Abstract

We present an optical method for measuring the real-time three-dimensional (3D) translational velocity of a diffusely scattering rigid object observed through an imaging system. The method is based on a combination of the motion of random speckle patterns and regular fringe patterns. The speckle pattern is formed in the observation plane of the imaging system due to reflection from an area of the object illuminated by a coherent light source. The speckle pattern translates in response to in-plane translation of the object, and the presence of an angular offset reference wave coinciding with the speckle pattern in the observation plane gives rise to interference, resulting in a fringe pattern that translates in response to the out-of-plane translation of the object. Numerical calculations are performed to evaluate the dynamic properties of the intensity distribution and the response of realistic spatial filters designed to measure the three components of the object’s translational velocity. Furthermore, experimental data are presented that demonstrate full 3D velocity measurement.

© 2011 Optical Society of America

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References

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2009 (1)

2008 (1)

2004 (2)

M. L. Jakobsen and S. G. Hanson, “Lenticular array for spatial filtering velocimetry of laser speckles from solid surfaces,” Appl. Opt. 43, 4643–4651 (2004).
[CrossRef] [PubMed]

S. Bergeler and H. Krambeer, “Novel optical spatial filtering methods based on two-dimensional photodetector arrays,” Meas. Sci. Technol. 15, 1309–1315 (2004).
[CrossRef]

1999 (1)

1998 (2)

1997 (1)

1987 (1)

1986 (1)

1982 (1)

1978 (1)

J. O’Shaughnessy and W. R. M. Pomeroy, “Single beam atmospheric transverse velocity measurement,” Opt. Quantum Electron. 10, 270–272 (1978).
[CrossRef]

1976 (1)

1966 (1)

Aizu, Y.

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry: Fundamentals and Applications (Springer-Verlag, 2006).

Asakura, T.

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry: Fundamentals and Applications (Springer-Verlag, 2006).

Bergeler, S.

S. Bergeler and H. Krambeer, “Novel optical spatial filtering methods based on two-dimensional photodetector arrays,” Meas. Sci. Technol. 15, 1309–1315 (2004).
[CrossRef]

Bilbro, J. W.

Chang, Y. H.

Churnside, J. H.

Dandliker, R.

DiMarzio, C.

Fitzjarrald, D.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1984), Chap. 2.

Hansen, R. S.

Hanson, R. S.

Hanson, S. G.

Jakobsen, M. L.

Johnson, S.

Jones, W.

Kennedy, L. Z.

Krambeer, H.

S. Bergeler and H. Krambeer, “Novel optical spatial filtering methods based on two-dimensional photodetector arrays,” Meas. Sci. Technol. 15, 1309–1315 (2004).
[CrossRef]

Lin, S. T.

O’Shaughnessy, J.

J. O’Shaughnessy and W. R. M. Pomeroy, “Single beam atmospheric transverse velocity measurement,” Opt. Quantum Electron. 10, 270–272 (1978).
[CrossRef]

Pedersen, C.

Piot, J.

Pomeroy, W. R. M.

J. O’Shaughnessy and W. R. M. Pomeroy, “Single beam atmospheric transverse velocity measurement,” Opt. Quantum Electron. 10, 270–272 (1978).
[CrossRef]

Rose, B.

Saldner, H. O.

Schnell, U.

Siegman, A. E.

Sjödahl, M.

Yeh, S. L.

Yura, H. T.

Appl. Opt. (6)

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (1)

S. Bergeler and H. Krambeer, “Novel optical spatial filtering methods based on two-dimensional photodetector arrays,” Meas. Sci. Technol. 15, 1309–1315 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

J. O’Shaughnessy and W. R. M. Pomeroy, “Single beam atmospheric transverse velocity measurement,” Opt. Quantum Electron. 10, 270–272 (1978).
[CrossRef]

Other (3)

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry: Fundamentals and Applications (Springer-Verlag, 2006).

P.Meinlschmidt, K.D.Hinsch, and R.S.Sirohi, eds., “Electronic Speckle Pattern Interferometry,” Vol.  MS 132 of SPIE Milestone Series (SPIE, 1996).

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1984), Chap. 2.

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Figures (17)

Fig. 1
Fig. 1

ABCD model geometry.

Fig. 2
Fig. 2

Spatial filter unit cell combining both the h 0 ( p ) and h 90 ( p ) filters. The rotation angle of the detector arrangement in relation to the observation plane coordinate system is Ω.

Fig. 3
Fig. 3

Spatial power spectral function of the spatial filter described by Eq. (21) for Λ Λ x , L L y , Ω 0 ° , and N = 8 .

Fig. 4
Fig. 4

Intensity distribution for w = 250 μm , f = 250 mm , P o = P r , θ x = 0.0316 rad , θ y = 0 rad , and σ = 1.5 mm .

Fig. 5
Fig. 5

Ensemble averaged spatial power spectrum | S I ( ξ x , ξ y ) | 2 for θ x = 0.0316 rad , and θ y = 0 rad . The data set is the result of averaging 50 power spectra.

Fig. 6
Fig. 6

Cross section along ξ x axis of the spatial power spectrum in Fig. 5 for different values of the aperture size σ.

Fig. 7
Fig. 7

Cross section along ξ y axis of the spatial power spectrum in Fig. 5 for different values of the aperture size σ.

