Calculation of the weighting function and determination of the depth of correlation in micro-PIV from experimental particle images

Micro-particle image velocimetry (µPIV) uses volume-illumination and imaging of particles through a single microscope objective. Displacement fields are obtained by image correlation and depend on all imaged particles, including defocused particles. The measured in-plane displacement is a weighted spatial average of the true displacement, with a weighting function W(z) that depends on the optical system and flow-gradients. The characteristic width of the weighting function W(z) is also referred to as depth of correlation (DOC) and is a measure up to which distance from the focal plane particles influence the measurement, which is crucial for the interpretation of measured flow fields. We present procedures to determine the W(z) from which the DOC can be derived and to directly determine the DOC from PIV double images, generated from experimentally recorded particle images. Both procedures provide comparable DOC results. Our approach allows determination of the DOC and W(z)as a function of out of plane gradients, optical setup parameters and PIV-analysis parameters. Experimental results for different objectives and particle sizes are discussed, revealing substantial deviations from theoretical predictions for high NA air-objectives. Moreover, using the determined weighting function W(z), the correction of measured flow profiles for errors introduced by the spatial averaging is demonstrated.