Abstract

This paper analyzes the dynamics of objective laser speckles as the distance between the object and the observation plane continuously changes. With the purpose of applying optical spatial filtering velocimetry to the speckle dynamics, in order to measure out-of-plane motion in real time, a rotational symmetric spatial filter is designed. The spatial filter converts the speckle dynamics into a photocurrent with a quasi-sinusoidal response to the out-of-plane motion. The spatial filter is here emulated with a CCD camera, and is tested on speckles arising from a real application. The analysis discusses the selectivity of the spatial filter, the nonlinear response between speckle motion and observation distance, and the influence of the distance-dependent speckle size. Experiments with the emulated filters illustrate performance and potential applications of the technology.

© 2012 Optical Society of America

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References

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  1. I. Yamaguchi, “Fringe formation in deformation and vibration and measurements using laser light,” Prog. Opt. 22, 271–340 (1985).
    [CrossRef]
  2. M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
    [CrossRef]
  3. M. Sjödahl, and H. O. Saldner, “Three-dimensional deformation field measurements with simultaneous TV holography and electronic speckle photography,” Appl. Opt. 36, 3645–3648 (1997).
    [CrossRef]
  4. Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Series in Optical Sciences (Springer, 2005).
  5. U. Schnell, J. Piot, and R. Dändliker, “Detection of movement with laser speckle patterns: statistical properties,” J. Opt. Soc. Am. A 15, 207–216 (1998).
    [CrossRef]
  6. M. L. Jakobsen and S. G. Hanson, “Miniaturized lenticular array for laser speckle from solid surfaces,” Meas. Sci. Technol. 15, 1949–1957 (2004).
    [CrossRef]
  7. N. Takai, T. Iwai, and T. Asakura, “Real time velocity measurements for a diffuse object using zero-crossing of laser speckle,” J. Opt. Soc. Am. 70, 450–455 (1980).
    [CrossRef]
  8. T. F. Q. Iversen, M. L. Jakobsen, and S. G. Hanson, “Speckle-based three-dimensional velocity measurement using spatial filtering velocimetry,” Appl. Opt. 50, 1523–1533 (2011).
    [CrossRef]
  9. I. Yamaguchi and S. Komatsu, “Theory and applications of dynamic laser speckles due to in-plane object motion,” Optica Acta 24, 705–724 (1977).
    [CrossRef]
  10. M. Giglio, S. Musazzi, and U. Perini, “Distance measurement from a moving object based on speckle velocity detection,” Appl. Opt. 20, 721–722 (1981).
    [CrossRef]
  11. D. V. Semenov, E. Nippolainen, and A. A. Kamshillin, “Fast distance measurements by use of dynamic speckles,” Opt. Lett. 30, 248–250 (2005).
    [CrossRef]
  12. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomenon, J. C. Dainty, ed. (Springer-Verlag, 1984), pp. 9–75.
  13. A. E. Siegman, Lasers (University Science, 1986).
  14. H. T. Yura, B. Rose, and S. G. Hanson, “Dynamics laser speckle in complex ABCD optical systems,” J. Opt. Soc. Am. A 15, 1160–1166 (1998).
    [CrossRef]
  15. T. Yoshimura and S. Iwamoto, “Dynamic properties of three-dimensional speckles,” J. Opt. Soc. Am. A 10, 324–328 (1993).
  16. H. T. Yura, S. G. Hanson, R. S. Hansen, and B. Rose, “Three-dimensional speckle dynamics in paraxial optical systems,” J. Opt. Soc. Am. A 16, 1402–1412 (1999).
    [CrossRef]
  17. S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 24, 46–159 (1945).
  18. H. Zhang, L. Wang, R. M. Jia, and J. W. Li, “A distance measuring method using visual image processing,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (IEEE, 2009), Vols. 1–9, pp. 2275–2279.
  19. N. Takai, T. Iwai, and T. Asakura, “Real time velocity measurements for a diffuse object using zero-crossing of laser speckle,” J. Opt. Soc. Am. 70, 450–455 (1980).
    [CrossRef]
  20. S. G. Hanson, M. L. Jakobsen, H. C. Petersen, C. Dam-Hansen, and J. Stubager, “Miniaturized optical speckle-based sensor for cursor control,” Proc. SPIE 6341, 63411U (2006).
  21. S. Wolfram, “The Mathematica Book,” 4th ed. (Wolfram Media/Cambridge University, 1999).

2011 (1)

2006 (1)

S. G. Hanson, M. L. Jakobsen, H. C. Petersen, C. Dam-Hansen, and J. Stubager, “Miniaturized optical speckle-based sensor for cursor control,” Proc. SPIE 6341, 63411U (2006).

