A general approach to evaluate the ensemble cross‑correlation response for PIV using Kernel density estimation

Cross-correlation in particle image velocimetry is well known to behave as a non-linear operator, depending heavily on the distribution of tracer images and image quality. While analytical descriptors of the correlation response have so far been dealt with for simplistic flow cases, in this work a methodology is presented based on Kernel density estimation to retrieve the inherent correlation response to any deterministic flow field. The new approach bypasses the need for Monte-Carlo simulations and its inherent sensitivity to parameter settings make it a more efficient alternative to analyse filtering of the underlying velocity field due to image cross-correlation. The derivation of the underlying equations is presented and a numerical assessment corroborates the suitability of the approach to mimic ensemble correlation.