Abstract

A holographic system has been developed to measure the velocity field in three-dimensional flow regions. The system records the position of small tracer particles on two in-line holograms of the flow obtained simultaneously. Two exposures are recorded on each hologram. The flow velocity is derived from the displacement of the particles between exposures. A general design procedure is described for selecting the particle diameter and the concentration on the basis of the configuration of the flow facility and the resolution characteristics of the holographic imaging system. The system was implemented in a 2 ft × 2 ft (1 ft = 30.48 cm) water channel to measure the velocity field in a turbulent free-surface jet. The spatial resolution of the system is 1 mm, and the field of view is 100 mm, approximately. Measurements performed with this system are compared with results reported in the literature and are found to be in good agreement.

© 1997 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. S. K. Sinha, “Improving the accuracy and resolution of particle image or laser speckle velocimetry,” Exp. Fluids 6, 67–68 (1988).
    [CrossRef]
  3. L. K. Su, W. J. A. Dahm, “Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows,” Phys. Fluids 8, 1869–1882 (1996).
    [CrossRef]
  4. D. H. Barnhart, R. J. Adrian, G. C. Papen, “Phase-conjugate holographic system for high-resolution particle-image velocimetry,” Appl. Opt. 33, 7159–7170 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. J. Scherer, L. P. Bernal, “HPIV study of the interaction of a vortex ring with a solid wall,” (American Institute of Aeronautics and Astronautics, New York, 1993).
  7. J. Scherer, L. P. Bernal, “Resolution characteristics of holographic particle image velocimetry,” AIAA J. 31, 434–437 (1993).
    [CrossRef]
  8. B. G. Parrent, B. J. Thompson, “On the Fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent backgrounds,” Opt. Acta 11, 183–193 (1964).
    [CrossRef]
  9. H. Meng, W. L. Anderson, F. Hussain, D. Liu, “Intrinsic speckle noise in in-line particle holography,” J. Opt. Soc. Am. A 10, 2046–2058 (1993).
    [CrossRef]
  10. G. Haussmann, W. Lauterborn, “Determination of size and position of fast moving gas bubbles in liquids by digital 3-D image processing of hologram reconstructions,” Appl. Opt. 19, 3529–3535 (1980).
    [CrossRef] [PubMed]
  11. B. J. Thompson, J. H. Ward, W. R. Zinky, “Application of hologram techniques for particle size analysis,” Appl. Opt. 6, 519–526 (1967).
    [CrossRef] [PubMed]
  12. S. J. Forbes, T. H. Kuehn, In-Line Particle Holography Using Photographic Threshold Technique (Fluid Engineering Division, American Society of Mechanical Engineering, New York, 1990), Vol. 95, pp. 45–47.
  13. W. K. Witherow, “A high resolution holographic particle sizing system,” Opt. Eng. 18, 249–255 (1979).
    [CrossRef]
  14. J. O. Scherer, “Whole-field velocity measurements in a turbulent free-surface jet,” Ph.D. dissertation (University of Michigan, Ann Arbor, Michigan, 1995).

1996 (1)

L. K. Su, W. J. A. Dahm, “Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows,” Phys. Fluids 8, 1869–1882 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (2)

J. Scherer, L. P. Bernal, “Resolution characteristics of holographic particle image velocimetry,” AIAA J. 31, 434–437 (1993).
[CrossRef]

H. Meng, W. L. Anderson, F. Hussain, D. Liu, “Intrinsic speckle noise in in-line particle holography,” J. Opt. Soc. Am. A 10, 2046–2058 (1993).
[CrossRef]

1991 (1)

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

1988 (1)

S. K. Sinha, “Improving the accuracy and resolution of particle image or laser speckle velocimetry,” Exp. Fluids 6, 67–68 (1988).
[CrossRef]

1980 (1)

1979 (1)

W. K. Witherow, “A high resolution holographic particle sizing system,” Opt. Eng. 18, 249–255 (1979).
[CrossRef]

1967 (1)

1964 (1)

B. G. Parrent, B. J. Thompson, “On the Fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent backgrounds,” Opt. Acta 11, 183–193 (1964).
[CrossRef]

Adrian, R. J.

Anderson, W. L.

Barnhart, D. H.

Bernal, L. P.

J. Scherer, L. P. Bernal, “Resolution characteristics of holographic particle image velocimetry,” AIAA J. 31, 434–437 (1993).
[CrossRef]

J. Scherer, L. P. Bernal, “HPIV study of the interaction of a vortex ring with a solid wall,” (American Institute of Aeronautics and Astronautics, New York, 1993).

Dahm, W. J. A.

L. K. Su, W. J. A. Dahm, “Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows,” Phys. Fluids 8, 1869–1882 (1996).
[CrossRef]

Forbes, S. J.

S. J. Forbes, T. H. Kuehn, In-Line Particle Holography Using Photographic Threshold Technique (Fluid Engineering Division, American Society of Mechanical Engineering, New York, 1990), Vol. 95, pp. 45–47.

Haussmann, G.

