## 4 Results and Discussion  
### Effect of the PD Grid Spacing and PD Horizon Size  
Plots of the absolute maximum values of the \(\varepsilon_{x}\) and \(\varepsilon_{y}\) Lagrangian strains computed on in-house tensile experiment specimen surface by applying the DIC-PDDO method, as function of the PD grid spacing \(\Delta x\) when the PD horizon size is fixed to \(\delta=3.1\Delta x\), are presented in Figure 7. Each dot in Figure 7 represents the DIC-PDDO maximum absolute strain value at selected PD grid spacing \(\Delta x\), while the strain-PD grid spacing relation approximation with linear function is shown with dashed line. The same strain values calculated by the DIC algorithm for different setup values of the DIC VSG, are also plotted in Figure 7. The PD grid spacing \(\Delta x\), as parameter independent on the particular specimen dimensions, is expressed as number of specimen pixels (calculated according to the Equation (5)).  
The results in Figure 7 show that the maximum values of \(\left|\varepsilon_{y}\right|_{max}\), \(\left|\varepsilon_{x}\right|_{max}\) absolute maximum strains are achieved for the minimum setup values for the PD grid spacing (for the DIC-PDDO strain calculation) and DIC VSG size (for the DIC strain calculation). This is because more localized strain values are calculated by decreasing the PD grid spacing and the DIC VSG, avoiding thus the averaging effect when using larger PD grid spacing and DIC VSG.  
Moreover, the results from the DIC-PDDO and DIC converge when using the minimum setup values for the PD grid spacing and DIC VSG showing thus the potential of the PDDO to capture localized strain values (situation in which the DIC results are highly prone to noise/oscillations [12; 13; 14], also see Figure 1). Relative differences of 1.6% for the \(\varepsilon_{y}\) and 2.6% for the \(\varepsilon_{x}\) strain components are obtained between the PDDO and DIC calculations, for the minimum setup value of 1 px for the PD grid spacing and VSG = 57 px for the DIC VSG.  
The effect of the PD horizon diameter 28 (measured in pixels) on the PDDO-calculated strain values, and comparison against the values calculated for different VSG sizes is shown in Figure 8 for the PD grid spacing \(\Delta x=1\) px. The same way as in Figure 7, the dots in Figure 8 represent the DIC-PPDO maximum absolute strain value at different PD horizon diameters while the linear strain-PD horizon diameter relationship is shown with dashed line. Although the same PD horizon size \(\delta=m\Delta x\) can be achieved by taking different PD grid spacings \(\Delta x\) and multipliers \(m\), our study shows that the maximum absolute strain value correlated well to the PD horizon size independently of the PD grid spacing \(\Delta x\) selected to achieve a particular value of the PD horizon in Figure 8.  
Figure 7: Effect of the PD grid spacing \(\Delta x\) on the strain values computed on in-house tensile experiment specimen surface by the DIC-PDDO method (\(\delta=3.1\Delta x\)): (**a**) \(\varepsilon_{y}\) strains, (**b**) \(\varepsilon_{x}\) strains.  
Similarly to the conclusions of Figure 7, the results in Figure 8 show that the maximum values of the PDDO strains are obtained for the minimum values of the PD horizon size and DIC VSG size, based on reduced strain averaging effect. The effect of the PD horizon for the PDDO method can be compared to the VSG/strain filter for the DIC method, namely strains peaks smoothening and averaging over the size of the horizon/filter, and the convergence of the PDDO and DIC strains with reducing the PD horizon size and the DIC VSG size can be noticed in Figure 8, which suggests the same possibility of using the PDDO strain calculation method to capture localized strains, for the situation when strain oscillations are obtained based on reducing the DIC VSG (in this case strain filter) size.