Astigmatic particle tracking velocimetry (APTV) has been developed in the last years to measure the three-dimensional displacement of tracer particles using a single-camera view. The measurement principle relies on an astigmatic optical system that provides aberrated particle images with a characteristic elliptical shape univocally related to the corresponding particle depth position. Because of the precision of this method, this concept is well established for measuring and controlling the distance between a CD/DVD and the reading head. The optical arrangement of an APTV system essentially consists of a primary stigmatic optics (e.g., a microscope, or a camera objective) and an astigmatic optics, typically a cylindrical lens placed in front of the camera sensor. This paper focuses on the uncertainty of APTV in the depth direction. First, an approximated analytical model is derived and experimentally validated. From the model, a set of three non-dimensional parameters that are the most significant in the optimization of the APTV performance are identified. Finally, the effect of different parameter settings and calibration approaches are studied systematically using numerical Monte Carlo simulations. The results allow for the derivation of general criteria to minimize the overall error in APTV measurements and provide the basis for reliable uncertainty estimation for a wide range of applications.
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Adrian RJ, Yao CS (1985) Pulsed laser technique application to liquid and gaseous flows and the scattering power of seed materials. Appl Opt 24(1):44–52
Born M, Wolf E (1980) Principles of optics. Pergamon Press, Oxford
Chen S, Angarita-Jaimes N, Angarita-Jaimes D, Pelc B, Greenaway AH, Towers CE, Lin D, Towers DP (2009) Wavefront sensing for three-component three-dimensional flow velocimetry in microfluidics. Exp Fluids 47(4–5):849–863
Cierpka C, Segura R, Hain R, Kähler CJ (2010) A simple single camera 3C3D velocity measurement technique without errors due to depth of correlation and spatial averaging for microfluidics. Meas Sci Technol 21(4):045401
Cierpka C, Rossi M, Segura R, Kähler CJ (2011) On the calibration of astigmatism particle tracking velocimetry for microflows. Meas Sci Technol 22(1):015401
Cierpka C, Kähler CJ (2012) Particle imaging techniques for volumetric three-component (3d3c) velocity measurements in microfluidics. J Vis 15(1):1–31
Cierpka C, Rossi M, Segura R, Mastrangelo F, Kähler CJ (2012) A comparative analysis of the uncertainty of astigmatism-microPTV, stereo-microPIV, and microPIV. Exp Fluids 52(3):605–615
Fuchs T, Hain R, Kähler CJ (2014) Three-dimensional location of micron-sized particles in macroscopic domains using astigmatic aberrations. Opt Lett 39(5):1298–1301
Hain R, Kähler CJ (2006) Single camera volumetric measurements using optical aberrations. In: International symposium on flow visualization. Göttingen, Germany, September, pp 10–14
Kajitani L, Dabiri D (2005) A full three-dimensional characterization of defocusing digital particle image velocimetry. Meas Sci Technol 16(3):790–804
Kao HP, Verkman AS (1994) Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position. Biophys J 67(3):1291–1300
Kumar A, Cierpka C, Williams SJ, Kähler CJ, Wereley ST (2011) 3D3C velocimetry measurements of an electrothermal microvortex using wavefront deformation PTV and a single camera. Microfluid Nanofluidics 10(2):355–365
Liu Z, Speetjens MFM, Frijns AJH, van Steenhoven AA (2014) Application of astigmatism \(\mu\)-PTV to analyze the vortex structure of AC electroosmotic flows. Microfluid Nanofluidics 16(3):553–569
Morgan BJT (1984) Elements of simulation. Chapman and Hall, London
Muller PB, Rossi M, Marin AG, Barnkob R, Augustsson P, Laurell T, Kähler CJ, Bruus H (2013) Ultrasound-induced acoustophoretic motion of microparticles in three dimensions. Phys Rev E 88(2):023006
Olsen MG, Adrian RJ (2000) Out-of-focus effects on particle image visibility and correlation in microscopic particle image velocimetry. Exp Fluids 29(1):S166–S174
Park JS, Kihm KD (2006) Three-dimensional micro-ptv using deconvolution microscopy. Exp Fluids 40(3):491–499
Rossi M, Lindken R, Westerweel J (2010) Optimization of multiplane μPIV for wall shear stress and wall topography characterization. Exp Fluids 48(2):211–223
Rossi M, Cierpka C, Segura R, Kähler CJ (2011) Volumetric reconstruction of the 3D boundary of stream tubes with general topology using tracer particles. Meas Sci Technol 22(10):105405
Rossi M, Segura R, Cierpka C, Kähler CJ (2012) On the effect of particle image intensity and image preprocessing on depth of correlation in micro-PIV. Exp Fluids 52(4):1063–1075
Rossi M, J. Kähler C (2014) On the uncertainty of astigmatic particle tracking velocimetry in the depth direction. In: 17th international symposium on applications of laser techniques to fluid mechanics. Lisbon, Portugal, 07–10 July, 2014
Tschulik K, Cierpka C, Gebert A, Schultz L, Kähler CJ, Uhlemann M (2011) In situ analysis of three-dimensional electrolyte convection evolving during the electrodeposition of copper in magnetic gradient fields. Anal Chem 83(9):3275–3281
Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8(12):1379–1392
Westerweel J (2000) Theoretical analysis of the measurement precision in particle image velocimetry. Exp Fluids 29(1):S3–S12
Willert CE, Gharib M (1992) Three-dimensional particle imaging with a single camera. Exp Fluids 12(6):353–358
Wu M, Roberts JW, Buckley M (2005) Three-dimensional fluorescent particle tracking at micron-scale using a single camera. Exp Fluids 38(4):461–465
Yoon SY, Kihm KD, Kim KC (2011) Correlation of fluid refractive index with calibration coefficient for micro-defocusing digital particle image velocimetry. Meas Sci Technol 22(3):037001
Financial support from German Research Foundation (DFG) within the Individual Grants Programme KA 1808/13-1 is gratefully acknowledged.
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Rossi, M., Kähler, C.J. Optimization of astigmatic particle tracking velocimeters. Exp Fluids 55, 1809 (2014). https://doi.org/10.1007/s00348-014-1809-2
- Focal Plane
- Particle Image
- Tracer Particle
- Cylindrical Lens