Abstract

We report on an original use of optical correlation techniques and holographic recording to provide three-dimensional velocity vector information from particle image velocimetry.

© 1992 Optical Society of America

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References

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  1. T. D. Dudderar, P. G. Simpkins, “Laser speckle photography in a fluid medium,” Nature (London) 270, 45–47 (1977).
    [CrossRef]
  2. C. J. D. Pickering, N. A. Halliwell, “Speckle photography in fluid flows: signal recovery with two step processing,” Appl. Opt. 23, 1128–1129 (1984).
    [CrossRef] [PubMed]
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, p. 60.
  4. J. M. Coupland, C. J. D. Pickering, “Particle image velocimetry: estimation of measurement confidence at low seeding densities,” Opt. Lasers Eng. 9, 201–210 (1988).
    [CrossRef]
  5. J. M. Coupland, N. A. Halliwell, “Particle image velocimetry: rapid transparency analysis using optical correlation,” Appl. Opt. 27, 1919–1921 (1988).
    [CrossRef] [PubMed]
  6. M. L. Jakobsen, P. Buchhave, “PIV processing: parallel processing with optical correlators,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 9–12 July 1990.
  7. N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), Chap. 3, p. 21.
  8. J. M. Coupland, C. J. D. Pickering, N. A. Halliwell, “Particle image velocimetry: theory of directional ambiguity removal using holographic image separation,” Appl. Opt. 26, 1576–1578 (1987).
    [CrossRef] [PubMed]

1988 (2)

J. M. Coupland, C. J. D. Pickering, “Particle image velocimetry: estimation of measurement confidence at low seeding densities,” Opt. Lasers Eng. 9, 201–210 (1988).
[CrossRef]

J. M. Coupland, N. A. Halliwell, “Particle image velocimetry: rapid transparency analysis using optical correlation,” Appl. Opt. 27, 1919–1921 (1988).
[CrossRef] [PubMed]

1987 (1)

1984 (1)

1977 (1)

T. D. Dudderar, P. G. Simpkins, “Laser speckle photography in a fluid medium,” Nature (London) 270, 45–47 (1977).
[CrossRef]

Abramson, N.

N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), Chap. 3, p. 21.

Buchhave, P.

M. L. Jakobsen, P. Buchhave, “PIV processing: parallel processing with optical correlators,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 9–12 July 1990.

Coupland, J. M.

Dudderar, T. D.

T. D. Dudderar, P. G. Simpkins, “Laser speckle photography in a fluid medium,” Nature (London) 270, 45–47 (1977).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, p. 60.

Halliwell, N. A.

Jakobsen, M. L.

M. L. Jakobsen, P. Buchhave, “PIV processing: parallel processing with optical correlators,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 9–12 July 1990.

Pickering, C. J. D.

Simpkins, P. G.

T. D. Dudderar, P. G. Simpkins, “Laser speckle photography in a fluid medium,” Nature (London) 270, 45–47 (1977).
[CrossRef]

Appl. Opt. (3)

Nature (London) (1)

T. D. Dudderar, P. G. Simpkins, “Laser speckle photography in a fluid medium,” Nature (London) 270, 45–47 (1977).
[CrossRef]

Opt. Lasers Eng. (1)

J. M. Coupland, C. J. D. Pickering, “Particle image velocimetry: estimation of measurement confidence at low seeding densities,” Opt. Lasers Eng. 9, 201–210 (1988).
[CrossRef]

Other (3)

M. L. Jakobsen, P. Buchhave, “PIV processing: parallel processing with optical correlators,” presented at the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 9–12 July 1990.

N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), Chap. 3, p. 21.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, p. 60.

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Figures (4)

Fig. 1
Fig. 1

(a) Recording and (b) reconstruction of a PIV hologram.

Fig. 2
Fig. 2

Generation of (a) the far-field fringe pattern and (b) the spatial autocorrelation function; f indicates focal length.

Fig. 3
Fig. 3

Far-field fringe pattern.

Fig. 4
Fig. 4

Spatial autocorrelation focused (a) in front, (b) behind, and (c) in the autocorrelation plane.

Equations (10)

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U ( x , y ) = U 1 ( x , y ) + U 2 ( x , y ) ,
U 1 ( x , y ) = l = 1 N A 1 1 j λ z 1 exp { π j λ z 1 [ ( x x 1 ) 2 + ( y y 1 ) 2 ] } ,
U 2 ( x , y ) = U 1 ( x , y ) 1 j λ Δ z exp { π j λ Δ z [ ( x Δ x ) 2 + ( y Δ y ) 2 ] } ,
U ( x , y ) = U 1 ( x , y ) ( δ ( x , y ) + 1 j λ Δ z exp { π j λ Δ z [ ( x Δ x ) 2 + ( y Δ y ) 2 ] } ) .
| U ˜ ( ξ, η ) | 2 = | U ˜ 1 ( ξ, η ) | 2 × { 2 + 2 cos [ πλ Δ z ( ξ 2 , η 2 ) 2 π ( Δ x ξ + Δ y η ) π / 2 ] } ,
λ Δ z ( ξ 2 + η 2 ) 2 ( Δ x ξ + Δ y η ) 1 / 2 = 2 n + 1 ,
R U U ( u , υ ) = + U ( x , y ) U * ( x + u , y + υ ) d x d y .
R U U ( u , υ ) = R U 1 U 1 ( u , υ ) ( 2 δ ( u , υ ) + 1 j λ Δ z exp { π j λ Δ z [ ( u Δ x ) 2 + ( υ Δ y ) 2 ] } + 1 j λ Δ z exp { π j λ Δ z [ ( u + Δ x ) 2 + ( υ Δ y ) 2 ] } ) ,
R U 1 U 1 ( u , υ ) = l = 1 N | A l | 2 δ ( u , υ ) + l , m = 1 ; N l = m A l A m * 1 j λ ( z l z m ) exp { π j λ ( z l z m ) × [ ( x l x m u ) 2 + ( y l y m υ ) 2 ] }
R U U ( u , υ ) = l = 1 N | A l | 2 × ( 2 δ ( u , υ ) + 1 j λ Δ z exp { π j λ Δ z [ ( u Δ x ) 2 + ( υ Δ y ) 2 ] } + 1 j λ Δ z exp { π j λ Δ z [ ( u + Δ x ) 2 + ( υ + Δ y ) 2 ] } ) .

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