Optical Considerations for Large 3D Volumetric Particle Tracking Velocimetry

TL;DR

This paper develops a model to estimate signal levels and image resolution limits in large-volume 3D particle tracking velocimetry, considering optical parameters and particle properties, supported by practical lab examples.

Contribution

It introduces a numerical model for predicting signal levels and resolution limits in 3D-PTV experiments with varying optical and particle parameters, aiding experimental design.

Findings

Model accurately predicts CMOS signal levels from Mie scattering particles.

Limits of image resolution depend on depth of field and particle density.

Practical examples demonstrate model application in real experiments.

Abstract

The continual increase in computational power and the improvement of algorithms for particle tracking in the past decade have been making it feasible to track larger amounts of particles in 3D Volumetric Particle Tracking Velocimetry (3D-PTV) experiments. Also, the relatively recent introduction of $15 \: \mu m$ Air Filled Soap Bubbles (AFSB) has been facilitating the usage of higher particle densities and hence the improvement of the spatial resolution of such measurements, compared with experiments that use $300 \: \mu m $ Hellium-Filled Air Bubbles (HFSB). The trend to conduct 3D-PTV experiments with ever increasing larger volumes or at higher particle densities with smaller particles sets an ever increasing strain on the power of the illumination source and upon the image analysis. On one hand it requires a reliable model to estimate the signal level that is measured on a CMOS detector from a Mie scattering particle. On the other hand it requires also a model for estimating the limiting factors upon the image resolution where a large amount of particles within a volume are mapped into a 2D image. Here, we present a model that estimates numerically the signal level on a CMOS detector from a Mie scattering particle within an arbitrary large volume in a 3D-PTV experiment. The model considers the effect of the depth of field, particle density, Mie factor, laser pulse energy and other optical parameters. Thereafter, we investigate the physical limit of the image resolution depending on the depth of field and the density of point-like particles. Finally, we supply three real lab examples that illustrate how to use the relevant expressions of the models in order to estimate the signal level and the image resolution