Measurement volume defined by peak-finding algorithms in cross-correlation particle image velocimetry

This note presents an analytical model that relates the displacement found by peak finding in cross-correlation particle image velocimetry using light-sheet illumination to the weighted volume average of the fluid velocity field. General equations are derived describing the cross-correlation function in light-sheet PIV. An approximate model is derived for light-sheet illumination by approximating the particle images as Gaussian, This results in a weighting function that can be used to define the measurement volume and to find biasing of the velocity measured for this volume.