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.
Experiments in Fluids – Springer Journals
Published: Dec 31, 2000
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