Out-of-focus effects on particle image visibility and correlation in microscopic particle image velocimetry

In microscopic particle image velocimetry (mu PIV) the entire volume of a flowfield is illuminated, resulting in all of the particles in the field of view contributing to the image, either by forming discrete particle images or contributing to a background glow. The theory of PIV is expanded to encompass this situation. Equations are derived for a particle image intensity function that yields image diameter and intensity as a function of distance from the object plane, as well as an equation for a new quantity, termed particle visibility. The effect of changing experimental parameters is discussed. Next, the contribution of out-of-focus particles to the correlation function is addressed. A weighting function that can be used to calculate either velocity measurement bias or the distance from the object plane beyond which particles no longer significantly contribute to the correlation function is derived. A new experimental parameter, the depth of correlation, is then introduced, and its dependence on experimental parameters is discussed.