Abstract
An analytical expression for the error in the sub-pixel displacement is derived. The expression relates the error to the second- and fourth-order moments of the intensity probability density function, which can both be expressed in terms of the source density. Scaling relations for the error as a function of the particle-image diameter are determined by means of the Cramèr–Rao lower bound, for both constant image density and constant source density. The analytical expression is evaluated for the error as a function of the sub-pixel displacement, the particle-image diameter, and the image density, and the results are validated against results from Monte-Carlo simulations. It is demonstrated that results obtained from synthetic PIV images that do not represent the correct image intensity probability density function systematically underestimate the displacement measurement error.
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Westerweel, J. Theoretical analysis of the measurement precision in particle image velocimetry. Experiments in Fluids 29 (Suppl 1), S003–S012 (2000). https://doi.org/10.1007/s003480070002
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DOI: https://doi.org/10.1007/s003480070002