## 1 The Technique and Origin of Digital Image Correlation (DIC)
The first case of no deformation was undertaken, to determine the minimum error that could be expected in the system, and this is now part of the standard procedure of DIC [4]. The second experiment consisted of translations of 500 \(\upmu\)m with a resolution of 87 pixels per cm (giving each translation at approximately 0.044 pixels) and the authors show good agreement between the actual and DIC results [3]. The third experiment the authors tried was rotation only, with ten rotations of 0.0157 radians, with two different subset sizes (\(50\times 50\) and \(20\times 20\) pixels). In this case, the authors reported that larger subset size gave an order of magnitude improvement in the standard deviation for the predicted results [3]. As the technique advanced, methods were described to increase the accuracy of displacement and gradient calculations in digital image correlation. [PERSON] and [PERSON] [5] described a more  
Figure 1: Example of an intensity pattern reconstructed using bilinear interpolation into a continuous form. Reproduced from [PERSON] et al. [1], with permission from Elsevier. robust algorithm when it is subjected to decorrelation and displacement gradients. The idea of the new technique is to cross-correlate sub-images digitally from two similar, but relatively displaced, speckle patterns and apply a maximum search routine near the correlation peak, in order to obtain sub-pixel accuracy. While the authors concede that the formula the authors present is more time consuming, it can be performed in the spectral domain, through the use of a Fourier transform, and is significantly faster in the spectral domain. The authors demonstrate that to obtain a greater than 80% success rate of their algorithm, the sub-image size should be at least 10 times the speckle size [5]. By adding a second camera and turning the imaging system into stereo, out-of-plane displacements can be quantified, allowing for an accurate measurement of the three-dimensional strain of the object surface. [PERSON] and [PERSON] [6] were the first to describe a three-dimensional DIC (3D DIC) technique and a calibration algorithm for such a system. The authors describe a physical model that relates points on an object with corresponding points in an image of that object. The shape of the object is measured by the cross-correlation of several sub-images from the two camera images, shown in Figure 2, through the algorithm described by [PERSON] and [PERSON]. The two cameras are oriented so that the optical lenses are in parallel. This means that each camera can view the same image as the other camera, by moving the camera perpendicular to its optical access. The difference in the image fields is predominantly due to the shape of the object, and in order to reconstruct the shape of the object, the system must be calibrated. The calibration routine should be (i) easy to use, (ii) with a calibration target that is easy to make, and (iii) it should give accurate results. [PERSON] and [PERSON] suggest a flat plate covered with a random dot pattern, that can move only in the z-direction (towards or away from the cameras), would satisfy the second requirement. The second calibration step would be to perform reference movements of the calibration plates. This is accomplished by moving the plate a known distance away from or towards the cameras and taking two sets of images, one before and one after the movement. The apparent movement due to the physical movement of the calibration plate is calculated for each camera. A least-squares optimization is then used to cross-correlate the apparent movement in one image, with the corresponding image from the other camera. To determine the accuracy of their 3D DIC method, [PERSON] and [PERSON] performed the rigid body translation of a small model car and rotation of a suspended cylinder.