The cross correlation function slides one curve in time across the other and returns a peak value when the curve shapes match.
2.
Where R _ { 12 } is the cross correlation function and k _ s is the originally found peak . k _ { int } is then used to find the displacement of scatterers after interpolation.
3.
There are generally two kinds of methods to obtain the sub pixel accuracy : interpolation methods, such as parabolic fit, and phase based methods in which the peak lag is found when the phase of the analytic cross correlation function crosses zero.