Poisson's ratio \(\mu=0.38\). Tensile loading of the specimen was performed by a Universal Testing Machine WDW-5 with a loading rate of 2 mm/min up to a maximum loading force of \(F_{\mathrm{max}}=1800\) N. Throughout the loading period, images were captured by a stereo-camera correlation system Q-400 Dantec Dynamics with a sampling frequency of \(F_{s}=1\) fps. The whole  
Figure 1: Dimensions (mm) and shape of the specimen with the cameras’ field of view marked. process of image acquisition, camera calibration, and correlation of the images was carried out in the Istra4D V.4.3.0 software delivered with the correlation systems Dantec Dynamics. This version of the software uses for image correlation an algorithm based on a pseudo-affine coordinates transformation according to the following relations:  
\[ \begin{array}{l}u(a_{0},\,a_{1},\,a_{2},\,a_{3},\,\widetilde{x},\,\widetilde{y })=a_{0}+a_{1}\cdot\widetilde{x}+a_{2}\cdot\widetilde{y}+a_{3}\cdot\widetilde{ x}\cdot\widetilde{y},\\ v(a_{4},\,a_{5},\,a_{6},\,a_{7},\,\widetilde{x},\,\widetilde{y})=a_{4}+a_{5} \cdot\widetilde{x}+a_{6}\cdot\widetilde{y}+a_{7}\cdot\widetilde{x}\cdot \widetilde{y},\end{array}  \tag{1}\]  
where \((u,\,v)\) are transformed coordinates, \((\widetilde{x},\,\widetilde{y})^{T}\) are lens-distorted 2D coordinates of the point in the normalized image plane and parameters \(a_{0}-a_{7}\) represent possible displacement, elongation, shear, and distortion of the facet according to Figure 2.  
The post-processing of the results obtained for four different loading levels of the specimen (\(F=400\) N, \(F=800\) N, \(F=1200\) N, and \(F=1600\) N) was realised either using the MOSTRAN V.1.0 program, developed at the authors' department, or in MATLAB R2020a (MathWorks, Natick, MA, USA). Experimental Analysis of the Influence of Calibration Parameters on the Results of Strain/Stress Analysis  
The reconstruction errors are related to the accuracy of the evaluation of the so-called imaging (calibration) parameters determined in the online calibration procedure integrated into the control software of the correlation system. The Dantec Dynamics correlation systems use a calibration method developed at the turn of the 20 th and 21 st centuries by [PERSON] [43; 44]. The principle of this method is based on projection geometry (pinhole camera model). It uses a specific technique of recording calibration targets (planar plates with a precisely defined geometry) from different angles of view and rotation to obtain the intrinsic and extrinsic parameters of the cameras. The extrinsic parameters express the transformation from the 3D world to the 3D camera coordinate system. The intrinsic parameters represent the projective transformation from the 3D camera to the 2D image coordinates (Figure 3). The dependence between the pixel coordinates \((x,\,y)\) of the image and the coordinates \((X,\,Y,Z)\) of the analysed specimen surface points is given by the relation:  
\[ \begin{pmatrix}x\\ y\\ 1\end{pmatrix} =\mathbf{K}[\mathbf{R}\,|\,\mathbf{t}] \begin{pmatrix}X\\ Y\\ Z\\ 1\end{pmatrix} , \tag{2}\]  
where the term \(\mathbf{K}[\mathbf{R}\,|\,\mathbf{t}]\) expresses the camera's matrix mapping a 3D world scene into the 2D image plane. The intrinsic camera's matrix \(\mathbf{K}\) is defined as follows:  
\[\mathbf{K}= \begin{bmatrix}f_{x}&s&c_{x}\\ 0&f_{y}&c_{y}\\ 0&0&1\end{bmatrix} , \tag{3}\]  
Figure 2: Transformation parameters used in the algorithm based on pseudo-affine transformation. where \(\left(f_{\rm x}\right.\)\(f_{\rm y}\)) represent the focal lengths (px) of both cameras, \(s\) is the distortion coefficient, \(\left[c_{\rm x}\right.\)\(c_{\rm y}\)\(\left.\right]\) are the camera's principal point coordinates (px).