Hui-Meng, D. L.

Hussain, F.

Kuehn, T. H.

S. J. Forbes, T. H. Kuehn, In-Line Particle Holography Using Photographic Threshold Technique (Fluid Engineering Division, American Society of Mechanical Engineering, New York, 1990), Vol. 95, pp. 45–47.

Lauterborn, W.

Liu, D.

Meng, H.

Papen, G. C.

Parrent, B. G.

B. G. Parrent, B. J. Thompson, “On the Fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent backgrounds,” Opt. Acta 11, 183–193 (1964).
[CrossRef]

Scherer, J.

J. Scherer, L. P. Bernal, “Resolution characteristics of holographic particle image velocimetry,” AIAA J. 31, 434–437 (1993).
[CrossRef]

J. Scherer, L. P. Bernal, “HPIV study of the interaction of a vortex ring with a solid wall,” (American Institute of Aeronautics and Astronautics, New York, 1993).

Scherer, J. O.

J. O. Scherer, “Whole-field velocity measurements in a turbulent free-surface jet,” Ph.D. dissertation (University of Michigan, Ann Arbor, Michigan, 1995).

Sinha, S. K.

S. K. Sinha, “Improving the accuracy and resolution of particle image or laser speckle velocimetry,” Exp. Fluids 6, 67–68 (1988).
[CrossRef]

Su, L. K.

L. K. Su, W. J. A. Dahm, “Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows,” Phys. Fluids 8, 1869–1882 (1996).
[CrossRef]

Thompson, B. J.

B. J. Thompson, J. H. Ward, W. R. Zinky, “Application of hologram techniques for particle size analysis,” Appl. Opt. 6, 519–526 (1967).
[CrossRef] [PubMed]

B. G. Parrent, B. J. Thompson, “On the Fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent backgrounds,” Opt. Acta 11, 183–193 (1964).
[CrossRef]

Ward, J. H.

Witherow, W. K.

W. K. Witherow, “A high resolution holographic particle sizing system,” Opt. Eng. 18, 249–255 (1979).
[CrossRef]

Zinky, W. R.

AIAA J. (1)

J. Scherer, L. P. Bernal, “Resolution characteristics of holographic particle image velocimetry,” AIAA J. 31, 434–437 (1993).
[CrossRef]

Annu. Rev. Fluid Mech. (1)

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

Appl. Opt. (4)

Exp. Fluids (1)

S. K. Sinha, “Improving the accuracy and resolution of particle image or laser speckle velocimetry,” Exp. Fluids 6, 67–68 (1988).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

B. G. Parrent, B. J. Thompson, “On the Fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent backgrounds,” Opt. Acta 11, 183–193 (1964).
[CrossRef]

Opt. Eng. (1)

W. K. Witherow, “A high resolution holographic particle sizing system,” Opt. Eng. 18, 249–255 (1979).
[CrossRef]

Phys. Fluids (1)

L. K. Su, W. J. A. Dahm, “Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows,” Phys. Fluids 8, 1869–1882 (1996).
[CrossRef]

Other (3)

J. Scherer, L. P. Bernal, “HPIV study of the interaction of a vortex ring with a solid wall,” (American Institute of Aeronautics and Astronautics, New York, 1993).

S. J. Forbes, T. H. Kuehn, In-Line Particle Holography Using Photographic Threshold Technique (Fluid Engineering Division, American Society of Mechanical Engineering, New York, 1990), Vol. 95, pp. 45–47.

J. O. Scherer, “Whole-field velocity measurements in a turbulent free-surface jet,” Ph.D. dissertation (University of Michigan, Ann Arbor, Michigan, 1995).

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Figures (9)

Fig. 1
Fig. 1

In-line holographic recording and reconstruction.

Fig. 2
Fig. 2

Reconstructed particle images showing depth of field, A = 4.

Fig. 3
Fig. 3

Resolution diagrams for holographic recording parameters. (a) Limits owing to experiment scale. (b) Limits owing to resolution requirement.

Fig. 4
Fig. 4

Coherence-length diagram.

Fig. 5
Fig. 5

Free-surface jet flow schematic.

Fig. 6
Fig. 6

HPIV recording system for jet flow experiments.

Fig. 7
Fig. 7

HPIV reconstruction system.

Fig. 8
Fig. 8

Reconstructed particle images (a) before and (b) after image processing.

Fig. 9
Fig. 9

HPIV data for the vertical plane through the jet centerline. (a) Velocity vector plot. (b) Vorticity field.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

V=Imax-Imin,
I=1-sinπFrd2J1πFr/dr/d+14J1πFr/dr/d2,
ri=2iλz1/2.
I/I0=exp-nLπd/22Qex<0.80,
nd2L<0.108.
dmax=0.05nL1/2.
dmin=Fminλzmax1/2,
=2d2/λ.
nmin=10/3,
L=zmax=d2/Fminλ2d2/λ=12Fmin=167.
α=z+δ2-z21/2=2δz+δ21/22δz1/2.
α2mλz1/2.

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