Abstract
Optically sliced microscopic-particle image velocimetry (micro-PIV) is developed using confocal laser scanning microscopy (CLSM). The developed PIV system shows a unique optical slicing capability allowing true depth-wise resolved micro-PIV vector field mapping. A comparative study between CLSM micro-PIV and conventional epi-fluorescence micro-PIV is presented. Both techniques have been applied to the creeping Poiseuille flows in two different microtubes of 99-μm (Re=0.00275) and 516-μm ID diameters (Re=0.021), which are respectively imaged by a 40×-0.75NA objective with an estimated 2.8-μm optical slice thickness, and by a 10×-0.30NA objective with a 26.7-μm slicing. Compared to conventional micro-PIV, CLSM micro-PIV consistently shows significantly improved particle image contrasts, definitions, and measured flow vector fields agreeing more accurately with predictions based on the Poiseuille flow fields. The data improvement due to the optical slicing of CLSM micro-PIV is more pronounced with higher magnification imaging with higher NA objectives for a smaller microtube.
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Notes
This is also called a “far-field” diffraction condition, which is defined as R>a 2/λ, where R is the smaller of the two distances from the particle to the objective lens and the objective lens to the imaging detector, a is the particle radius, and λ is the wavelength in the medium. For typical conditions for micro-PIV, R~1 mm, a~200 nm, and λ~500 nm, the inequality is well satisfied by a ratio of greater than 12,000.
Numerical aperture, NA, is defined as \(NA \equiv n_{i} \sin \theta _{{\max }} \), where n i is the refractive index of the immersing medium (air, water, oil, etc.) adjacent to the objective lens, and θ max is the half-angle of the maximum cone of the light apertured by the lens.
Modified pinhole diameter, PD, is defined as pinhole diameter/magnification, with the pinhole diameter measured in μm.
Airy unit, \({\text{AU}} \equiv {1.22\lambda _{{{\text{ex}}}} } \mathord{\left/ {\vphantom {{1.22\lambda _{{{\text{ex}}}} } {NA}}} \right. \kern-\nulldelimiterspace} {NA} \), with λ ex being the fluorescent excitation wavelength.
The mean wavelength is defined as, \(\ifmmode\expandafter\bar\else\expandafter\=\fi{\lambda } = {\sqrt 2 }\frac{{\lambda _{{{\text{ex}}}} \cdot \lambda _{{{\text{em}}}} }}{{{\sqrt {\lambda _{{{\text{ex}}}} ^{2} + \lambda _{{{\text{em}}}} ^{2} } }}} \).
The spatial uncertainty of the imaging planes is estimated as an rms of the one-half of the micro-stage reading resolution, 0.5 μm, and the uncertainty level for identifying the top-end point is estimated to be approximately identical to the image depth-of-field (DOF), 0.92 µm for 40× and 5.72 µm for 10× magnification, for the conventional microscope. Note that the values of DOF for CLSM are 0.63 µm and 4.66 µm for 40× and 10× magnification, respectively.
The background noise from the off-focus particle images can be reduced to an acceptable level by limiting the PIV measurement depth to a base-cut level where the field-wide-averaged image intensity reaches one-tenth of the maximum in-focus image intensity (Meinhart et al. 2000).
The actual recorded image of a seed particle on the CCD is a convolution of the geometric particle image, Md p, with the FPS, d s, of the recording optics. Approximating both of the geometric and diffraction-limited images as Gaussian functions, the image diameter, d e, can be expressed as (Born and Wolf 1999) \(d_{{\text{e}}} = {\left[ {M^{2} d_{{\text{p}}} ^{2} + d_{{\text{s}}} ^{2} } \right]}^{{1/2}} \) where d e is the effective particle diameter in the CCD, M is the magnification of the microscope, d p is the particle diameter, and d s is the characteristic diameter of the PSF. For magnifications much larger than unity, the diameter of the diffraction-limited PSF, in the image plane, is given by \(d_{{\text{s}}} = 2.44M\frac{\lambda }{{2NA}} \) where NA is the numerical aperture and λ is the wavelength of light.
Optical path length (OPL) is defined as the local medium thickness multiplied by the local refractive index.
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Acknowledgement
The confocal laser scanning microscope (CLSM) system was purchased by the Texas A&M Permanent University Facility (PUF) Award granted to Dr. Kihm’s Micro/nano-scale Fluidics and Heat Transport Laboratory http://go.to/microlab. The authors acknowledge that the current research has been partially sponsored by the NASA-Fluid Physics Research Program, grant no. NAG 3–2712, and partially by a subcontract from the R4D Program at the National Center for Microgravity Research (NCMR). The presented technical contents are not necessarily the representative views of NASA or NCMR.
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Park, J.S., Choi, C.K. & D. Kihm, K. Optically sliced micro-PIV using confocal laser scanning microscopy (CLSM). Exp Fluids 37, 105–119 (2004). https://doi.org/10.1007/s00348-004-0790-6
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DOI: https://doi.org/10.1007/s00348-004-0790-6