Abstract

A novel holographic particle-image velocimeter system has been developed for the study of three-dimensional (3-D) fluid velocity fields. The recording system produces 3-D particle images with a resolution, a signal-to-noise ratio, an accuracy, and derived velocity fields that are comparable to high-quality two-dimensional photographic particle-image velocimetry (PIV). The high image resolution is accomplished through the use of low f-number optics, a fringe-stabilized processing chemistry, and a phase conjugate play-back geometry that compensates for aberrations in the imaging system. In addition, the system employs a reference multiplexed, off-axis geometry for the determination of velocity directions with the cross-correlation technique, and a stereo camera geometry for the determination of the three velocity components. The combination of the imaging and reconstruction subsystems makes the analysis of volumetric PIV domains feasible.

© 1994 Optical Society of America

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References

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  1. R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
    [CrossRef]
  2. M. P. Arroyo, C. A. Greated, “Stereoscopic particle velocimetry,” Meas. Sci. Technol. 2, 1181–1186 (1991).
    [CrossRef]
  3. A. K. Prasad, R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Exp. Fluids 15, 49–60 (1993).
    [CrossRef]
  4. J. C. Kent, A. R. Eaton, “Stereo photography of neutral density He-filled bubbles for 3-D fluid motion in an engine cylinder,” Appl. Opt. 21, 904–912 (1982).
    [CrossRef] [PubMed]
  5. K. Nishino, N. Kasagi, M. Hirata, “Three-dimensional particle tracking velocimetry based on automated digital image processing,” ASME J. Fluids Eng. 111, 384–391 (1989).
    [CrossRef]
  6. D. Papantoniou, H.-G. Maas, “Recent advances in 3-D particle tracking velocimetry,” in Proceedings of the 5th International Symposium on the Application of Laser Technology to Fluid Mechanics (Instituto Superior Tecnico, Lisbon, 1990), pp. 18.4.1–18.4.6.
  7. H. Royer, “Holographic velocimetry of submicron particles,” Opt. Commun. 20, 84–86 (1977).
    [CrossRef]
  8. W. Lauterborn, A. Vogel, “Modern optical techniques in fluid mechanics,” Annu. Rev. Fluid Mech. 16, 223–244 (1984).
    [CrossRef]
  9. P. H. Malyak, B. J. Thompson, “Particle displacement and velocity measurement using holography,” Opt. Eng. 23, 567–576 (1984).
  10. K. Hinsch, H. Hinrichs, G. Kufahl, P. Meinlschmidt, “Holography with controlled coherence for 3-D particle image velocimetry (PIV),” in Holographics 1990, T. Tschudi, ed. (Mesago, Nürnberg, Germany, 1990), pp. 51–57.
  11. M. Stanislas, M. Dadi, O. Rodriguez, A. Dyment, “A study by holographic velocimetry of the behavior of free small particles in a flow,” Exp. Fluids 10, 285–294 (1991).
  12. L. M. Weinstein, G. B. Beeler, A. M. Lindemann, “High-speed holocinematographic velocimeter for studying turbulent flow control physics,” in Proceedings of the 1985 Conference on Shear Flow Control, AIAA paper 85-0526 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1985), pp. 1–9.
  13. J. A. Liburdy, “Holocinematographic velocimetry: resolution limitation for flow measurement,” Appl. Opt. 26, 4250–4255 (1987).
    [CrossRef] [PubMed]
  14. J. M. Coupland, N. A. Halliwell, “Particle image velocimetry: three-dimensional fluid velocity measurements using holographic recording and optical correlation,” Appl. Opt. 31, 1005–1007 (1992).
    [CrossRef] [PubMed]
  15. H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interaction, coherent structures, and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
    [CrossRef]
  16. C. S. Moraitas, “Optical processing of holographic particle records,” Ph.D. dissertation (Technical University of Denmark, Lingby, Denmark, 1992).
  17. C. Kocher, “A study of the effects of processing chemistry of the holographic image space,” Ph.D. dissertation (Brighton Polytechnic, Brighton, England, 1988). Experiments described in this paper used Agfa 8E56HD plates processed with Agfa-Gevaert GP62 developer followed with a rehalogenating bleach. The 15% shrinkage value is representative of fixed or solvent-bleached processes.
  18. Y. A. Carts, “Mathematica supports electro-optics users,” Laser Focus World 29, 107–108 (1993).
  19. R. D. Keane, R. J. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
    [CrossRef]
  20. C. D. Meinhart, A. K. Prasad, R. J. Adrian, “A parallel digital processor system for particle image velocimetry,” Meas. Sci. Technol. 4, 619–626 (1993).
    [CrossRef]

