Particle Image Velocimetry Correlation Signal-to-noise Metrics, Particle Image Pattern Mutual Information 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 inherent amount of signal mutual information between consecutive images governs the strength of the resulting PIV cross correlation and ultimately the accuracy and uncertainty of the produced PIV measurements. Hence we posit that the correlation signal-to-noise-ratio (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. A new SNR metric termed "mutual information" (MI) which quantifies the amount of common information (particle pattern) between two consecutive images is also introduced and investigated. This measure provides a direct estimation of the apparent NIFIFO parameter of an image pair providing an alternative approach towards uncertainty estimation but also connecting the current development to one of the most fundamental principles of PIV and the previous established theory. We extend the original work by Charonko and Vlachos and present a framework for evaluating the correlation strength 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 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 robust uncertainty estimation models, which are tested against both synthetic benchmark data as well as actual experimental measurements. In this work, U68.5 uncertainties are estimated at the 68.5% confidence level while U95 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.