## 1 The Technique and Origin of Digital Image Correlation (DIC)  
DIC is a method by which strain fields can be recorded across the surface of object as it deforms, without the need for strain gauges or other contact methods that may interfere with the deformation. This is accomplished by taking digital images of a random, high-contrast speckle pattern on the surface of the object. As the object deforms, the pattern on the surface also deforms and the changes in the pattern can be used to quantify the strain the object undergoes. The method to carry out digital image correlation was first described in 1983 by [PERSON] et al. [1]. The authors described a method of taking digital images of an object prior to and post deformation and using the generated light intensity levels to convert the discrete data into a continuous form via a surface fit, shown in Figure 1. Due to the limits of computer technology in the 1980s, the overall images were broken down into small subsets for processing by the algorithm that the authors describe. The algorithm takes the subsets of the pattern pre-deformation and correlates them to the same subsets in the post-deformation surface. By using the algorithm that the authors describe, [PERSON] et al. were able to successfully measure beam deflections greater than 0.1 pixels [1]. This method does require a couple of basic assumptions; (i) the pattern deforms exactly as the surface of the pattern, (ii) the light intensity patterns of the pre- and post-deformation surface have a unique one-to-one correspondence with the respective pre- and post-deformation surfaces [2]. In two-dimensional DIC, there is also a requirement that any out-of-plane displacement does not affect the in-plane deformation or displacement of the characteristic intensity surfaces and any derivatives of the out-of-plane displacement are significantly smaller than the derivatives of the in-plane displacements [2]. This is due to the deformation theory, described in [1], demonstrating that the observed intensity pattern is a two-dimensional projection of the object onto a plane [2]. [PERSON] et al. [2] took the algorithm described in [1] and conducted a number of experiments to determine the accuracy of the system in three situations, (i) uniform translation, (ii) rigid body rotation, and (iii) uniform finite-strain test. The authors also compared the use of two different interpolation methods in the conversion of the discrete intensity map from the camera into continuous data; bi-linear and polynomial interpolation. The authors reported that the displacement components were within reasonable accuracy for both interpolation methods for the uniform translation experiments, while the rotation cases only agreed well (less than 4% error) for cases below 6 degrees of rotation. The last test the authors reported on found that the results for the uniform finite-strain test were very dependent on the image resolution, with large image resolution giving results between \(-18\%\) to \(8\%\), but lower resolutions giving up to \(-136\%\) error [2]. In order to increase the accuracy of the DIC method, [PERSON] et al. [3] explored, using the Newton-Raphson method of partial differential corrections to increase the accuracy of displacement and gradient calculation. The Newton-Raphson method is based on the calculation of correction terms that improve the initial guesses of the DIC algorithm. By using the displacement of the subset centre, estimated to within one pixel, the algorithm is less likely to find a local minimum and more likely to find the absolute minimum. The authors also found that the Newton-Raphson method reduced computational time, when compared to the previously described coarse-fine search method. To evaluate the accuracy of the Newton-Raphson method in predicting displacement and gradient terms, the authors used three cases: (i) no deformation, (ii) translation only, and (iii) rotation only [3].