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Theoretical analysis of direct and phase-filtered cross-correlation response to a sinusoidal displacement for PIV image processing

The response of PIV image processing routines adopting cross-correlation is commonly categorized as that of a moving average (MA) filter. This paper addresses the intrinsic response of the statistical operator to a sinusoidal displacement from a theoretical perspective. Evaluation of the derived analytical expressions for the correlation indicates the response not to behave as that of an MA filter contrary to the generally adopted simplification. Instead the inherent signal modulation is non-linear and is determined by the ratio between displacement amplitude and particle image diameter. This finding is expected to be of importance and have considerable implications for recursive image processing routines. In addition, readily available spectral filtering techniques are assessed in terms of effectiveness in minimization of correlation deterioration due to pixelization and displacement filtering inherent to particle image self-correlation. It is shown that the best possible correlation response in digital PIV is dictated by the convolution between particle image self-correlation and displacement distribution function, inevitably retaining particle image inherent amplitude modulation.