Skip to main content
SpringerLink
Log in

Spatial resolution of the Stereo PIV technique

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

A theoretical analysis of the spatial resolution in terms of modulation transfer function of the Stereo PIV technique with and without the correction of the misalignment error is performed, and the results show that some wavelengths of the flow field can be significantly dephased and modulated. A performance assessment has been conducted with both synthetic and real images and shows a good agreement with the theoretical analysis. The reconstruction of the three-dimensional displacement field is achieved using both the methods proposed by Soloff et al. (Meas Sci Technol 8:1441–1454, 1997) and by Willert (Meas Sci Technol 8:1465–1479, 1997).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Notes

  1. This happens because the stereoscopic setup used here is same side symmetric. For an opposite side symmetric setup, both the local viewing angles and the MTF2C relative to the two cameras are equal in the same physical point, but they change inside the image and then, also in this case, the MTF of the 3C vector is not uniform on the object plane.

  2. An analogous conclusion can not be drawn if the two 2C vectors with different modulations are v 1 and v 2, as the Formulas 2–4 suggest.

Abbreviations

2C:

Two components (u, v)

2D:

Bidimensional

3C:

Three components (u, v, w)

3D:

Tridimensional

CS:

3C reconstruction proposed by Soloff et al. (1997) with correction of misalignment error

CW:

3C reconstruction proposed by Willert (1997) with correction of misalignment error

IDM:

Image deformation method

MTF:

Modulation transfer function

MTF2C :

Modulation transfer function associated to the PIV process

MTFΔz :

Modulation transfer function associated to the misalignment

MTFLT :

Modulation transfer function associated to the laser thickness for the 3C displacement

MTFLTc :

Modulation transfer function associated to the laser thickness for the camera c

NCS:

3C reconstruction proposed by Soloff et al. (1997) without correction of misalignment error

NCW:

3C reconstruction proposed by Willert (1997) without correction of misalignment error

PIV:

Particle image velocimetry

THMA:

Top hat moving average

c :

camera (1, 2), dimensionless

dx = [dx, dy, dz]:

infinitesimal displacement vector in object space, mm

dx, dy, dz :

3C infinitesimal displacement in object space, mm

dX c  = [dX c , dY c ]:

infinitesimal displacement vector in the image plane relative to camera c, pixels

dX c , dY c :

2C infinitesimal displacement in the image plane relative to camera c, pixels

D u :

disparity vector, mm

E 21 :

power spectra of the v component evaluated along the x direction, mm2

F (c) = [X (c), Y (c)]:

vectorial mapping function relative to camera c, pixels/mm

\( \underline{k} = \left[ {k_{x} ,\;k_{y} ,\;k_{z} } \right] = \left[ {\frac{2\pi }{{\lambda_{x} }},\;\frac{2\pi }{{\lambda_{y} }},\;\frac{2\pi }{{\lambda_{z} }}} \right] \) :

wavenumber, rad/mm or rad/pixels

LT:

laser thickness, pixels or mm

P:

point in the measurement plane, dimensionless

R cl (R cr):

resolution measured in the left (right) side of the image recorded by the camera c, pixels/mm

RR max :

maximum ratio between the resolutions measured in the same measurement point of the images recorded by the two cameras, dimensionless

t c :

phase of the sinusoidal component relative to camera c used in 3C reconstruction without correction of the misalignment errors, mm

u, v, w :

3C displacement in object space, mm

u c , v c :

2C displacement relative to camera c, mm

W :

interrogation windows linear dimension, pixels or mm

x, y, z :

coordinates in object space, mm

X c , Y c :

coordinates relative to camera c in the image plane, pixels

X (c) :

mapping function of the image coordinates X c , pixels/mm

Y (c) :

mapping function of the image coordinates Y c , pixels/mm

α c :

angle between the viewing ray and the plane yz measured in the xz plane, rad

β c :

angle between the viewing ray and the plane xz measured in the yz plane, rad

Δα = |α 2| − |α 1|:

difference in the same measurement point between the absolute values of the viewing angles of the two cameras, rad

