Abstract

A method for measuring flow velocity distribution in the interior of a transparent fluid is proposed. The method utilizes a thin sheet of laser light, which illuminates fluid containing small scattering particles. A double-exposure hologram is made with the scattered light as a signal wave. In the reconstructed image we can observe interference fringes which correspond to the distribution of particle displacements between the two exposures and consequently to the distribution of flow velocity. Simple experiments were performed that confirmed the usefulness of the method. A discussion of the relation of this method to laser Doppler velocimetry shows that the two methods utilize different aspects of the same phenomenon.

© 1977 Optical Society of America

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References

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  1. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971),p. 418.
  2. During the preparation of this paper, an investigation was published in which a similar optical arrangement is used for speckle interferometry. The arrangement was used for measuring displacements in the interior of a transparent solid. [D. B. Baker and M. E. Fourney, Exp. Mech.16, (6), 209 (1976)]. A similar experiment was independently reported by two of the present authors and their colleague [H. Uozato, K. Iwata, and R. Nagata, in Preprints of the Spring Meeting of the Japan Society of Applied Physics, Tokyo, March, 1976 p. 122).
  3. Reference 1,p. 428.
  4. T. Matsumoto, K. Iwata, and R. Nagata, Bull. Univ. of Osaka Prefect.Ser. A 22, 101 (1973).
  5. Reference 1,p. 431.
  6. H. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 178 (1964).
    [Crossref]
  7. F. Durst, A. Melling, and J. H. Whitelaw, Principles and Practice of Laser-Doppler Anemometry (Academic, London, 1976),p. 104.
  8. T. Suzuki and R. Hioki, J. Opt. Soc. Am. 57, 1551 (1967).
    [Crossref]
  9. T. Matsumoto, K. Iwata, and R. Nagata, Appl. Opt. 12, 960 (1973).
  10. From a catalogue of International Laser Systems, Inc., Catalog #C 1012, August, 1974.

1973 (2)

T. Matsumoto, K. Iwata, and R. Nagata, Bull. Univ. of Osaka Prefect.Ser. A 22, 101 (1973).

T. Matsumoto, K. Iwata, and R. Nagata, Appl. Opt. 12, 960 (1973).

1967 (1)

1964 (1)

H. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 178 (1964).
[Crossref]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971),p. 418.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971),p. 418.

Cummins, H. Z.

H. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 178 (1964).
[Crossref]

Durst, F.

F. Durst, A. Melling, and J. H. Whitelaw, Principles and Practice of Laser-Doppler Anemometry (Academic, London, 1976),p. 104.

Hioki, R.

Iwata, K.

T. Matsumoto, K. Iwata, and R. Nagata, Appl. Opt. 12, 960 (1973).

T. Matsumoto, K. Iwata, and R. Nagata, Bull. Univ. of Osaka Prefect.Ser. A 22, 101 (1973).

Lin, L. H.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971),p. 418.

Matsumoto, T.

T. Matsumoto, K. Iwata, and R. Nagata, Bull. Univ. of Osaka Prefect.Ser. A 22, 101 (1973).

T. Matsumoto, K. Iwata, and R. Nagata, Appl. Opt. 12, 960 (1973).

Melling, A.

F. Durst, A. Melling, and J. H. Whitelaw, Principles and Practice of Laser-Doppler Anemometry (Academic, London, 1976),p. 104.

Nagata, R.

T. Matsumoto, K. Iwata, and R. Nagata, Bull. Univ. of Osaka Prefect.Ser. A 22, 101 (1973).

T. Matsumoto, K. Iwata, and R. Nagata, Appl. Opt. 12, 960 (1973).

Suzuki, T.

Whitelaw, J. H.

F. Durst, A. Melling, and J. H. Whitelaw, Principles and Practice of Laser-Doppler Anemometry (Academic, London, 1976),p. 104.

Yeh, H.

H. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 178 (1964).
[Crossref]

Appl. Opt. (1)

T. Matsumoto, K. Iwata, and R. Nagata, Appl. Opt. 12, 960 (1973).

Appl. Phys. Lett. (1)

H. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 178 (1964).
[Crossref]

Bull. Univ. of Osaka Prefect.Ser. A (1)

T. Matsumoto, K. Iwata, and R. Nagata, Bull. Univ. of Osaka Prefect.Ser. A 22, 101 (1973).

J. Opt. Soc. Am. (1)

Other (6)

Reference 1,p. 431.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971),p. 418.

During the preparation of this paper, an investigation was published in which a similar optical arrangement is used for speckle interferometry. The arrangement was used for measuring displacements in the interior of a transparent solid. [D. B. Baker and M. E. Fourney, Exp. Mech.16, (6), 209 (1976)]. A similar experiment was independently reported by two of the present authors and their colleague [H. Uozato, K. Iwata, and R. Nagata, in Preprints of the Spring Meeting of the Japan Society of Applied Physics, Tokyo, March, 1976 p. 122).

Reference 1,p. 428.

F. Durst, A. Melling, and J. H. Whitelaw, Principles and Practice of Laser-Doppler Anemometry (Academic, London, 1976),p. 104.

From a catalogue of International Laser Systems, Inc., Catalog #C 1012, August, 1974.

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Figures (6)

FIG. 1
FIG. 1

Optical arrangement for measuring distribution of flow velocity by holographic interferometry.

FIG. 2
FIG. 2

Optical arrangement used for the experiments. A glass case filled with glycerine is illuminated by a light sheet. Flow is caused by a point heat source.

FIG. 3
FIG. 3

(a) Reconstructed image of a double-exposure hologram. These fringes show flow velocity distribution in the section at height H = 30 mm in Fig. 2. (b) Flow velocity distribution along the line AB shown in Fig. 2. Open circles are obtained from Fig. 3(a). Values represented by vertical bars are obtained from observation through a microscope.

FIG. 4
FIG. 4

Reconstructed images in the section at various heights H (in mm): (a) 41.5, (b) 34.5, (c) 27.5, (d) 20.5, (e) 13.5, (f) 6.5.

FIG. 5
FIG. 5

Optical system for laser Doppler velocimetry used by Yeh and Cummins.

FIG. 6
FIG. 6

(a) Optical arrangement for interpreting the relation between holographic interferometry and laser Doppler velocimetry. P is a single scattering particle. S is the scattered wave. R is the plane reference wave. (b) Optical disturbance at two moments near a point Q in Fig. 6(a). Solid lines represent the crests of the waves at a moment. Broken lines represent the crest of the reference wave at the moment λ′/c later. Finally, d is the fringe spacing on a plane O parallel to the wave front of the scattered wave.

Equations (8)

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( s 0 s i ) v τ = m λ .
v s = m λ | s 0 s i | τ ,
s = s 0 s i | s 0 s i | .
d = λ / sin θ .
υ m = Δ d / ( λ / c ) = c ( λ λ ) / ( λ sin θ ) .
υ f = υ m / d = ν ν ,
υ f τ = m ( m : integer ) .
ν ν = ( s 0 s i ) v / λ .