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Three-dimensional micro-PTV using deconvolution microscopy

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Abstract

A three-dimensional micro-particle tracking velocimetry (micro-PTV) scheme is presented using a single camera with deconvolution microscopy. This method devises tracking of the line-of-sight (z) flow vectors by correlating the diffraction pattern ring size variations with the defocusing distances of small particle locations. The working principle is based on optical serial sectioning microscopy, or equivalently deconvolution microscopy, that records images of an infinitesimally small particle, and generates a point-spread function of the three-dimensional diffraction patterns. A new image-processing algorithm has also been developed to digitally identify the center locations and measure the radii of the diffraction rings, which allows simultaneous tracking of all three-vector components. The developed PTV technique uses a 40×, 0.75 NA dry objective lens with 500-nm fluorescent seeding particles of SG=1.05, and successfully measures the fully three-dimensional fields flowing over a spherical obstacle snuggly fitted inside a 100 μm × 100 μm micro-channel. The volumetric measurement resolution of the present system is equivalent to a 5.16 μm × 5.16 μm × 5.16 μm cube, and the overall measurement uncertainty for single-point velocity vector detection is estimated to ±7.58%.

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Notes

  1. M (overall magnification of microscopy)=40, NA=0.75, λ (emission light wavelength)=515 nm (Ar-ion laser source), t g (cover glass thickness)=0.21 mm, t i (immersion thickness)=0.483 mm, n g (refractive index of cover glass)=1.51, n s (refractive index of specimen medium)=1.33 (water), and n i (refractive index of immersion)=1.0 (air).

  2. A regression of the calculated correlation provides a third-order polynomial approximation of \( {\left[ {\Delta z\, = \,A \cdot r^{3} + B \cdot r^{2} + C \cdot r + D} \right]} \) with fitting coefficients of A=0.0003, B = -0.028, C=1.0747, and D=0.4326. This functional form of the correlation will be useful in computational determination of the ring radii as will be discussed in the later section.

  3. For instances, it can represent a practical situation such as a hydrogen bubble trapped in a PEM fuel cell operation, or an air bubble trapped in a lab-on-a-chip microfluidic device for various bio-processings.

  4. The average gray level of “1” means that the entire 24 pixels fall on the fringe ring, and “0” means that the entire 24 pixels fall on the background. The criterion for identification of a ring is differently specified in-between “1” and “0” depending on the ring size and the image quality. For a larger ring, a relatively low value is used since large circular fringes often conform to incomplete circles. For a smaller ring, a relatively high value close to “1” since most of small circular fringes are well defined with completed circles.

  5. Before a median filtering, the wrong directional vectors are eliminated. If the center vector deviates beyond a tolerable range from the median vector of the surrounding 26 vectors, the center vector is replaced by an average of both center vector and median vector. The tolerance is ranged from 0.1 to 0.5 depending on the image quality.

  6. The effective viscosity (μ eff) of a particle-laid suspension is given by (Deen 1998); μ eff=(1+2.5φ)μ 0 , where φ is the volume fraction of spheres and μ 0 is the viscosity of the suspending fluid (959×10-6 Ns/m2 for a water at 22°C). The tested low volume fraction of 0.001% does not alter the effective viscosity from the viscosity of the suspending fluid. Thus, the applied flow rate of 1 μL/h at a mean velocity of 28 μm/s yields the Reynolds number of approximately 0.003.

  7. The diffusion coefficient is given by (Einstein 1905), \( D = \kappa \,T/6\pi \mu \,r_{{\text{p}}} \) where κ is the Boltzmann's constant (1.3805×10-23 J/K), T is the suspension temperature in absolute, μ is the effective viscosity of the suspension, and r p is the particle radius.

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Acknowledgements

The authors wish to acknowledge financial support provided partly by the University of Tennessee Research Initiation Grant and partly by the Korea Institute of Science and Technology Evaluation Policy (KISTEP).

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  1. Micro/Nano-Scale Fluidics and Energy Transport (MINSFET) Laboratory, Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, TN, 37996, USA

    J. S. Park & K. D. Kihm

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  1. J. S. Park
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  2. K. D. Kihm
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Correspondence to K. D. Kihm.

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Park, J.S., Kihm, K.D. Three-dimensional micro-PTV using deconvolution microscopy. Exp Fluids 40, 491–499 (2006). https://doi.org/10.1007/s00348-005-0090-9

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