Some considerations on the accuracy and frequency response of some derivative filters applied to particle image velocimetry vector fields

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Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry (2005, methodology): “However, this technique was not available at the time of the analysis and it has been demonstrated since then that this peak-locking behaves as a high-frequency random noise (see Foucaut & Stanislas 2002).”
Dissipation rate estimation from PIV in zero-mean isotropic turbulence (2009, background): “sively analyzed in the experimental and computational literature (Lele 1992; Fouras and Sorla 1998; Saarenrinne and Piirto 2000; Lecordier et al. 2001; Saarenrinne et al. 2001; Foucaut and Stanislas 2002; Etebari and Vlachos 2005; Lavoie et al. 2007; Wang et al. 2007; Tanaka and Eaton 2007).”
Experimental study of an impinging jet with different swirl rates (2007, methodology): “In the present work for the derivatives estimation, the second-order centered difference scheme was used, which is considered as the optimal one in the case of a 50% IA overlap (according to Raffel et al., 1998; Foucaut and Stanislas, 2002).”
Assessment of pressure field calculations from particle image velocimetry measurements (2010, methodology): “Specific forms of (12) for several common derivative schemes were given in the analysis of Foucaut and Stanislas [33].”