1993 (3)

A. K. Prasad, R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Exp. Fluids 15, 49–60 (1993).
[CrossRef]

Y. A. Carts, “Mathematica supports electro-optics users,” Laser Focus World 29, 107–108 (1993).

C. D. Meinhart, A. K. Prasad, R. J. Adrian, “A parallel digital processor system for particle image velocimetry,” Meas. Sci. Technol. 4, 619–626 (1993).
[CrossRef]

1992 (2)

1991 (4)

H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interaction, coherent structures, and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
[CrossRef]

M. Stanislas, M. Dadi, O. Rodriguez, A. Dyment, “A study by holographic velocimetry of the behavior of free small particles in a flow,” Exp. Fluids 10, 285–294 (1991).

R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

M. P. Arroyo, C. A. Greated, “Stereoscopic particle velocimetry,” Meas. Sci. Technol. 2, 1181–1186 (1991).
[CrossRef]

1989 (1)

K. Nishino, N. Kasagi, M. Hirata, “Three-dimensional particle tracking velocimetry based on automated digital image processing,” ASME J. Fluids Eng. 111, 384–391 (1989).
[CrossRef]

1987 (1)

1984 (2)

W. Lauterborn, A. Vogel, “Modern optical techniques in fluid mechanics,” Annu. Rev. Fluid Mech. 16, 223–244 (1984).
[CrossRef]

P. H. Malyak, B. J. Thompson, “Particle displacement and velocity measurement using holography,” Opt. Eng. 23, 567–576 (1984).

1982 (1)

1977 (1)

H. Royer, “Holographic velocimetry of submicron particles,” Opt. Commun. 20, 84–86 (1977).
[CrossRef]

Adrian, R. J.

A. K. Prasad, R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Exp. Fluids 15, 49–60 (1993).
[CrossRef]

C. D. Meinhart, A. K. Prasad, R. J. Adrian, “A parallel digital processor system for particle image velocimetry,” Meas. Sci. Technol. 4, 619–626 (1993).
[CrossRef]

R. D. Keane, R. J. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[CrossRef]

R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

Arroyo, M. P.

M. P. Arroyo, C. A. Greated, “Stereoscopic particle velocimetry,” Meas. Sci. Technol. 2, 1181–1186 (1991).
[CrossRef]

Beeler, G. B.

L. M. Weinstein, G. B. Beeler, A. M. Lindemann, “High-speed holocinematographic velocimeter for studying turbulent flow control physics,” in Proceedings of the 1985 Conference on Shear Flow Control, AIAA paper 85-0526 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1985), pp. 1–9.

Carts, Y. A.

Y. A. Carts, “Mathematica supports electro-optics users,” Laser Focus World 29, 107–108 (1993).

Coupland, J. M.

Dadi, M.

M. Stanislas, M. Dadi, O. Rodriguez, A. Dyment, “A study by holographic velocimetry of the behavior of free small particles in a flow,” Exp. Fluids 10, 285–294 (1991).

Dyment, A.

M. Stanislas, M. Dadi, O. Rodriguez, A. Dyment, “A study by holographic velocimetry of the behavior of free small particles in a flow,” Exp. Fluids 10, 285–294 (1991).

Eaton, A. R.

Greated, C. A.

M. P. Arroyo, C. A. Greated, “Stereoscopic particle velocimetry,” Meas. Sci. Technol. 2, 1181–1186 (1991).
[CrossRef]

Halliwell, N. A.

Hinrichs, H.

K. Hinsch, H. Hinrichs, G. Kufahl, P. Meinlschmidt, “Holography with controlled coherence for 3-D particle image velocimetry (PIV),” in Holographics 1990, T. Tschudi, ed. (Mesago, Nürnberg, Germany, 1990), pp. 51–57.

Hinsch, K.

K. Hinsch, H. Hinrichs, G. Kufahl, P. Meinlschmidt, “Holography with controlled coherence for 3-D particle image velocimetry (PIV),” in Holographics 1990, T. Tschudi, ed. (Mesago, Nürnberg, Germany, 1990), pp. 51–57.