Δz :

local misalignment between calibration and measurement planes, mm

φ :

phase in measured sinusoidal component caused by misalignment, rad

λ :

wavelength, mm or pixels

ξ c :

vector obtained by intersecting the optical axis of camera c and the laser sheet, mm

References

  • Astarita T (2006) Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution. Exp Fluids 40:977–987

    Article  Google Scholar 

  • Coudert S, Schon JP (2001) Back-projection algorithm with misalignment corrections for 2D3C stereoscopic PIV. Meas Sci Technol 12:1371–1381

    Article  Google Scholar 

  • Coudert S, Westerweel J (2000) Comparison between warping and mapping methods on a Stereoscopic 2D3C DPIV system with Scheimpflug conditions. In: EuroMech 411 colloquium, Rouen, 29–31 May 2000

  • Fei R, Merzkirch W (2004) Investigation of the measurement accuracy of stereo particle image velocimetry. Exp Fluids 37:559–565

    Article  Google Scholar 

  • Foucaut JM, Carlier J, Stanislas M (2004) PIV optimization for the study of turbulent flow using spectral analysis. Meas Sci Technol 15:1046–1058

    Article  Google Scholar 

  • Lawson N, Wu J (1997) Three-dimensional particle image velocimetry: experimental error analysis of digital angular stereoscopic system. Meas Sci Technol 8:1455–1464

    Article  Google Scholar 

  • Lecordier B, Westerweel J (2004) The EUROPIV synthetic image generator. In: Stanislas M, Westerweel J, Kompenhans J (eds) Particle image velocimetry: recent improvements. Springer, Heidelberg

    Google Scholar 

  • Prasad A (2000) Stereoscopic particle image velocimetry. Exp Fluids 29:103–116

    Article  Google Scholar 

  • Prasad A, Jensen K (1995) Scheimpflug stereocamera for particle image velocimetry in liquid flows. Appl Opt 34:7092–7099

    Article  Google Scholar 

  • Raffel M, Willert C, Wereley S, Kompenhans J (2007) Particle image velocimetry: a practical guide. Springer, Berlin, pp 213–214. doi:10.1007/978-3-540-72308-0

  • Scarano F, David L, Bsibsi M, Calluaud D (2005) S-PIV comparative assessment: image dewarping + misalignment correction and pinhole + geometric projection. Exp Fluids 39:257–266

    Article  Google Scholar 

  • Soloff S, Adrian R, Liu Z (1997) Distortion compensation for generalized stereoscopic particle image velocimetry. Meas Sci Technol 8:1441–1454

    Article  Google Scholar 

  • Stanislas M, Okamoto K, Kähler CJ, Westerweel J, Scarano F (2008) Main results of the third international PIV challenge. Exp Fluids 45:27–71

    Article  Google Scholar 

  • Tsai RY (1987) A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses. IEEE J Rob Autom 4:RA-3

    Google Scholar 

  • Westerweel J, van Oord J (2000) Stereoscopic PIV measurement in a turbulent boundary layer. In: Stanislas M et al (eds) Particle image velocimetry: progress towards industrial application. Kluwer, Dordrecht, pp 459–478

    Google Scholar 

  • Wieneke B (2005) Stereo-PIV using self-calibration on particle images. Exp Fluids 39:267–280

    Article  Google Scholar 

  • Willert C (1997) Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas Sci Technol 8:1465–1479

    Article  Google Scholar 

  • Willert C (2006) Assessment of camera models for use in planar velocimetry calibration. Exp Fluids 41:135–143

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DIAS-University of Naples “Federico II”, p.le Tecchio 80, 80125, Naples, Italy

    R. Giordano & T. Astarita

Authors
  1. R. Giordano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Astarita
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Giordano.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Giordano, R., Astarita, T. Spatial resolution of the Stereo PIV technique. Exp Fluids 46, 643–658 (2009). https://doi.org/10.1007/s00348-008-0589-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-008-0589-y

Keywords

Search

Navigation