On the stability of iterative PIV image interrogation methods

The stability of cross-correlation based PIV iterative interrogation methods is investigated. The iterative image interrogation equation is formulated and two different options are considered for the implementation of the predictorcorrector principle. The first is based on the simplest approach, which sums up the intermediate results of the crosscorrelation; the second applies the displacement predictor as the average value over the interrogation window. The numerical assessment is performed making use of computer-generated one-dimensional particle recordings where a known displacement distribution is applied. The difference between the result of each interrogation and the exact displacement is monitored as measurement residual. The convergence of the iterative process is monitored through the difference between subsequent results. The problem relevance relies in the broad adoption of iterative interrogation methods by the scientific community as well as by PIV systems manufacturers. Methods applying continuous window deformation are discussed. In general terms the stability analysis of predictor-corrector algorithm shows that an integral condition of the predictor must be fulfilled in order to obtain a stable and converging process. However in the latter case the spatial resolution is that of a moving average filter. Finally an analytical justification of the phenomenon of the most amplified unstable wavelengths is given, followed with a numerical assessment.