## 2 Digital Image Correlation Technique
### Working Principle of the DIC Technique  
For mechanical performance tests, DIC works to obtain micro details of targeted process information including local and average strain and displacement. To achieve this, DIC processes the digital images collected during physical experiments through image processing techniques and statistical cross-correlations. More specifically, as in Figure 1a, it first defines the specific pixel intensity subsets referring to the small regions of interest on the raw pre-deformation image and then, as in Figure 1b, the cross-correlations between pre-deformation and post-deformation are computed. With the pre-deformation image as the reference, best cross-correlation coefficients between the subsets, which define the fundamental computing units in DIC, on pre-deformation and post-deformation images are calculated to seek the mapping correspondences between subsets. After the mapping process, displacements are calculated for each subset center point to get the information of full-field deformation. Strains are then calculated based on the obtained information on displacements, as in Figure 1c. Among many options, the standardized covariance correlation function [22; 23] definesan alternative approach for the computation of the two-dimensional discrete correlation \(C(u,v)\) (Equation (1)):  
\[C(u,v)=\frac{\sum\limits_{x=-M}^{M}\sum\limits_{y=-M}^{M}[f(x,y)-f_{m}][g(x+u,y+ v)-g_{m}]}{\sqrt{\sum\limits_{x=-M}^{M}\sum\limits_{y=-M}^{M}[f(x,y)-f_{m}]^{2}} \sqrt{\sum\limits_{x=-M}^{M}\sum\limits_{y=-M}^{M}[g(x+u,y+v)-g_{m}]^{2}}} \tag{1}\]  
where \(f(x,y)\) and \(g(x+u,y+v)\) represent the grey-scale function values of all the pixels on the images taken before and after deformation (\(x,y\) indicate point locations prior to deformation.); \(f_{m}\) and \(g_{m}\) are the average grey-scale values of image subsets; \(u\), \(v\) mean the displacement values in the center of relevant subset in terms of pixels.  
This assumes that maximum correlations indicate correspondence [24]. That is, for a specific pre-deformation subset, the subset on the post-deformation image having the largest correlation with this designated subset, is regarded as its counterpart after deformation. The corresponding matching accuracy can be in the order of 0.01 pixels. By contrasting the counterpart pairs on pre- and post-deformation images, the desired deformation information at all points can finally be derived. The full-field strain can further be estimated based on the deformations of all these individual points.  
In general, the DIC method uses charge-coupled device (CCD) camera systems with specific resolutions to record the images for the irregular distribution profiles of speckles on the surfaces of specimens before and after deformations. These digital images are then processed and analyzed using the chosen numerical methods to acquire such process information as displacement and strain. For image shooting, additional lighting sources may be required where natural lights are not capable of providing enough luminance. The demand of lighting intensity depends on the quality requirements of images taken by the CCD. In addition, for the use of DIC, the cross-correlation calculation requires detailed information of randomly scattered speckles on the surfaces of studied objects. As such, when natural speckles are of insufficient utility, extra speckles can be artificially created by painting the targeted surfaces in either black or white [25].