Peaklocking errors:

The peaklocking effect is a well known bias of PIV, which tends to favor integer values for velocity components, measured in pixel displacements. Indeed the calculation of image correlation is influenced by the image discretization in pixels. Peaklocking is clearly visible in velocity histograms as a modulation with period unity (in terms of pixel displacement). This is visible on histograms of a single field, but time series provide better statistics. Pressing the button 'peaklocking' in the 'plotgraph' interface, we can compare the histogram with its smoothed version, obtained by a spline method which preserves the integral over each unit (curve plotted in red). The resulting systematic error $e(u)$ is also plotted in pixel displacement, see Fig. 7. This is the transform $u\to u+e(u)$ which converts the smoothed histogram, assumed for $u$ , into the observed one for the measured velocity $u+e(u)$ .

This error is rather small in this example, of the order of 0.1 pixel, even for civ1, but it is clearly reduced by civ2, see Fig. 7, lower part.

**Figure 7:** histogram from civ1 processing (upper left) compared to its smoothed interpolation (in red), and systematic error(upper right) for each velocity component, deduced from histogram comparison, expressed in pixel displacement ( civ1 pair -8|8). In the lower part, the same results are shown for civ3 with the pair -12|12. We observe a reduced peaklocking in comparison with civ1.
$\resizebox{0.48\textwidth}{!}{\includegraphics{histu_civ1.eps}}$ $\resizebox{0.48\textwidth}{!}{\includegraphics{error_civ1.eps}}$ $\resizebox{0.48\textwidth}{!}{\includegraphics{histo_civ2.eps}}$ $\resizebox{0.48\textwidth}{!}{\includegraphics{error_civ2.eps}}$