This paper concerns the computation of derivatives from particle image velocimetry (PIV) velocity fields with the goal of obtaining the vorticity component normal to the plane. A variety of derivative schemes are characterized by their transfer function, taking into account the truncation and noise amplification. The PIV measurement noise is supposed to be a white one in the Fourier space. A spectral approach is used in order to choose the best filter for turbulent flows. The derivative spectra are discussed. An application is presented on a real turbulent flow with two interrogation window sizes and different derivative schemes. The most significant schemes are also applied to a velocity field containing a single vortex. A comparison of the maximum of vorticity obtained with each scheme and through a least-square fit with an Oseen vortex, allows us to quantify the effect of the band pass filter and to select the best scheme.
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Foucaut et al. (2002) studied this question.