The performance of seven different correlation functions applied in Digital Image Correlation has been investigated using simulated and experimentally acquired laser speckle patterns. The correlation functions were constructed as combinations of the pure intensity correlation function, the gradient correlation function and the Hessian correlation function, respectively. It was found that the correlation function that was constructed as the product of all three pure correlation functions performed best for the small speckle sizes and large correlation values, respectively. The difference between the different functions disappeared as the speckle size increased and the correlation value dropped. On average, the random error of the combined correlation function was half that of the traditional intensity correlation function within the optimum region.