Autocorrelation-based estimate of particle image density for diffraction limited particle images

In particle image velocimetry (PIV), the number of particle images per interrogation region, or particle image density, impacts the strength of the correlation and, as a result, the number of valid vectors and the measurement uncertainty. For some uncertainty methods, an a priori estimate of the uncertainty of PIV requires knowledge of the particle image density. An autocorrelation-based method for estimating the local, instantaneous, particle image density is presented. The method assumes that the particle images are diffraction limited and thus Gaussian in shape. Synthetic images are used to develop an empirical relationship between the autocorrelation peak magnitude and the particle image density, particle image diameter, particle image intensity, and interrogation region size. This relationship is tested using experimental images. The experimental results are compared to particle image densities obtained through implementing a local maximum method and are found to be more robust. The effect of varying particle image intensities was also investigated and is found to affect the measurement of the particle image density. Knowledge of the particle image density in PIV facilitates uncertainty estimation, and can alert the user that particle image density is too low or too high, even if these conditions are intermittent. This information can be used as a new vector validation criterion for PIV processing. In addition, use of this method is not limited to PIV, but it can be used to determine the density of any image with diffraction limited particle images.