Analytic evaluation of single-pass cross-correlation response for the case of a sinusoidal displacement

Raf Theunissen

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)


This paper addresses the intrinsic response of the cross-correlation operator to a one-dimensional sinusoidal displacement field to assess the general assumption of cross-correlation behaving as a moving average (MA) filter. Analytic expressions are derived describing the correlation map, which further allow the identification of pivotal parameters influencing the response. Contrary to common belief, the analysis indicates the response not to generally behave as that of an MA filter, but instead to be non-linear and determined by the ratio between displacement amplitude and particle image diameter. This is shown to have implications for recursive image processing necessitating predictorcorrector filtering. 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 elfcorrelation. 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.
Original languageEnglish
Title of host publicationDelft University of Technology, Faculty of Mechanical, Maritime and Materials Engineering, and Faculty of Aerospace Engineering
Place of PublicationTUDelft
ISBN (Electronic)uuid:e58f305e-9de4-4997-b5b9-7625748750b2
Publication statusPublished - 1 Jul 2013


  • PIV, Correlation, sinusoid

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