Fig. 8
Fig. 8

Ensemble averaged spatial power spectrum | S I ( ξ x , ξ y ) | 2 for θ x = 0.0316 rad , θ y = 0 rad shown along with the center frequency locations of spatial frequency bands corresponding to spatial filters observing the v x , v y , and v z components of translation. The data set is the result of averaging 50 power spectra.

Fig. 9
Fig. 9

Temporal power spectra as a function of normalized frequency obtained by FFT. The quantity P i ( f ) for i = { x , y , z } denotes the power spectrum of the output signal of the spatial filter observing the v x , v y , and v z components, respectively. The data set is the result of averaging 10 power spectra.

Fig. 10
Fig. 10

Experimental setup.

Fig. 11
Fig. 11

Integrated optical spatial filter. The physical parameters of the filter are Λ z = 15 μm , R 3 = 18 μm , R 4 = 1 mm , and W d = 187.5 μm .

Fig. 12
Fig. 12

Intensity distribution obtained using a high-resolution CCD camera.

Fig. 13
Fig. 13

Spatial power spectrum of the intensity distribution obtained with the high-resolution CCD camera.

Fig. 14
Fig. 14

Spatial filter output signals. Vertical lines delimit the excerpts shown in the main plot. Top, v obj = 0.1 mm / s . Bottom, v obj = 0.1 mm / s . Plots (A)–(C) correspond to v x , v y and v z , respectively.

Fig. 15
Fig. 15

Power spectra of output signal from the spatial filter observing the v x velocity component for different values of v obj .

Fig. 16
Fig. 16

Power spectra of output signal from the spatial filter observing the v y velocity component for different values of v obj .

Fig. 17
Fig. 17

Power spectra of output signal from the spatial filter observing the v z velocity component for different values of v obj .

Tables (3)

Tables Icon

Table 1 Spatial Passband Center Frequencies for the Spatial Filters Used in the Numerical Model

Tables Icon

Table 2 Spatial Passband Center Frequencies for the Spatial Filters Used in the Experiment

Tables Icon

Table 3 Best Fitting Parameters of the Linear Relationship Relating the Measured Velocity to the Actual Velocity

Equations (33)

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U i ( r ) = E i exp ( r 2 w i 2 ) ,
U s ( r , t ) = U i ( r ) Ψ ( r , t ) ,
U o ( p , t ) = + d 2 r U s ( r ) G ( r , p ) ,
G ( r , p ) = i k 2 π B exp [ i k L ] exp [ i k 2 B ( A r 2 2 r · p + D p 2 ) ] .
A = f 2 f 1 ,
B = 2 i f 1 f 2 k σ 2 ,
D = f 1 f 2 .
G ( r , p ) = k 2 σ 2 4 π f 1 f 2 exp [ i k L ] exp [ k 2 σ 2 4 f 2 2 ( f 2 f 1 r + p ) 2 ] .
U r ( p ) = E r exp ( p 2 w r 2 i k θ · p ) ,
I ( p , t ) = | U o ( p , t ) + U r ( p ) | 2 .
P o = d 2 p | U o ( p , t ) | 2 .
P r = d 2 p | U r ( p ) | 2 .
Ψ ( x , y , t ) Ψ ( x v x τ , y v y τ , t + τ ) exp ( i k v z τ ) ,
i ( p 1 ) = + d 2 p I ( p 1 p ) h ( p ) ,
P ( ξ ) = | S I ( ξ ) | 2 | H ( ξ ) | 2 ,
F = M v Λ ,
h ( p ) = [ h win ( p ) m = δ ( p x m Λ x ) ] [ h unit ( p x ) h det ( p x ) ] ,
h win ( p ) = Rect ( p x L x ) Rect ( p y L y ) ,
h unit ( p x ) = δ ( p x + p φ ) δ ( p x p φ ) ,
h det ( p x ) = Rect ( p x W d ) ,
| H ( ξ ) | 2 = sinc 2 ( L y ξ y ) m = sinc 2 [ N ( Λ x ξ x m ) ] [ 1 cos ( π Λ x ξ x ) ] sinc 2 ( Λ x ξ x 4 ) ,
ξ x = ξ x cos ( Ω ) + ξ y sin ( Ω ) ,
ξ y = ξ y cos ( Ω ) ξ x sin ( Ω ) .
PDF ( ϕ ) = { 1 2 π , π ϕ π 0 , | ϕ | > π .
i ( t ) = d 2 p I ( p , t ) h ( p ) .
f x FUN = F x τ = Δ x Λ x = 5 μm 80 μm = 1 16 ,
f z FUN = F z τ = α v z Λ z τ = 1 4 .
f x z ( ) = f z FUN f x FUN ,
f x z ( + ) = f z FUN + f x FUN .
θ = ( λ / ( Λ z 2 ) , λ / ( Λ z 2 ) ) ,
d 180 = Λ z R 4 2 R 3 .
( v x , v y , v z ) = ( v obj cos ( 45 ° ) sin ( 93.3 ° ) , v obj sin ( 45 ° ) sin ( 93.3 ° ) , v obj cos ( 93.3 ° ) ) ,
v i measured = c 0 + c 1 v i actual ,

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