2005 (1)

2004 (1)

M. L. Jakobsen and S. G. Hanson, “Miniaturized lenticular array for laser speckle from solid surfaces,” Meas. Sci. Technol. 15, 1949–1957 (2004).
[CrossRef]

1999 (1)

1998 (3)

1997 (1)

1993 (1)

1985 (1)

I. Yamaguchi, “Fringe formation in deformation and vibration and measurements using laser light,” Prog. Opt. 22, 271–340 (1985).
[CrossRef]

1981 (1)

1980 (2)

1977 (1)

I. Yamaguchi and S. Komatsu, “Theory and applications of dynamic laser speckles due to in-plane object motion,” Optica Acta 24, 705–724 (1977).
[CrossRef]

1945 (1)

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 24, 46–159 (1945).

Aizu, Y.

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Series in Optical Sciences (Springer, 2005).

Asakura, T.

Dam-Hansen, C.

S. G. Hanson, M. L. Jakobsen, H. C. Petersen, C. Dam-Hansen, and J. Stubager, “Miniaturized optical speckle-based sensor for cursor control,” Proc. SPIE 6341, 63411U (2006).

Dändliker, R.

Giglio, M.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomenon, J. C. Dainty, ed. (Springer-Verlag, 1984), pp. 9–75.

Hansen, R. S.

Hanson, S. G.

Iversen, T. F. Q.

Iwai, T.

Iwamoto, S.

Jakobsen, M. L.

T. F. Q. Iversen, M. L. Jakobsen, and S. G. Hanson, “Speckle-based three-dimensional velocity measurement using spatial filtering velocimetry,” Appl. Opt. 50, 1523–1533 (2011).
[CrossRef]

S. G. Hanson, M. L. Jakobsen, H. C. Petersen, C. Dam-Hansen, and J. Stubager, “Miniaturized optical speckle-based sensor for cursor control,” Proc. SPIE 6341, 63411U (2006).

M. L. Jakobsen and S. G. Hanson, “Miniaturized lenticular array for laser speckle from solid surfaces,” Meas. Sci. Technol. 15, 1949–1957 (2004).
[CrossRef]

Jia, R. M.

H. Zhang, L. Wang, R. M. Jia, and J. W. Li, “A distance measuring method using visual image processing,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (IEEE, 2009), Vols. 1–9, pp. 2275–2279.

Kamshillin, A. A.

Komatsu, S.

I. Yamaguchi and S. Komatsu, “Theory and applications of dynamic laser speckles due to in-plane object motion,” Optica Acta 24, 705–724 (1977).
[CrossRef]

Li, J. W.

H. Zhang, L. Wang, R. M. Jia, and J. W. Li, “A distance measuring method using visual image processing,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (IEEE, 2009), Vols. 1–9, pp. 2275–2279.

Musazzi, S.

Nippolainen, E.

Perini, U.

Petersen, H. C.

S. G. Hanson, M. L. Jakobsen, H. C. Petersen, C. Dam-Hansen, and J. Stubager, “Miniaturized optical speckle-based sensor for cursor control,” Proc. SPIE 6341, 63411U (2006).

Piot, J.

Rice, S. O.

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 24, 46–159 (1945).

Rose, B.

Saldner, H. O.

Schnell, U.

Semenov, D. V.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Sjödahl, M.

Stubager, J.

S. G. Hanson, M. L. Jakobsen, H. C. Petersen, C. Dam-Hansen, and J. Stubager, “Miniaturized optical speckle-based sensor for cursor control,” Proc. SPIE 6341, 63411U (2006).

Takai, N.

Wang, L.

H. Zhang, L. Wang, R. M. Jia, and J. W. Li, “A distance measuring method using visual image processing,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (IEEE, 2009), Vols. 1–9, pp. 2275–2279.

Wolfram, S.

S. Wolfram, “The Mathematica Book,” 4th ed. (Wolfram Media/Cambridge University, 1999).

Yamaguchi, I.

I. Yamaguchi, “Fringe formation in deformation and vibration and measurements using laser light,” Prog. Opt. 22, 271–340 (1985).
[CrossRef]

I. Yamaguchi and S. Komatsu, “Theory and applications of dynamic laser speckles due to in-plane object motion,” Optica Acta 24, 705–724 (1977).
[CrossRef]

Yoshimura, T.

Yura, H. T.

Zhang, H.

H. Zhang, L. Wang, R. M. Jia, and J. W. Li, “A distance measuring method using visual image processing,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (IEEE, 2009), Vols. 1–9, pp. 2275–2279.