Hirata, M.

K. Nishino, N. Kasagi, M. Hirata, “Three-dimensional particle tracking velocimetry based on automated digital image processing,” ASME J. Fluids Eng. 111, 384–391 (1989).
[CrossRef]

Hussain, F.

H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interaction, coherent structures, and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
[CrossRef]

Kasagi, N.

K. Nishino, N. Kasagi, M. Hirata, “Three-dimensional particle tracking velocimetry based on automated digital image processing,” ASME J. Fluids Eng. 111, 384–391 (1989).
[CrossRef]

Keane, R. D.

R. D. Keane, R. J. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[CrossRef]

Kent, J. C.

Kocher, C.

C. Kocher, “A study of the effects of processing chemistry of the holographic image space,” Ph.D. dissertation (Brighton Polytechnic, Brighton, England, 1988). Experiments described in this paper used Agfa 8E56HD plates processed with Agfa-Gevaert GP62 developer followed with a rehalogenating bleach. The 15% shrinkage value is representative of fixed or solvent-bleached processes.

Kufahl, G.

K. Hinsch, H. Hinrichs, G. Kufahl, P. Meinlschmidt, “Holography with controlled coherence for 3-D particle image velocimetry (PIV),” in Holographics 1990, T. Tschudi, ed. (Mesago, Nürnberg, Germany, 1990), pp. 51–57.

Lauterborn, W.

W. Lauterborn, A. Vogel, “Modern optical techniques in fluid mechanics,” Annu. Rev. Fluid Mech. 16, 223–244 (1984).
[CrossRef]

Liburdy, J. A.

Lindemann, A. M.

L. M. Weinstein, G. B. Beeler, A. M. Lindemann, “High-speed holocinematographic velocimeter for studying turbulent flow control physics,” in Proceedings of the 1985 Conference on Shear Flow Control, AIAA paper 85-0526 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1985), pp. 1–9.

Maas, H.-G.

D. Papantoniou, H.-G. Maas, “Recent advances in 3-D particle tracking velocimetry,” in Proceedings of the 5th International Symposium on the Application of Laser Technology to Fluid Mechanics (Instituto Superior Tecnico, Lisbon, 1990), pp. 18.4.1–18.4.6.

Malyak, P. H.

P. H. Malyak, B. J. Thompson, “Particle displacement and velocity measurement using holography,” Opt. Eng. 23, 567–576 (1984).

Meinhart, C. D.

C. D. Meinhart, A. K. Prasad, R. J. Adrian, “A parallel digital processor system for particle image velocimetry,” Meas. Sci. Technol. 4, 619–626 (1993).
[CrossRef]

Meinlschmidt, P.

K. Hinsch, H. Hinrichs, G. Kufahl, P. Meinlschmidt, “Holography with controlled coherence for 3-D particle image velocimetry (PIV),” in Holographics 1990, T. Tschudi, ed. (Mesago, Nürnberg, Germany, 1990), pp. 51–57.

Meng, H.

H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interaction, coherent structures, and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
[CrossRef]

Moraitas, C. S.

C. S. Moraitas, “Optical processing of holographic particle records,” Ph.D. dissertation (Technical University of Denmark, Lingby, Denmark, 1992).

Nishino, K.

K. Nishino, N. Kasagi, M. Hirata, “Three-dimensional particle tracking velocimetry based on automated digital image processing,” ASME J. Fluids Eng. 111, 384–391 (1989).
[CrossRef]

Papantoniou, D.

D. Papantoniou, H.-G. Maas, “Recent advances in 3-D particle tracking velocimetry,” in Proceedings of the 5th International Symposium on the Application of Laser Technology to Fluid Mechanics (Instituto Superior Tecnico, Lisbon, 1990), pp. 18.4.1–18.4.6.

Prasad, A. K.

A. K. Prasad, R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Exp. Fluids 15, 49–60 (1993).
[CrossRef]

C. D. Meinhart, A. K. Prasad, R. J. Adrian, “A parallel digital processor system for particle image velocimetry,” Meas. Sci. Technol. 4, 619–626 (1993).
[CrossRef]

Rodriguez, O.

M. Stanislas, M. Dadi, O. Rodriguez, A. Dyment, “A study by holographic velocimetry of the behavior of free small particles in a flow,” Exp. Fluids 10, 285–294 (1991).

