Optical Considerations for Designing Laser-Based Volumetric Particle Tracking Velocimetry

Abstract

The trend to conduct volumetric particle tracking velocimetry (PTV) experiments with ever-increasing volumes, at a given particle density, poses increasing challenges on the design of such experiments in terms of the power of the laser source and the image analysis. These challenges, on one hand, require a reliable model to estimate the current signal from a pixel on a complementary metal-oxide semiconductor (CMOS) detector due to a Mie scattering particle. On the other hand, they require also a model for estimating the limiting factors upon the image resolution, where a large amount of particles within a three-dimensional (3D) volume are mapped into a two-dimensional (2D) image. Herein, we present a model that provides an analytical expression to estimate the current signal from a pixel of a CMOS detector due to a Mie scattering particle within an arbitrary large volume in a volumetric PTV experiments. We begin with a model for planar experiments and extend it into volumetric measurements. Our model considers the effect of the depth of field, particle density, Mie scattering signal and total Mie scattering loss, laser pulse energy, and other relevant optical parameters. Later, we investigate the consequence of the Rayleigh criterion upon the spatial resolution when it is applied to Mie particles within a volume of interest (VOI). Finally, we demonstrate how we applied our model to estimate the current signal and the limit upon the spatial resolution in three experiments carried out in our lab.