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 24, 46–159 (1945).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

Meas. Sci. Technol. (1)

M. L. Jakobsen and S. G. Hanson, “Miniaturized lenticular array for laser speckle from solid surfaces,” Meas. Sci. Technol. 15, 1949–1957 (2004).
[CrossRef]

Opt. Lasers Eng. (1)

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

Opt. Lett. (1)

Optica Acta (1)

I. Yamaguchi and S. Komatsu, “Theory and applications of dynamic laser speckles due to in-plane object motion,” Optica Acta 24, 705–724 (1977).
[CrossRef]

Proc. SPIE (1)

S. G. Hanson, M. L. Jakobsen, H. C. Petersen, C. Dam-Hansen, and J. Stubager, “Miniaturized optical speckle-based sensor for cursor control,” Proc. SPIE 6341, 63411U (2006).

Prog. Opt. (1)

I. Yamaguchi, “Fringe formation in deformation and vibration and measurements using laser light,” Prog. Opt. 22, 271–340 (1985).
[CrossRef]

Other (5)

S. Wolfram, “The Mathematica Book,” 4th ed. (Wolfram Media/Cambridge University, 1999).

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomenon, J. C. Dainty, ed. (Springer-Verlag, 1984), pp. 9–75.

A. E. Siegman, Lasers (University Science, 1986).

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Series in Optical Sciences (Springer, 2005).

H. Zhang, L. Wang, R. M. Jia, and J. W. Li, “A distance measuring method using visual image processing,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (IEEE, 2009), Vols. 1–9, pp. 2275–2279.

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Figures (10)

Fig. 1.
Fig. 1.

Schematics of the setup used for the theoretical description. The object is considered a transparent diffuser.

Fig. 2.
Fig. 2.

Intensity transmission function in Eq. (21) plotted as a function of radius in the observation plane. The plot uses the following parameters; r 0 = 1 , θ 0 = 0 , α = 10 and for the range of r p [ 1 ; 512 ] . For r p > 512 we set t ( r p ) = 0 .

Fig. 3.
Fig. 3.

Power of the Fourier–Bessel transform of the transmission function in Fig. 2 plotted as a function of radial frequency, normalized with the sample frequency.

Fig. 4.
Fig. 4.

Intensity transmission function in Eq. (22) plotted as a function of radius in the observation plane. The plot uses the following parameters; r 0 = 1 , θ 0 = 0 , α = 10 and for the range of r p [ 1 ; 512 ] . For r p > 512 we set t ( r p ) = 0 .

Fig. 5.
Fig. 5.

Schematics of the experimental setup are illustrated. The object is a glass plate with a diffuse surface facing the CCD camera.

Fig. 6.
Fig. 6.

Vector map is obtained by measuring the local speckle movement as the object moves away from the observation plane from position z = 54.5 mm to z + Δ z = 55.0 mm .

Fig. 7.
Fig. 7.

Photocurrents of i 0 ( z ) and i π / 2 ( z ) are plotted as a function of object positions z . Left plot (a) illustrates the filter function described in Eq. (21), while right plot (b) illustrates the filter function described in Eq. (22). The common parameters for the filters are; α = 40 for r p [ 1 ; 512 ] , while t ( r p ) = 0 for r p > 474 .

Fig. 8.
Fig. 8.

To the left, the measured displacement of the object is plotted as a function of steps of the stage. The amplitude of the oscillation is 0.15 mm. To the right , the power spectrum obtained for 67 oscillations is plotted. The filter [Eq. (22)] parameters are; α = 40 for r p [ 1 ; 512 ] , while t ( r p ) = 0 for r p > 474 .

Fig. 9.
Fig. 9.

Displacement is measured as the angle of the phasor based on the polar form of the two photocurrents in mutual phase quadrature. The angle is plotted as a function of the distance z between the object and the filter. The filter [Eq. (22)] parameters are α = 40 for r p [ 1 ; 512 ] , while t ( r p ) = 0 for r p > 474 .

Fig. 10.
Fig. 10.

Power of Fourier–Bessel transforms of the filter function [Eq. (21)] is illustrated together with the power spectra of the speckle patterns expected at z = 48.4 mm and z = 25.4 mm . The filter parameters follows as α = 40 for α = 40 , while t ( r p ) = 0 for r p > 512 .

