Subsample interpolation bias error in time of flight estimation by direct correlation in digital domain

Automatic simultaneous measurement of phase velocity and thickness in composite plates using iterative deconvolution

“…Thus, in this context, the peak position of the cross-correlation function will provide the best estimate of the TOF [26].…”

“…4 insert): In ideal case sinc function should be used for the TOF estimation between samples, but it is not possible in real time application. Although several truncated interpolation techniques exist [25,27], cosine fitting techniques have recently demonstrated to produce the smallest bias error [26]. According to [26,27], the estimated subsample shift that should be added is given by the following expression:…”

“…This procedure can achieve a resolution in the order of picoseconds [26], while maximum resolution achieved using centroid is in the order of nanoseconds [27], thus an improvement in the thickness and phase velocity measurements is expected. Furthermore, due to matched filter properties to align the frequency components of the phases, cross-correlation method is less sensitive to dispersion than centroid based methods [24,26].…”

“…Furthermore, due to matched filter properties to align the frequency components of the phases, cross-correlation method is less sensitive to dispersion than centroid based methods [24,26].…”

“…Now, the cross-correlation result is shifted using the T OF T W calculated previously in order to avoid the 2mπ ambiguity in the phase. To take advantage of the accuracy achieved in T OF T W calculation, time shift is performed in a subsample basis using the frequency domain [26,28,29], so that the shifted version of x T W (t) is calculated as:…”