Validation of Analytical Solution for Depth-of-Correlation in Microscopic Particle Image Velocimetry

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Abstract
Because the entire flowfield is generally illuminated in microscopic particle image velocimetry (microPIV), determining the depth over which particles will contribute to the measured velocity is more difficult than in traditional, light-sheet PIV. This paper experimentally and computationally measures the influence that volume illumination, optical parameters, and particle size have on the depth of correlation for typical microPIV system. First, it is demonstrated mathematically that the relative contribution to the measured velocity at a given distance from the object plane is proportional to the curvature of the local cross-correlation function at the distance. The depth of correlation is then determined in both the physical experiments and in computational simulations by directly measuring the relative contribution to the correlation function of particles located at a known separation from the object plane. These results are then compared with a previously derived analytical model that predicts the depth of correlation from the basic properties of the imaging sytem and seed particles used for the microPIV measurements. Excellent agreement was obtained between the analytical model and both computational and physical experiments, verifying the accuracy of the previously derived analytical model.

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