Royer, H.

H. Royer, “Holographic velocimetry of submicron particles,” Opt. Commun. 20, 84–86 (1977).
[CrossRef]

Stanislas, M.

M. Stanislas, M. Dadi, O. Rodriguez, A. Dyment, “A study by holographic velocimetry of the behavior of free small particles in a flow,” Exp. Fluids 10, 285–294 (1991).

Thompson, B. J.

P. H. Malyak, B. J. Thompson, “Particle displacement and velocity measurement using holography,” Opt. Eng. 23, 567–576 (1984).

Vogel, A.

W. Lauterborn, A. Vogel, “Modern optical techniques in fluid mechanics,” Annu. Rev. Fluid Mech. 16, 223–244 (1984).
[CrossRef]

Weinstein, L. M.

L. M. Weinstein, G. B. Beeler, A. M. Lindemann, “High-speed holocinematographic velocimeter for studying turbulent flow control physics,” in Proceedings of the 1985 Conference on Shear Flow Control, AIAA paper 85-0526 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1985), pp. 1–9.

Annu. Rev. Fluid Mech. (2)

R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

W. Lauterborn, A. Vogel, “Modern optical techniques in fluid mechanics,” Annu. Rev. Fluid Mech. 16, 223–244 (1984).
[CrossRef]

Appl. Opt. (3)

Appl. Sci. Res. (1)

R. D. Keane, R. J. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[CrossRef]

ASME J. Fluids Eng. (1)

K. Nishino, N. Kasagi, M. Hirata, “Three-dimensional particle tracking velocimetry based on automated digital image processing,” ASME J. Fluids Eng. 111, 384–391 (1989).
[CrossRef]

Exp. Fluids (2)

A. K. Prasad, R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Exp. Fluids 15, 49–60 (1993).
[CrossRef]

M. Stanislas, M. Dadi, O. Rodriguez, A. Dyment, “A study by holographic velocimetry of the behavior of free small particles in a flow,” Exp. Fluids 10, 285–294 (1991).

Fluid Dyn. Res. (1)

H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interaction, coherent structures, and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991).
[CrossRef]

Laser Focus World (1)

Y. A. Carts, “Mathematica supports electro-optics users,” Laser Focus World 29, 107–108 (1993).

Meas. Sci. Technol. (2)

C. D. Meinhart, A. K. Prasad, R. J. Adrian, “A parallel digital processor system for particle image velocimetry,” Meas. Sci. Technol. 4, 619–626 (1993).
[CrossRef]

M. P. Arroyo, C. A. Greated, “Stereoscopic particle velocimetry,” Meas. Sci. Technol. 2, 1181–1186 (1991).
[CrossRef]

Opt. Commun. (1)

H. Royer, “Holographic velocimetry of submicron particles,” Opt. Commun. 20, 84–86 (1977).
[CrossRef]

Opt. Eng. (1)

P. H. Malyak, B. J. Thompson, “Particle displacement and velocity measurement using holography,” Opt. Eng. 23, 567–576 (1984).

Other (5)

K. Hinsch, H. Hinrichs, G. Kufahl, P. Meinlschmidt, “Holography with controlled coherence for 3-D particle image velocimetry (PIV),” in Holographics 1990, T. Tschudi, ed. (Mesago, Nürnberg, Germany, 1990), pp. 51–57.

D. Papantoniou, H.-G. Maas, “Recent advances in 3-D particle tracking velocimetry,” in Proceedings of the 5th International Symposium on the Application of Laser Technology to Fluid Mechanics (Instituto Superior Tecnico, Lisbon, 1990), pp. 18.4.1–18.4.6.

L. M. Weinstein, G. B. Beeler, A. M. Lindemann, “High-speed holocinematographic velocimeter for studying turbulent flow control physics,” in Proceedings of the 1985 Conference on Shear Flow Control, AIAA paper 85-0526 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1985), pp. 1–9.

C. S. Moraitas, “Optical processing of holographic particle records,” Ph.D. dissertation (Technical University of Denmark, Lingby, Denmark, 1992).

C. Kocher, “A study of the effects of processing chemistry of the holographic image space,” Ph.D. dissertation (Brighton Polytechnic, Brighton, England, 1988). Experiments described in this paper used Agfa 8E56HD plates processed with Agfa-Gevaert GP62 developer followed with a rehalogenating bleach. The 15% shrinkage value is representative of fixed or solvent-bleached processes.

