A super-resolution particle image velocimetry interrogation approach by means of velocity second derivatives correlation

The present study proposes a super-resolution approach for the analysis of particle image velocimetry (PIV) recordings. The method is based on image correlation with respect to the second spatial derivatives of the particle image displacement distribution. The direct measurement of the displacement second derivatives (spatial curvature) is obtained by maximizing the product of deformed particle image patterns. The paper describes the performance of the cross-correlation approach in terms of spatial resolution in analogy with linear filters (moving average) as directly applied to the displacement distribution over the interrogation window. The proposed method aims at reducing the evaluation error and introduces a correlation scheme, which directly measures the local second derivatives of the displacement distribution over the interrogation window. The window product is maximized separately for each spatial derivative term in order to reduce the large computational cost associated with image deformation resampling and image product. The method's performance is assessed first by evaluating the modulation transfer function using synthetic PIV images with a one-dimensional sinusoidal displacement, where results show a factor of three spatial resolution enhancement. The extension to the two-dimensional case is obtained by simulation of homogeneous random fluctuations. The measurement uncertainty is kept at the same level as that of the window deformation iterative and multi-grid method (WIDIM). The assessment of the method's performances in actual experimental conditions is made by analysing a wall jet flow, focusing the attention on the steep velocity profile across the free shear layer. The assessment compares the velocity and vorticity profiles obtained by varying the size of the interrogation window. The factor of three improvement of the spatial resolution is also confirmed for the experimental case. However, a slight increase of the measurement uncertainty is observed.