Depth from Defocus Technique Applied to Unsteady Shock-Drop Secondary atomization, Resolution considerations for structured illumination microscale particle tracking velocimetry

Abstract

The talk will focus on further enhancing a two-sensor depth from defocus (DFD) technique for measuring drop sizes in a spray. The aim is to achieve higher spatial and temporal resolution, to improve estimates of spatial size distribution and number concentration, and to provide additional guidelines for the calibration and design of the optical system for a specific application. The technique and these improvements are demonstrated using the case of secondary atomization when a shock wave interacts with a single drop. This is an application in which both high spatially and temporally resolved number density and size distributions of secondary droplets generated in the wake of the original drop are necessary. In microscale particle velocimetry, the spatial resolution of velocity measurements along the optical axis is often degraded by signal from tracer particles outside the focal plane. Structured illumination microscopy particle tracking velocimetry (SIM PTV) can eliminate most of this out-of-focus signal by using illumination with a non-zero spatial frequency to preferentially illuminate the in-focus particles. Two such (raw) images can then be combined to eliminate the background signal and demodulate the image. The objective of this study was to quantify and optimize the spatial and temporal resolution of SIM PTV based upon Poiseuille flow in a microchannel at Reynolds numbers Re ≈ 0.02. The axial spatial resolution, estimated for this known velocity profile from the standard deviation of the velocity measurements, is improved by at least a factor of 2 compared with the results for a uniformly illuminated flow. This axial spatial resolution is in good agreement with that given by the point spread function of the imaging system derived by Neil et al. (Opt Lett 22:1905-1907, 1997). The spatial frequency of the illumination that optimizes the spatial resolution is a function of the scattering area of the tracer particles. Interestingly, increasing the number of raw images does not appear to improve the axial resolution. Finally, the temporal resolution of SIM PTV is estimated based upon both image and velocity acquisition times.