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Figures (9)

Fig. 1
Fig. 1

Optical system used in recording the hologram. Light pulses I01[t1] and I02[t2] are generated by a dual-pulsed Nd:YAG laser system. A V-shaped beam splitter (BS) is used to combine the two pulses through mirrors (M) and lenses (L) into a common illumination path (BS, M4, M6, L4, M7, L7), as well as to produce separated reference beams through different paths: R2 = BS, L2, M5, L5, L8, and M9 and R1 = BS, L1, M3, L3, L6, and M8.

Fig. 2
Fig. 2

Imaging subsystem used for phase conjugate reconstruction. One perspective channel is shown being reconstructed. The stereo-produced images of a single particle are shown in the interrogation volume as crossed ellipsoids.

Fig. 3
Fig. 3

Grating wave vectors within the film emulsion: (a) During film exposure, the refracted reference beam k ¯ r and refracted object beam k ¯ o produce a grating wave vector K within the emulsion with a perpendicular component K and a parallel component K||. (b) After development, the tilt of Kd produces an angular distortion θs between the reconstructed object wave vector kod and the original object wave vector ko. (c) In-line recording geometry (θr = 90°). (d) Off-axis transmission geometry (θr = 40°). (o) Reflection geometry (θr = −40°).

Fig. 4
Fig. 4

Film-distortion effects on absolute image displacement: (a) Contour plot of the absolute image displacement θsds as a function of the object and reference-beam angles for a 0.5% emulsion shrinkage S and an effective distance ds = 250 mm. Contours have 10-μm intervals. Two of the recording geometries are labeled on the y axis. The reflection geometry (θr = −40°) is not shown. Also shown are slices of the contour plot for fixed reference-beam angles and each geometry (in-line, off-axis, reflection): (b) θr = 90° and S = 15%, (c) θr = 40° and S = 0.5%, and (d) θr = −40° and S = 0.1%.

Fig. 5
Fig. 5

Contour plot of the wave-vector displacement range dsmax − θmin) |window as a function of the window-center angle and reference-beam angle for a 10° window, a 0.5% emulsion shrinkage, and an effective distance ds = 250 mm. Contours have 5-μm intervals. Two of the recording geometries are labeled on the y axis. The reflection geometry (θr = −40°) is not shown. Also shown are contour plots for fixed reference-beam angles for each geometry (in-line, off-axis, and reflection) and for different values of S: (b) θr = 90° and S = 15%, (c) θr = 40° and S = 0.5%, and (d) θr = −40° and S = 0.1%. Note that the off-axis geometry produces smaller displacement sizes over the entire range of angles that are imaged by the system.

Fig. 6
Fig. 6

A single reconstructed particle image: (a) horizontal scan showing a 30-μm-particle image size, and (b) vertical scan showing a 15-μm-particle image size. The larger horizontal image size is due to the recorded grating vectors being horizontal.

Fig. 7
Fig. 7

The sampled 3-D particle images are shown within a 1-mm3 volume cell, imaged from a single reconstruction channel. Each stack of image slices forms an elongated ellipsoid structure, whose length ranges between 100 and 700 μm and provides a measure of depth of focus. The original particles were 0.5–1 μm in size.

Fig. 8
Fig. 8

Schematic of the two images at times t1 and t2 within the image volume for a single imaging channel. For clarity, the phase-conjugate recording and reconstruction through L11–P1–L12 is depicted as a single lens projection system (L) having unity magnification. The displacement along the CCD array is dX and the actual displacement of the particle is dx = udt.

Fig. 9
Fig. 9

Complete 3-D vector field volume, from a pipe channel flow, showing the measured vectors along the sides of the 24.5 mm × 24.5 mm × 60 mm measurement volume, based on cross correlation of the particle images. More than 400,000 three-dimensional velocity vectors have been extracted from the measurement volume. Vectors have their mean velocity (0.8 m/s) subtracted.

Equations (5)

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K = k ¯ o - k ¯ r ,
K d = K + 1 1 - S K ,
C ( s ) = I 1 ( X ) I 2 ( X - s ) d X .
d X = u d t - w d t q x / q z ,
d Y = v d t - w d t q y / q z ,

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