## 2 Digital Image Correlation (DIC) System  
The following processes should be executed to acquire the displacement and strain of a material by applied force per unit time with Digital Image Correlation (DIC) method: (1) The reference image should be obtained and should not be deformed; (2) deformed image should be taken; (3) digital image correlation coefficients should be determined between two images to use for brightness distribution; (4) displacement and strain should be computed with position data of (by) the DIC coefficient results. The minimum unit of brightness distribution for correlation comparison is called subset image [17]. The size of subset image is (2n + 1) by (2n + 1) of square shape. The reference subset image is the image separated from reference image, and the deformed subset image is the image separated from the deformed image. The center of reference subset image is the tracking position for material displacement. The same deformed subset image to reference subset image is determined by finding out the highest correlation coefficient between two reference and deformed subset images, which is comparison iteration. If determined by computation, the distance between two centers of those images should be the displacement of specimen deformation by applied force. Additionally, the displacement vector is calculated by the coordinates of two centers and, finally, the displacement and strain of material are driven by several equations. Figure 1 shows the basic measurement principle of the DIC.  
There are two methods to analyze the image correlation: one is to use the cross-correlation (CC) criterion, and the other is to apply the sum of squared differences (SSD) criterion. These methods measure the brightness values of spots on the image for analysis [18; 19]. The CC criterion uses the maximum value of the highest correlation from the calculation. In contrast, the SSD criterion uses the minimum value of the highest correlation [20; 21; 22]. Table 1 shows commonly used cross-correlation criteria and their definitions, and Table 2 shows those for the sum of squared differences criteria. Two more equations can be adopted for each criterion by averaging or normalizing the brightness  
Figure 1: The principle of measuring the displacement by using the digital image correlation method.  
distribution. The equations for zero-normalized cross-correlation (ZNCC) and zero-normalized sum of squared differences (ZNSSD) have a mutual conversion.  
where  
\[f_{m} = \frac{1}{(2M+1)^{2}}{\sum\
olimits_{i=-M}^{M}{\sum\
olimits_{j=-M}^{M}{f( x_{i},y_{j})}}} \tag{1}\] \[g_{m} = \frac{1}{(2M+1)^{2}}{\sum\
olimits_{i=-M}^{M}{\sum\
olimits_{j=-M }^{M}{g(x_{i}^{\prime},y_{j}^{\prime})}}}\] (2) \[\overline{f} = \sqrt{{\sum\
olimits_{i=-M}^{M}{\sum\
olimits_{j=-M}^{M}{f(x_{i}, y_{j})}}}^{2}}\] (3) \[\overline{g} = \sqrt{{\sum\
olimits_{i=-M}^{M}{\sum\
olimits_{j=-M}^{M}{g(x_{i}^ {\prime},y_{j}^{\prime})}}}^{2}}\] (4) \[\Delta f = \sqrt{{\sum\
olimits_{i=-M}^{M}{\sum\
olimits_{j=-M}^{M}{\left[{f( x_{i},y_{j})-f_{m}}\right]}}}^{2}}\] (5) \[\Delta g = \sqrt{{\sum\
olimits_{i=-M}^{M}{\sum\
olimits_{j=-M}^{M}{\left[{g( x_{i}^{\prime},y_{j}^{\prime})-g_{m}}\right]}}}^{2}} \tag{6}\]