Accurate droplet depth displacement measurement with time-resolved astigmatic interferometric particle imaging

The astigmatic interferometric particle imaging (AIPI) model reveals that the fringe orientation shifts with droplet depth displacement, and their relationships are quantitatively formulated. The depth displacement is directly evaluated from the relative angular shift of the fringes with angular cross power spectral density, and this algorithm isolates the uncertainty of droplet depth position from depth displacement. Proof-of-concept experiments on micrometer-sized transparent droplets with a 5 kHz AIPI system demonstrates that droplet three-dimensional (3D) trajectories are accurately obtained with the accuracy of depth displacement up to tens of micrometers, improving an order of magnitude from hundreds of microns in a traditional Lagrangian framework by comparing droplet depth positions.