On the loss-of-correlation due to PIV image noise

Abstract

The effect of image noise on the uncertainty of velocity fields measured with particle image velocimetry (PIV) is still an unsolved problem. Image noise reduces the correlation signal and thus affects the estimation of the particle image displacement. However, a systematic quantification of the effect of the noise level on the loss-of-correlation is missing. In this work, a new method is proposed to estimate the loss-of-correlation due to image noise $F_{\sigma }$ from the autocorrelation function of PIV images. Furthermore, a new definition of the signal-to-noise ratio (SNR) for PIV images is suggested, which results in a bijective relation between $F_{\sigma }$ and SNR. Based on the newly defined SNR, it becomes possible to estimate the signal level and the noise level itself. The presented method is very general because the estimation of $F_{\sigma }$ and SNR works independently of various parameters, including the particle image intensity, the particle image density, the particle image size, the image noise distributions and the laser light-sheet profile. The findings lead to an extension of the fundamental PIV equation $N=N_{\mathrm {I}} F_{\mathrm {I}} F_{\mathrm {O}} F_{\Delta }$ and enable PIV users to optimize their measurement setup with respect to the image noise and not only based on the loss-of-correlation due to in-plane motion, out-of-plane motion and displacement gradients. Furthermore, the new definition of SNR allows for a characterization and comparison of PIV images. The new approaches are validated by using synthetic images, and the predictions are confirmed by using experimental data.

Appendix

The MATLAB code for the estimation of $F_{\sigma }$, SNR, $\sigma _{A}$ and $\sigma _{n}$ is shown in the following: