Abstract

This Letter presents a stereoscopic imaging concept for measuring the locations of particles in three-dimensional space. The method is derived from astigmatism particle tracking velocimetry (APTV), a powerful technique that is capable of determining 3D particle locations with a single camera. APTV locates particle xy coordinates with high accuracy, while the particle z coordinate has a larger location uncertainty. This is not a problem for 3D2C (i.e., three dimensions, two velocity components) measurements, but for highly three-dimensional flows, it is desirable to measure three velocity components with similar accuracy. The stereoscopic APTV approach discussed in this report has this capability. The technique employs APTV for giving an initial estimate of the particle locations. With this information, corresponding particle images on both sensors of the stereoscopic imaging system are matched. Particle locations are then determined by mapping the two particle image sensor locations to physical space. The measurement error of stereo APTV, determined by acquiring images of 1-μm DEHS particles in a 40mm×40mm×20mm measurement volume in air at Δxyz0 between two frames, is less than 0.012 mm for xy and 0.025 mm for z. This error analysis proves the excellent suitability of stereo APTV for the measurement of three-dimensional flows in macroscopic domains.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2014 (2)

T. Fuchs, R. Hain, and C. J. Kähler, Opt. Lett. 39, 1298 (2014).
[Crossref]

M. Rossi and C. J. Kähler, Exp. Fluids 55, 1809 (2014).
[Crossref]

2013 (1)

B. Wieneke, Meas. Sci. Technol. 24, 024008 (2013).
[Crossref]

2012 (1)

C. Cierpka and C. J. Kähler, J. Vis. 15(1):9, 1–32 (2012).

2011 (1)

C. Cierpka, M. Rossi, R. Segura, and C. J. Kähler, Meas. Sci. Technol. 22, 015401 (2011).
[Crossref]

2010 (1)

C. Cierpka, R. Segura, R. Hain, and C. J. Kähler, Meas. Sci. Technol. 21, 045401 (2010).
[Crossref]

2006 (1)

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, Exp. Fluids 41, 933 (2006).
[Crossref]

1997 (2)

C. E. Willert, Meas. Sci. Technol. 8, 1465 (1997).
[Crossref]

S. M. Soloff, R. J. Adrian, and Z. C. Liu, Meas. Sci. Technol. 8, 1441 (1997).
[Crossref]

1993 (2)

N. A. Malik, T. Dracos, and D. A. Papantoniou, Exp. Fluids 15, 279 (1993).

H. G. Maas, A. Gruen, and D. A. Papantoniou, Exp. Fluids 15, 133 (1993).
[Crossref]

1992 (1)

C. E. Willert and M. Gharib, Exp. Fluids 12, 353 (1992).
[Crossref]

Adrian, R. J.

S. M. Soloff, R. J. Adrian, and Z. C. Liu, Meas. Sci. Technol. 8, 1441 (1997).
[Crossref]

Cierpka, C.

C. Cierpka and C. J. Kähler, J. Vis. 15(1):9, 1–32 (2012).

C. Cierpka, M. Rossi, R. Segura, and C. J. Kähler, Meas. Sci. Technol. 22, 015401 (2011).
[Crossref]

C. Cierpka, R. Segura, R. Hain, and C. J. Kähler, Meas. Sci. Technol. 21, 045401 (2010).
[Crossref]

Dracos, T.

N. A. Malik, T. Dracos, and D. A. Papantoniou, Exp. Fluids 15, 279 (1993).

Elsinga, G. E.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, Exp. Fluids 41, 933 (2006).
[Crossref]

Fuchs, T.

Gharib, M.

C. E. Willert and M. Gharib, Exp. Fluids 12, 353 (1992).
[Crossref]

Gruen, A.

H. G. Maas, A. Gruen, and D. A. Papantoniou, Exp. Fluids 15, 133 (1993).
[Crossref]

Hain, R.

T. Fuchs, R. Hain, and C. J. Kähler, Opt. Lett. 39, 1298 (2014).
[Crossref]

C. Cierpka, R. Segura, R. Hain, and C. J. Kähler, Meas. Sci. Technol. 21, 045401 (2010).
[Crossref]

Kähler, C. J.

T. Fuchs, R. Hain, and C. J. Kähler, Opt. Lett. 39, 1298 (2014).
[Crossref]

M. Rossi and C. J. Kähler, Exp. Fluids 55, 1809 (2014).
[Crossref]

C. Cierpka and C. J. Kähler, J. Vis. 15(1):9, 1–32 (2012).

C. Cierpka, M. Rossi, R. Segura, and C. J. Kähler, Meas. Sci. Technol. 22, 015401 (2011).
[Crossref]

C. Cierpka, R. Segura, R. Hain, and C. J. Kähler, Meas. Sci. Technol. 21, 045401 (2010).
[Crossref]

Liu, Z. C.

S. M. Soloff, R. J. Adrian, and Z. C. Liu, Meas. Sci. Technol. 8, 1441 (1997).
[Crossref]

Maas, H. G.

