Sub-pixel Analysis

A three-point curve fitting technique is used to calculate the `real' peak of the correlated results in both the correlation and MQD algorithms with sub-pixel accuracy. With this process, the sub-pixel accuracy is achieved in comparison to the accuracy of 0.5 pixel without the fit. The Gaussian function is used for the fitting in both the correlation and MQD algorithms. The formula is as following:

$$P_{sub} = i - \frac{1}{2} \frac{\ln C_{i+1} - \ln C_{i-1}}{\ln C_{i+1} - 2\ln C_{i} + \ln C_{i-1}}$$ (3)