Theory of cross-correlation analysis of PIV images

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability. For the direct cross-correlation method of single-exposure, double-frame systems which model video array detector interrogation and of double-exposure single-frame systems which generalize earlier direct auto-correlation methods of interrogation of photographic recordings, optimal system parameters are recommended for a range of velocity fields in order to eliminate signal bias and to minimize loss of signal strength. The signal bias resulting from velocity gradients in auto-correlation analysis can be eliminated in cross-correlation interrogation by appropriate choice of the optimal parameters. Resolution, detection rate, accuracy and reliability are compared with direct auto-correlation methods for double- and multiple-pulsed systems.