Investigation, implementation, and comparison of fitting methods for sub-pixel analysis of particle displacement images

Particle image velocimetry (PIV) is an optical flow measurement technique, which is capable of measuring instantaneous flow velocity. In this method, visualized flow patterns by small tracer particles, which follow the fluid flow and reflect an incident light, is recorded by a camera successively, and an analysis of particle movements in the recorded images results in the velocity of flow field. Correlation analysis is commonly used for the analysis of particle shift images, in which the images are divided into smaller windows called interrogation windows. The common displacement vector of particles in each interrogation window is determined by correlation analysis, which in turn results in the displacement vectors for the entire image. The accuracy of this method is dependent on the estimation of the location of the maximum value of correlation with subpixel accuracy. The objective of this research is the evaluation of function fit methods to estimate of the correlation peak location with subpixel accuracy. For this purpose, parabolic curve and second order surface fitting are investigated theoretically and experimentally. To achieve definite displacements, deformation of a solid part under uniform loading is investigated instead of fluid flow and the displacement of point patterns painted on the solid surface are analyzed. The results show that both function fit methods are capable of resolving subpixel movements with the accuracy of 0.035 pixel or one micrometer in this research.