Abstract

Previous methods for analyzing double-exposed speckle photographs provide point-by-point velocity information by using two-dimensional Fourier analysis, or constant velocity contours by using spatial filtering techniques. A new method using an anamorphic optical system to measure one component of the velocity throughout a section of the flow is analyzed and demonstrated. A laser sheet, thin in the x direction and extended in the y direction, is used to probe a line of the photograph of which the anamorphic optical system forms a one-dimensional Fourier transform in the x direction and images the speckle pattern in the y direction for measuring the x-velocity component. This results in curved fringes, which have a local spacing inversely proportional to the x-velocity component at that point. Thus it is possible to measure a velocity component along a selected line in the flow. This differs from spatial filtering techniques that produce contours showing the points where a selected velocity occurs.

© 1986 Optical Society of America

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References

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  1. R. Meynart, Appl. Opt. 22, 4 (1983).
    [CrossRef]
  2. R. Meynart, Appl. Opt. 19, 9 (1980).
    [CrossRef]
  3. P. G. Simpkins, T. D. Dudderar, J. Fluid Mech. 89, 4 (1978).
    [CrossRef]
  4. M. Christopher et al., Opt. Acta 32, 5 (1985).
    [CrossRef]
  5. R. Meynart, Phys. Fluids 26, 8 (1983).
    [CrossRef]
  6. C. S. Yao, R. J. Adrian, Appl. Opt. 23, 11 (1984).
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  8. R. Meynart, L. M. Lourenco, “Laser speckle velocimetry in fluid dynamic applications,” presented at the von Kármán Institute for Fluid Dynamics Lecture Series 1984–03, Brussels, Belgium, 1984.

1985 (1)

M. Christopher et al., Opt. Acta 32, 5 (1985).
[CrossRef]

1984 (1)

1983 (2)

R. Meynart, Phys. Fluids 26, 8 (1983).
[CrossRef]

R. Meynart, Appl. Opt. 22, 4 (1983).
[CrossRef]

1980 (1)

R. Meynart, Appl. Opt. 19, 9 (1980).
[CrossRef]

1978 (1)

P. G. Simpkins, T. D. Dudderar, J. Fluid Mech. 89, 4 (1978).
[CrossRef]

Adrian, R. J.

Christopher, M.

M. Christopher et al., Opt. Acta 32, 5 (1985).
[CrossRef]

Dudderar, T. D.

P. G. Simpkins, T. D. Dudderar, J. Fluid Mech. 89, 4 (1978).
[CrossRef]

Goodman, J. W.

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

Lourenco, L. M.

R. Meynart, L. M. Lourenco, “Laser speckle velocimetry in fluid dynamic applications,” presented at the von Kármán Institute for Fluid Dynamics Lecture Series 1984–03, Brussels, Belgium, 1984.

Meynart, R.

R. Meynart, Appl. Opt. 22, 4 (1983).
[CrossRef]

R. Meynart, Phys. Fluids 26, 8 (1983).
[CrossRef]

R. Meynart, Appl. Opt. 19, 9 (1980).
[CrossRef]

R. Meynart, L. M. Lourenco, “Laser speckle velocimetry in fluid dynamic applications,” presented at the von Kármán Institute for Fluid Dynamics Lecture Series 1984–03, Brussels, Belgium, 1984.

Simpkins, P. G.

P. G. Simpkins, T. D. Dudderar, J. Fluid Mech. 89, 4 (1978).
[CrossRef]

Yao, C. S.

Appl. Opt. (3)

R. Meynart, Appl. Opt. 22, 4 (1983).
[CrossRef]

R. Meynart, Appl. Opt. 19, 9 (1980).
[CrossRef]

C. S. Yao, R. J. Adrian, Appl. Opt. 23, 11 (1984).
[CrossRef]

J. Fluid Mech. (1)

P. G. Simpkins, T. D. Dudderar, J. Fluid Mech. 89, 4 (1978).
[CrossRef]

Opt. Acta (1)

M. Christopher et al., Opt. Acta 32, 5 (1985).
[CrossRef]

Phys. Fluids (1)

R. Meynart, Phys. Fluids 26, 8 (1983).
[CrossRef]

Other (2)

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

R. Meynart, L. M. Lourenco, “Laser speckle velocimetry in fluid dynamic applications,” presented at the von Kármán Institute for Fluid Dynamics Lecture Series 1984–03, Brussels, Belgium, 1984.

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Figures (4)

Fig. 1
Fig. 1

Anamorphic processor. fx = 300 mm, fy = 100 mm, Z01 = 300 mm, Z12 = 172.2 mm, Z23 = 127.8 mm. The X0Y0 plane is the input plane, and X3Y3 is the output plane. A laser beam is shaped into a sheet and illuminates the double-exposure speckle pattern in the input plane. The fringe pattern is recorded in the output plane.

Fig. 2
Fig. 2

Circular jet and speckle-recording optics.

Fig. 3
Fig. 3

Photograph of fringes in the output plane.

Fig. 4
Fig. 4

Axial-velocity profile. One-half diameter downstream from exit, Re = 700, diameter = 19 mm.

Equations (6)

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U 0 ( X 0 , Y 0 ) = a + b S ( X 0 , Y 0 ) * { δ ( X 0 , Y 0 ) + δ [ X 0 + d x ( Y 0 ) , Y 0 + d y ( Y 0 ) ] } .
1 Z 01 + Z 12 + 1 Z 23 = 1 f y .
Z 01 = Z 12 + Z 23 ,             Z 01 = f x .
U 3 ( u , Y 3 ) = F x [ U 0 ( X 0 , - Y 3 M y ) * h im ( Y 3 ) ] * F x { P x ( x 1 ) } ,             u = ( X 3 / λ f x ) ,
I 3 ( u , Y 3 ) = A δ ( u , Y 3 ) + B S ˜ ( u , Y 0 ) + S ˜ [ u , Y 0 + d y ( Y 0 ) ] 2 cos 2 [ π d x ( Y 0 ) u ] ,             Y 0 = - ( Y 3 / M y ) ,
V x ( Y 0 ) = λ f x d f ( Y 3 ) τ M im ,             Y 3 = - Y 0 M y ,

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