The effect of out-of-plane shear within the depth of correlation in macroscopic planar particle shadow velocimetry

The depth of correlation and the effects of out-of-plane shear within the depth of correlation are examined for a typical macroscopic particle shadow velocimetry (PSV) setup. PSV is a type of particle image velocimetry (PIV) that replaces the planar illumination source with an in-line LED or other source of backlight, so particle shadows are imaged instead of scattered light from the particles. Despite the advantages that PSV offers over PIV, the correlation algorithm used to determine the two-dimensional displacement field can be biased by particles off of the focal plane, since the imaged region is more volumetric than planar PIV. The thickness around the focal plane where this effect is non-negligible is called the depth of correlation. One consequence of a non-zero depth of correlation is that shear of in-plane velocities along the out-of-plane direction will bias the measured displacement along the focal plane. In this work we show that the depth of correlation for macroscopic PSV can be sufficiently estimated using expressions derived for µPIV. We also show that out-of-plane shear reduces the effective depth of correlation of the imaging system.