A Correlation Mapping Method to Eliminate the Peak-Locking Effect in PIV Analysis

Abstract

“Peak-locking” causes deterministic mean measurement bias in most of the existing cross-correlation based algorithms for PIV data analysis. This phenomenon is inherent to the typical smooth curve-fitting through discrete correlation values which are used to obtain the sub-pixel accuracy in velocity. In this paper we introduce a new algorithm/method for obtaining the sub-pixel accuracy, which eliminates the peak-locking effect. We refer to this procedure as “correlation mapping method”. In an ideal case, the second exposure (image 2) in a PIV measurement can be regarded as a mapping of the first exposure (image 1) where the mapping rules are affected by displacement, deformation, out of plane motion, etc. The correlation mapping method is based on shifting of image 1 by certain sub-pixel value, thus generating a virtual image (2′), whose gray level can be expressed in terms of the original image and the sub-pixel displacement. Thus, the correlation map of images 1 and 2′ is also a function of the intensity distribution in image 1 and the displacement. This correlation map is matched with the measured correlation map of images 1 and 2, providing a system of equations, one for discrete point in the correlation map with the sub-pixel values as unknowns. Solving these equations for each point in the vicinity of the correlation peak generates a series of sub-pixel displacements. Least square fitting is then used to determine the sub-pixel displacement with minimal difference between the real and virtual correlation values. This method is applied to several experimental and synthetic flow image pairs. In most cases the results show substantial improvements in sub-pixel accuracy in comparison to other algorithms and it eliminates the peak locking bias.