Particle image velocimetry correlation signal-to-noise ratio metrics and measurement uncertainty quantification

In particle image velocimetry (PIV) the measurement signal is contained in the recorded intensity of the particle image pattern superimposed on a variety of noise sources. The signal-to-noise-ratio (SNR) strength governs the resulting PIV cross correlation and ultimately the accuracy and uncertainty of the resulting PIV measurement. Hence we posit that correlation SNR metrics calculated from the correlation plane can be used to quantify the quality of the correlation and the resulting uncertainty of an individual measurement. In this paper we extend the original work by Charonko and Vlachos and present a framework for evaluating the correlation SNR using a set of different metrics, which in turn are used to develop models for uncertainty estimation. Several corrections have been applied in this work. The SNR metrics and corresponding models presented herein are expanded to be applicable to both standard and filtered correlations by applying a subtraction of the minimum correlation value to remove the effect of the background image noise. In addition, the notion of a 'valid' measurement is redefined with respect to the correlation peak width in order to be consistent with uncertainty quantification principles and distinct from an 'outlier' measurement. Finally the type and significance of the error distribution function is investigated. These advancements lead to more robust and reliable uncertainty estimation models compared with the original work by Charonko and Vlachos. The models are tested against both synthetic benchmark data as well as experimental measurements. In this work, U-68.5 uncertainties are estimated at the 68.5% confidence level while U-95 uncertainties are estimated at 95% confidence level. For all cases the resulting calculated coverage factors approximate the expected theoretical confidence intervals, thus demonstrating the applicability of these new models for estimation of uncertainty for individual PIV measurements.