Elimination of peak-locking error in PIV analysis using the correlation mapping method

Abstract

The peak-locking effect causes mean bias in most of the existing cross-correlation based algorithms for PIV data analysis. This phenomenon is inherent to the smooth curve-fitting through discrete correlation values, which is used to obtain the sub-pixel part of the displacement. Almost all of the existing effective methods to solve this problem require iterations. In this paper we introduce a new technique for obtaining sub-pixel accuracy, which bypasses the sub-pixel curve fitting, and eliminates the peak-locking effect, but does not require iterations. The principles of the ‘correlation mapping method’ (CMM) are based on the following logic: if one uses a bi-cubic interpolation to express the second image based on the first one and the unknown displacement, the correlation between them becomes a third-order polynomial of the displacement, whose coefficients depend on the first image. Matching this polynomial with the measured correlation provides an equation for the displacement for each point of the correlation map. A least-squares fit to the correlation values in the vicinity of the correlation peak (e.g. 5 × 5 points) provides an estimate for the particle displacement, including its sub-pixel part. We combine the new correlation mapping method with corrections for particle image distortion (PID) to further reduce the uncertainty in the velocity measurements. Three iterations typically achieve converged results. The CMM-PID method is tested using synthetic and experimental data. The peak-locking bias disappears in all cases. Even the ‘random’ error is substantially smaller than that obtained using a conventional sub-pixel curve fit. Issues related to streamline curvature and uncertainty in estimates of velocity gradients are also discussed.