Finite Difference Approximation of Spatial Gradient in Spatio-Temporal Derivative Method for PIV Sub-Pixel Analysis

Some calculation schemes of spatial gradient for the spatio-temporal derivative method, which was used for sub-pixel displacement detection in PIV measurements, were evaluated. It was found that the second-order central finite difference scheme tends to underestimate the gradient of tracer-particle's intensity, so that it leads to overestimation of sub-pixel displacements. In this study, a combined upstream and downstream finite difference scheme was proposed and evaluated for one-dimensional flow measurements. Furthermore, the proposed scheme was modified for two-dimensional flow. Two important things for small tracer particle PIV images were shown : 1) the direction of the sub-pixel correction should be taken into account, 2) distant pixels should not be used. It was found that the proposed scheme has high accuracy even if images contain some noises.