Calibration of astigmatic particle tracking velocimetry based on generalized Gaussian feature extraction

Abstract

Flow and transport in porous media are driven by pore scale processes. Particle tracking in transparent porous media allows for the observation of these processes at the time scale of ms. We demonstrate an application of defocusing particle tracking using brightfield illumination and a CMOS camera sensor. The resulting images have relatively high noise levels. To address this challenge, we propose a new calibration for locating particles in the out-of-plane direction. The methodology relies on extracting features of particle images by fitting generalized Gaussian distributions to particle images. The resulting fitting parameters are then linked to the out-of-plane coordinates of particles using flexible machine learning tools. A workflow is presented which shows how to generate a training dataset of fitting parameters paired to known out-of-plane locations. Several regression models are tested on the resulting training dataset, of which a boosted regression tree ensemble produced the lowest cross-validation error. The efficiacy of the proposed methodology is then examined in a laminar channel flow in a large measurement volume of 2048, 1152 and 3000 μm in length, width and depth respectively. The size of the test domain reflects the representative elementary volume of many fluid flow phenomena in porous media. Such large measurement depths require the collection of images at different focal levels. We acquired images at 21 focal levels 150 μm apart from each other. The error in predicting the out-of-plane location in a single slice of 240 μm thickness was found to be 7 μm, while in-plane locations were determined with sub-pixel resolution (below 0.8 μm). The mean relative error in the velocity measurement was obtained by comparing the experimental results to an analytic model of the flow. The estimated displacement errors in the axial direction of the flow were 0.21 pixel and 0.22 pixel at flows rates of 1.0 mL/h and 2.5 mL/h, respectively. These results demonstrate that it is possible to conduct three-dimensional particle tracking in a representative elementary volume based on a simple apparatus comprising a microscope with standard brightfield illumination and a camera with CMOS sensor.

Utilizing the ball lens effect for astigmatism particle tracking velocimetry

“…An overview of z , F xz , F yz , * z , z for all investigated parameter combinations of d p , M, material of the particles and wt% of the glycerol-water solution is given in Table 3 of "Appendix". For the investigated cases, z ∕ z is around 0.7-5.2% for BLAPTV (except for two cases) which is comparable to the accuracies obtained by Cierpka et al (2010b), Buchmann et al (2014) and Franchini et al (2019). In the present study, the uncertainty relative to the particle diameter is in the range 1.8% ≤ z ∕d p ≤ 16% (except for two cases), see Table 3 in "Appendix".…”

“…They concluded it was due to the less bright particle images obtained with a white light source. Using a backlight illumination, Franchini et al (2019) performed APTV measurements with a calibration based on fitting a 2D, generalized Gaussian distribution to each particle image. They could resolve the velocity profile of a laminar flow in a 2 × 1.2 × 3 mm 3 channel covering a measurement volume depth of 240 μm .…”

X-ray Tomographic Micro-Particle Velocimetry in Porous Media

“…Most flow field measurements are based on optical particle velocimetry, using visible light to image the movement of flow-tracing particles in (index-matched) fluids over time. With microparticles and microscopes, this principle can be used to measure micron-scale flow fields in transparent 2D micromodels (Roman et al, 2015;Zarikos et al, 2018) and even in optically transparent 3D porous media, using multi-camera set-ups (Schanz, Gesemann, and Schröder, 2016), astigmatic optics (Franchini et al, 2019) or confocal microscopy (Datta et al, 2013;Datta, Ramakrishnan, and Weitz, 2014). However, these techniques are inherently unsuited for optically opaque -and thus most -porous materials.…”

On the calibration of Astigmatism particle tracking velocimetryfor suspensions of different volume fractions

“…Most recent works increasingly focus on using machine learning tools such as deep neural networks to further increase the degree of automatization of APTV (Rossi and Barnkob 2019) or to apply it on scenarios with low signal-to-noise ratios (Franchini et al 2019). König et al 2020 compared the performance of conventional and neural network supported APTV utilizing a bidisperse suspension in a laminar channel flow.…”