## 5 Summary and Conclusions  
The improvement of the DIC strain calculation algorithm based on the PDDO was analyzed in this study. Several conclusions can be underlined based on our results.  
1. Although displacements can be directly and accurately measured by DIC, the strain field requires additional post processing-numerical differentiation. This mathematical operation is problematic in the case of discrete displacement field measured by the DIC in the case of high strain gradients, and also induces noise in the calculated strains. Because of this, there is a need for better differentiation algorithms for the raw displacement data provided by the DIC. The PDDO based on the PD theory integral equations offers an alternative approach to cope with the aforementioned numerical differentiation issues. A differentiation algorithm based on the integro-differential PDDO can be formulated and applied to the DIC displacement field for strain calculation.
2. The PDDO strain calculation method was validated considering the synthetic images from DIC Challenge [11] and in-house experimental measurements. The PDDO-calculated strains and DIC-calculated strains converge to each other, and to the FE validation calculated strains, when reducing the PD grid spacing and PD horizon size for the PDDO calculation, and the DIC VSG size for the DIC calculation. Based on the PDDO evaluation using MEI, the proposed strain calculation method for DIC resulted in at least 40% lower MEI values and thus at the same time better performance than conventional DIC algorithm used in VIC-2D software. Moreover, the PDDO method efficiency is prone to be increasing for the case of localized strains (e.g., when high spatial resolution is required).
3. Analysis of both synthetic and experimental DIC images showed that the PDDO method can effectively reduce the effect of the noisy input (displacement) data on the calculated strain field, while the DIC method of strain evaluation amplifies the effect of the input data of the calculated strains. Moreover, the PDDO method has the ability to preserve the accuracy of the strain results calculated based on oscillatory/noisy input data, while the DIC strain filter smooths out the localized strain values (high strain gradients).
4. Reducing the DIC VSG size induces oscillations for the DIC-calculated strain fields and then high strain gradients cannot be effectively captured by the DIC. The aforementioned problem can be solved applying PDDO method to DIC displacement field calculated with the same small VSG size, and owing to the PDDO method DIC measurements spatial resolution can be increased without changing the DIC setup (speckle size, cameras).  
Conceptualization, T.V., P.G. and A.A.; formal analysis, T.V., P.G., and A.A.; investigation, T.V. and P.G.; methodology, T.V., P.G. and A.A.; software, T.V.; writing--original draft, T.V.; writing--review and editing, T.V., P.G. and A.A. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Research Council of Lithuania (Project CompExSHM No.: P-MIP-19-523).  
Data Availability Statement: Not applicable.  
The laboratory equipment preparation was performed by [PERSON].