H. G. Maas, A. Gruen, and D. A. Papantoniou, Exp. Fluids 15, 133 (1993).
[Crossref]

Malik, N. A.

N. A. Malik, T. Dracos, and D. A. Papantoniou, Exp. Fluids 15, 279 (1993).

Papantoniou, D. A.

H. G. Maas, A. Gruen, and D. A. Papantoniou, Exp. Fluids 15, 133 (1993).
[Crossref]

N. A. Malik, T. Dracos, and D. A. Papantoniou, Exp. Fluids 15, 279 (1993).

Rossi, M.

M. Rossi and C. J. Kähler, Exp. Fluids 55, 1809 (2014).
[Crossref]

C. Cierpka, M. Rossi, R. Segura, and C. J. Kähler, Meas. Sci. Technol. 22, 015401 (2011).
[Crossref]

Scarano, F.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, Exp. Fluids 41, 933 (2006).
[Crossref]

Segura, R.

C. Cierpka, M. Rossi, R. Segura, and C. J. Kähler, Meas. Sci. Technol. 22, 015401 (2011).
[Crossref]

C. Cierpka, R. Segura, R. Hain, and C. J. Kähler, Meas. Sci. Technol. 21, 045401 (2010).
[Crossref]

Soloff, S. M.

S. M. Soloff, R. J. Adrian, and Z. C. Liu, Meas. Sci. Technol. 8, 1441 (1997).
[Crossref]

van Oudheusden, B. W.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, Exp. Fluids 41, 933 (2006).
[Crossref]

Wieneke, B.

B. Wieneke, Meas. Sci. Technol. 24, 024008 (2013).
[Crossref]

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, Exp. Fluids 41, 933 (2006).
[Crossref]

Willert, C. E.

C. E. Willert, Meas. Sci. Technol. 8, 1465 (1997).
[Crossref]

C. E. Willert and M. Gharib, Exp. Fluids 12, 353 (1992).
[Crossref]

Exp. Fluids (5)

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, Exp. Fluids 41, 933 (2006).
[Crossref]

H. G. Maas, A. Gruen, and D. A. Papantoniou, Exp. Fluids 15, 133 (1993).
[Crossref]

C. E. Willert and M. Gharib, Exp. Fluids 12, 353 (1992).
[Crossref]

N. A. Malik, T. Dracos, and D. A. Papantoniou, Exp. Fluids 15, 279 (1993).

M. Rossi and C. J. Kähler, Exp. Fluids 55, 1809 (2014).
[Crossref]

J. Vis. (1)

C. Cierpka and C. J. Kähler, J. Vis. 15(1):9, 1–32 (2012).

Meas. Sci. Technol. (5)

B. Wieneke, Meas. Sci. Technol. 24, 024008 (2013).
[Crossref]

C. E. Willert, Meas. Sci. Technol. 8, 1465 (1997).
[Crossref]

S. M. Soloff, R. J. Adrian, and Z. C. Liu, Meas. Sci. Technol. 8, 1441 (1997).
[Crossref]

C. Cierpka, M. Rossi, R. Segura, and C. J. Kähler, Meas. Sci. Technol. 22, 015401 (2011).
[Crossref]

C. Cierpka, R. Segura, R. Hain, and C. J. Kähler, Meas. Sci. Technol. 21, 045401 (2010).
[Crossref]

Opt. Lett. (1)

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Figures (5)

Fig. 1.
Fig. 1.

Sketch of the qualitative accuracy improvement of the particle z location estimation using stereoscopic APTV compared to single-camera APTV. At β=90°, the uncertainty is equal for x and z.

Fig. 2.
Fig. 2.

From the sensor locations X1=X1Y1 and X2=X2Y2 of the corresponding particle images, the particle locations, x=xyz, are determined using third-order polynomial mapping functions (capital letters denote image/sensor coordinates; lowercase letters denote physical coordinates).

Fig. 3.
Fig. 3.

Intensity inverted gray-scale image of the pinhole matrix serving as calibration target. Note that the displacement between the pinholes, Δx and Δy, are given in physical coordinates. The diameter of the pinholes is 5 μm.

Fig. 4.
Fig. 4.

Particle location scheme using stereoscopic APTV. Single-camera APTV gives an initial estimate of the particle locations for both cameras. Thus, particle images are matched using the location information with a search radius in space. Particles are then located more accurately employing the stereoscopic view.

Fig. 5.
Fig. 5.

Error of the pinhole location reconstruction calculated at every pinhole matrix z position. For the y coordinate, the location error is the lowest, while the z uncertainty is the highest (measurement volume size: 40mm×40mm×20mm).

Equations (5)

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x=i,j,k,lci,j,k,lX1iY1jX2kY2l,i+j+k+l3
(STS)cx=STx,
x=f(X,Y,aX,aY),
x=Scx,
E=Δx2n1,

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