Tables (1)

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Table 1. Data and Measurements on Oscillating Motions

Equations (31)

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C n ( p 1 , p 2 ; τ ) = I ( p 1 , t 1 ) I ( p 2 , t 1 + τ ) I ( p 1 , t 1 ) I ( p 2 , t 1 + τ ) { [ I ( p 1 , t 1 ) 2 I ( p 1 , t 1 ) 2 ] [ I ( p 2 , t 1 + τ ) 2 I ( p 2 , t 1 + τ ) 2 ] } 1 / 2 ,
C n ( p 1 , p 2 ; τ ) = | Γ ( p 1 , p 2 ; τ ) | 2 Γ ( p 1 , p 1 ; 0 ) Γ ( p 2 , p 2 ; 0 ) ,
Γ ( p 1 , p 2 ; τ ) = U ( p 1 , t 1 ) U * ( p 2 , t 2 )
U ( p , t ) = S d 2 r U s ( r ) G ( r , p ; t ) ,
G ( r , p ; t ) = i k 2 π ( z v z ( t t 1 ) ) exp ( i k 2 ( z v z ( t t 1 ) ) ( r 2 2 r · p + p 2 ) )
U s ( r ) = U i ( r , t ) Ψ ( r , t ) ,
Ψ ( r 1 , t ) Ψ * ( r 2 , t ) = const . × δ ( r 1 r 2 ) ,
Γ s ( r 1 , r 2 ; τ ) = U s ( r 1 , t 1 ) U s * ( r 2 , t 2 ) U i ( r 1 ) U i * ( r 2 ) δ ( r 2 r 1 ) ,
Γ ( p 1 , p 2 ; τ ) = S d 2 r U i ( r ) U i * ( r ) G ( r , p 1 ; t 1 ) G * ( r , p 2 ; t 1 + τ ) ,
U i ( r ) = exp ( ( x 2 + y 2 ) ( 1 w 0 2 + i k 2 R ) ) .
C n ( p , Δ p , v z ; τ ) = exp ( ( v x y τ w 0 ) 2 ) ( ( 1 + v z τ z ) 2 + ( v z τ l z ) 2 ) × exp ( 1 ρ z 2 [ Δ p ( 1 + z R ) v x y τ + v z τ z ( p + ( 1 2 + z R ) v x y τ ) ] 2 ) ,
ρ z 2 = ρ 0 2 ( ( 1 + v z τ z ) 2 + ( v z τ l z ) 2 ) ,
ρ 0 2 = 8 z 2 k 2 w 0 2 ( mean speckle radius ) ,
l z = 4 z 2 k w 0 2 ( mean speckle length ) .
Δ p = v z τ z p .
Δ p = v x y τ v z τ z ( p + 1 2 v x y τ ) ,
i ( q ) = d p I ( p ) t ( p q ) .
d θ ( r p ) d r p = 2 π α r p ,
θ 0 θ d θ ( r p ) = 2 π α r 0 r d r p r p ,
θ ( r p ) θ 0 = 2 π α ln ( r p r 0 ) .
t ( r p ) = cos ( 2 π α ln ( r p r 0 ) + θ 0 ) .
t ( r p ) = { cos ( 2 π α ln ( r p r 0 ) + θ 0 ) , for π 2 n < φ π 2 ( n + 1 2 ) , n = 2 , 1 , 0 , 1 cos ( 2 π α ln ( r p r 0 ) + π + θ 0 ) , for π 2 ( n + 1 2 ) < φ π 2 ( n + 1 ) , n = 2 , 1 , 0 , 1 .
r c ( r , c ) = ( r = 1 1024 c = 1 1280 r | Δ p ( r , c ) | 2 , r = 1 1024 c = 1 1280 c | Δ p ( r , c ) | 2 ) r = 1 1024 c = 1 1280 1 | Δ p ( r , c ) | 2 .
i θ ( z ) = r = 1 1024 c = 1 1280 I s p ( r , c ; z ) s θ ( r , c ) .
d θ = 2 π α r p d r p = 2 π α z d z .
θ ( z ) = 2 π α ln ( z 1 z ) ,
G ( f p ) = 0 R r p cos ( 2 π α ln ( r p r 0 ) + θ 0 ) J 0 ( 2 π r p f p ) d r p ,
G ( f p ) = R 4 16 ( 1 + π 2 α 2 ) 2 Im [ ( 2 π α 2 i ) exp ( i 2 π α ln ( R r o ) ) × 1 F 2 ( 1 i π α , { 1 , 2 i π α } , π 2 R 2 f 2 ) ] 2 ,
F p q ( a , b , z ) = k = 0 ( a 1 ) k ( a p ) k ( b 1 ( b q ) k z k k ! .
R I ( r p ) = exp ( r p 2 ρ 0 2 ) .
G ( f p ) = 0 R r p R I ( r p ) J 0 ( 2 π r p f p ) d r p = ρ 0 2 2 exp ( π 2 ρ 0 2 f p 2 ) .

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