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

Abstract

The Peak-locking effect causes mean bias in most of the existing correlation based algorithms for PIV data analysis. This phenomenon is inherent to the Sub-pixel Curve Fitting (SPCF) through discrete correlation values, which is used to obtain the sub-pixel part of the displacement. A new technique for obtaining sub-pixel accuracy, the Correlation Mapping Method (CMM), was proposed by Chen & Katz [1, 2]. This new method works effectively and the peak-locking disappears in all the previous test cases, including applying to both synthetic and experimental images. The random errors are also significantly reduced. In this paper, an optimization of the algorithm is reported. Using sub-pixel interpolation, the cross-correlation function between image 1 and image 2 is expressed as a polynomial function with unknown displacement, in which the coefficients are determined by the autocorrelation function of the image 1. This virtual correlation function can be matched with the exact correlation value at every point in the vicinity of the discrete correlation peak (a 5×5 pixels area is chosen in the present study). A least square method is used to find the optimal displacement components that minimize the difference between the real and virtual correlation values. The performances of this method at the presence of background noise and out-of-plane motion are investigated by using synthetic images, as well as the influence of under-resolved particle images, and compared with the result of the SPCF method. The advantage of the CMM over SPCF is demonstrated in these studies.