Abstract

We use speckle photography to measure the motion of a rough body. We show experimental results for lateral and longitudinal motions. The output of our experiments is a direct display of the motion path. Our methods are based upon a mixture of concepts from speckle photography and from holography.

© 1976 Optical Society of America

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References

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  1. “Laser Speckle and Related Phenomena,” in Topics in Applied Physics, edited by J. C. Dainty (Springer, Berlin, 1975).
  2. E. Archbold and A. E. Ennos, “Two-dimensional vibrations analysed by speckle photography,” Opt. Laser Technol. 7, 17–21 (1975).
    [Crossref]
  3. A. W. Lohmann and G. P. Weigelt, “The Measurement of Motion Trajectories by Speckle Photography,” Opt. Commun. 14, 252–259 (1975).
    [Crossref]
  4. A. W. Lohmann and G. P. Weigelt, “The Measurement of Depth Motion by Speckle Photography,” Opt. Commun. 17, 47–51 (1976).
    [Crossref]

1976 (1)

A. W. Lohmann and G. P. Weigelt, “The Measurement of Depth Motion by Speckle Photography,” Opt. Commun. 17, 47–51 (1976).
[Crossref]

1975 (2)

E. Archbold and A. E. Ennos, “Two-dimensional vibrations analysed by speckle photography,” Opt. Laser Technol. 7, 17–21 (1975).
[Crossref]

A. W. Lohmann and G. P. Weigelt, “The Measurement of Motion Trajectories by Speckle Photography,” Opt. Commun. 14, 252–259 (1975).
[Crossref]

Archbold, E.

E. Archbold and A. E. Ennos, “Two-dimensional vibrations analysed by speckle photography,” Opt. Laser Technol. 7, 17–21 (1975).
[Crossref]

Ennos, A. E.

E. Archbold and A. E. Ennos, “Two-dimensional vibrations analysed by speckle photography,” Opt. Laser Technol. 7, 17–21 (1975).
[Crossref]

Lohmann, A. W.

A. W. Lohmann and G. P. Weigelt, “The Measurement of Depth Motion by Speckle Photography,” Opt. Commun. 17, 47–51 (1976).
[Crossref]

A. W. Lohmann and G. P. Weigelt, “The Measurement of Motion Trajectories by Speckle Photography,” Opt. Commun. 14, 252–259 (1975).
[Crossref]

Weigelt, G. P.

A. W. Lohmann and G. P. Weigelt, “The Measurement of Depth Motion by Speckle Photography,” Opt. Commun. 17, 47–51 (1976).
[Crossref]

A. W. Lohmann and G. P. Weigelt, “The Measurement of Motion Trajectories by Speckle Photography,” Opt. Commun. 14, 252–259 (1975).
[Crossref]

Opt. Commun. (2)

A. W. Lohmann and G. P. Weigelt, “The Measurement of Motion Trajectories by Speckle Photography,” Opt. Commun. 14, 252–259 (1975).
[Crossref]

A. W. Lohmann and G. P. Weigelt, “The Measurement of Depth Motion by Speckle Photography,” Opt. Commun. 17, 47–51 (1976).
[Crossref]

Opt. Laser Technol. (1)

E. Archbold and A. E. Ennos, “Two-dimensional vibrations analysed by speckle photography,” Opt. Laser Technol. 7, 17–21 (1975).
[Crossref]

Other (1)

“Laser Speckle and Related Phenomena,” in Topics in Applied Physics, edited by J. C. Dainty (Springer, Berlin, 1975).

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Figures (6)

FIG. 1
FIG. 1

Speckle photography in four steps. Upper sketch: the motion path p and the shift of the reference exposure (to the right); below: magnified small portion of the total speckle photograph; below: Fraunhofer diffraction pattern of the total speckle pattern (like a Fourier hologram); below: holographic reconstruction from the Fraunhofer pattern.

FIG. 2
FIG. 2

Holographic reconstruction of a lateral motion path (over exposed) of a rough body. The motion path (like a S) was reconstructed from a multiexposure speckle photograph.

FIG. 3
FIG. 3

Holographic reconstruction of the same motion path as shown in Fig. 2 (but proper exposure).

FIG. 4
FIG. 4

Fraunhofer diffraction pattern of the speckle photograph (acting as a Fourier hologram) from which Figs. 2. and 3 were reconstructed.

FIG. 5
FIG. 5

Holographic reconstruction of the depth motion graph z(t) of a rough body.

FIG. 6
FIG. 6

Geometrical visualizations of the various movements during signal and reference exposures for measuring the depth motion z(t).

Equations (17)

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I S ( x ) = I 0 [ x - s ( t ) ] d t .
I S ( x ) = I 0 ( x ) δ [ x - x - s ( t ) ] d t d x = I 0 ( x ) p ( x - x ) d x = I 0 ( x ) * p ( x ) , p ( x ) = δ [ x - s ( t ) ] d t .
I ˜ S ( ν ) 2 = I ˜ 0 ( ν ) 2 · p ˜ ( ν ) 2 ,
E [ I ˜ 0 ( ν ) 2 ] A δ ( ν ) + B
I T ( x ) = I S ( x ) + I R ( x ) , I R ( x ) = I 0 ( x - x R ) = I 0 ( x ) * δ ( x - x R ) , I T ( x ) = I 0 ( x ) * [ p ( x ) + δ ( x - x R ) ] .
I ˜ T ( ν ) 2 = I ˜ 0 ( ν ) 2 · p ˜ ( ν ) + exp ( - 2 π i ν · x R ) 2 , p ˜ + exp 2 = 1 + p ˜ 2 + p ˜ exp ( 2 π i ν · x R ) + p ˜ * exp ( - ) .
p ˜ + exp 2 exp ( 2 π i ν · x ) d x δ ( x ) + p ( x + x R ) + p * ( - x + x R ) .
I S ( x ) = M ( t ) I 0 [ x - s ( t ) ] d t .
p ( x ) = M ( t ) δ [ x - s ( t ) ] d t .
M ( t ) = ( n ) δ ( t - n τ ) , p ( x ) = ( n ) δ [ x - s ( n τ ) ] .
I S ( x , y ) = M ( t ) I 0 [ x - v x t , y , z ( t ) ] d t
= ( n ) I 0 [ x - n v x τ , y , z ( n τ ) ] .
I R ( x , y ) = ( m ) I 0 ( x + x R , y + m v y τ , m v z τ ) .
I T ( x , y ) = I S ( x , y ) + I R ( x , y ) .
I ˜ T 2 exp [ 2 π i ( x ν x + y ν y ) ] d ν x d ν y = I T I T = I S I R +
z ( n τ ) = m v z τ .
x = n v x τ + x R , y = m v y τ = z ( n τ ) v y / v x .