Abstract

We analyze statistical properties of dynamic speckles formed when an optically rough surface is illuminated by a fast-deflecting laser beam. The modified space-time correlation function of the light-intensity fluctuations has been introduced to estimate the correlation parameters of a dynamic speckle pattern. Dynamic speckles are considered in their application to range sensing using evaluation of the light-power-modulation frequency of a signal obtained from the integrating photodetector after spatial filtering of the scattered light. Multichannel configuration is suggested to improve the system accuracy. Conditions that should be fulfilled to get uncorrelated responses of photodiode are found. Proper averaging of the multichannel data allows designing a non-interferometric range sensor capable for measuring distance with accuracy of 1 εm during as short time as 1 ms.

© 2008 Optical Society of America

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References

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  1. J. D. Rigden and E. I. Gordon, "The granularity of scattered optical maser light," Proc. IRE 50, 2367-2368 (1962).
  2. B. M. Oliver, "Sparkling spots and random diffraction," Proc. IEEE 51,220-221 (1963).
    [CrossRef]
  3. G. Stavis, "Optical diffraction velocimeter," Instrum. Control Syst. 39,99-102 (1966).
  4. V. V. Anisimov, S. M. Kozel, and G. R. Lokshin, "Space-time statistical properties of coherent radiation scattered by a moving diffuse reflector," Opt. Spectrosc. 27,258-262 (1969).
  5. S. Komatsu, I. Yamaguchi, and H. Saito, "Velocity measurements using structural change of speckle," Opt. Commun. 18,314-316 (1976).
    [CrossRef]
  6. 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] [PubMed]
  7. D. V. Semenov, E. Nippolainen, and A. A. Kamshilin, "Fast distance measurements by use of dynamic speckles," Opt. Lett. 30,248-250 (2005).
    [CrossRef] [PubMed]
  8. T. Yoshimura, "Statistical properties of dynamic speckles," J. Opt. Soc. Am. A 3, 1032-1054 (1986).
    [CrossRef]
  9. L. M. Veselov and I. A. Popov, "Statistical properties of modulated dynamic speckles," Opt. Spectrosc. 84, 268-272 (1998).
  10. E. Nippolainen, D. V. Semenov, and A. A. Kamshilin, "Dynamic speckle effect induced by acousto-optic deflector for fast range sensing," Opt. Lett. 30, 3147-3149 (2005).
    [CrossRef] [PubMed]
  11. D. V. Semenov, E. Nippolainen, and A. A. Kamshilin, "Accuracy and resolution of a dynamic-speckle profilometer," Appl. Opt. 45, 411-418 (2006).
    [CrossRef] [PubMed]
  12. I. Yamaguchi and S. Komatsu, "Theory and applications of dynamic laser speckles due to in-plane object motion," Opt. Acta. 24, 705-724 (1977).
    [CrossRef]
  13. Y. Aizu and T. Asakura, "Principles and development of spatial filtering velocimetry," Appl. Phys. B 43, 209-224 (1987).
    [CrossRef]
  14. D. V. Semenov, E. Nippolainen, A. A. Kamshilin, A. V. Belyaev, S. V. Andreev, and B. S. Gurevich, "An ultra-fast distance sensor based on dynamic speckles generated by acousto-optic deflection," Meas. Sci. Technol. 17, 2906-2912 (2006).
    [CrossRef]

2006

D. V. Semenov, E. Nippolainen, and A. A. Kamshilin, "Accuracy and resolution of a dynamic-speckle profilometer," Appl. Opt. 45, 411-418 (2006).
[CrossRef] [PubMed]

D. V. Semenov, E. Nippolainen, A. A. Kamshilin, A. V. Belyaev, S. V. Andreev, and B. S. Gurevich, "An ultra-fast distance sensor based on dynamic speckles generated by acousto-optic deflection," Meas. Sci. Technol. 17, 2906-2912 (2006).
[CrossRef]

2005

1998

L. M. Veselov and I. A. Popov, "Statistical properties of modulated dynamic speckles," Opt. Spectrosc. 84, 268-272 (1998).

1987

Y. Aizu and T. Asakura, "Principles and development of spatial filtering velocimetry," Appl. Phys. B 43, 209-224 (1987).
[CrossRef]

1986

1981

1977

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

1976

S. Komatsu, I. Yamaguchi, and H. Saito, "Velocity measurements using structural change of speckle," Opt. Commun. 18,314-316 (1976).
[CrossRef]

1969

V. V. Anisimov, S. M. Kozel, and G. R. Lokshin, "Space-time statistical properties of coherent radiation scattered by a moving diffuse reflector," Opt. Spectrosc. 27,258-262 (1969).

1966

G. Stavis, "Optical diffraction velocimeter," Instrum. Control Syst. 39,99-102 (1966).

1963

B. M. Oliver, "Sparkling spots and random diffraction," Proc. IEEE 51,220-221 (1963).
[CrossRef]

Aizu, Y.

Y. Aizu and T. Asakura, "Principles and development of spatial filtering velocimetry," Appl. Phys. B 43, 209-224 (1987).
[CrossRef]

Andreev, S. V.

D. V. Semenov, E. Nippolainen, A. A. Kamshilin, A. V. Belyaev, S. V. Andreev, and B. S. Gurevich, "An ultra-fast distance sensor based on dynamic speckles generated by acousto-optic deflection," Meas. Sci. Technol. 17, 2906-2912 (2006).
[CrossRef]

Anisimov, V. V.

V. V. Anisimov, S. M. Kozel, and G. R. Lokshin, "Space-time statistical properties of coherent radiation scattered by a moving diffuse reflector," Opt. Spectrosc. 27,258-262 (1969).

Asakura, T.

Y. Aizu and T. Asakura, "Principles and development of spatial filtering velocimetry," Appl. Phys. B 43, 209-224 (1987).
[CrossRef]

Belyaev, A. V.

D. V. Semenov, E. Nippolainen, A. A. Kamshilin, A. V. Belyaev, S. V. Andreev, and B. S. Gurevich, "An ultra-fast distance sensor based on dynamic speckles generated by acousto-optic deflection," Meas. Sci. Technol. 17, 2906-2912 (2006).
[CrossRef]

Giglio, M.

Gurevich, B. S.

D. V. Semenov, E. Nippolainen, A. A. Kamshilin, A. V. Belyaev, S. V. Andreev, and B. S. Gurevich, "An ultra-fast distance sensor based on dynamic speckles generated by acousto-optic deflection," Meas. Sci. Technol. 17, 2906-2912 (2006).
[CrossRef]

Kamshilin, A. A.

Komatsu, S.

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

S. Komatsu, I. Yamaguchi, and H. Saito, "Velocity measurements using structural change of speckle," Opt. Commun. 18,314-316 (1976).
[CrossRef]

Kozel, S. M.

V. V. Anisimov, S. M. Kozel, and G. R. Lokshin, "Space-time statistical properties of coherent radiation scattered by a moving diffuse reflector," Opt. Spectrosc. 27,258-262 (1969).

Lokshin, G. R.

V. V. Anisimov, S. M. Kozel, and G. R. Lokshin, "Space-time statistical properties of coherent radiation scattered by a moving diffuse reflector," Opt. Spectrosc. 27,258-262 (1969).

Musazzi, S.

Nippolainen, E.

Oliver, B. M.

B. M. Oliver, "Sparkling spots and random diffraction," Proc. IEEE 51,220-221 (1963).
[CrossRef]

Perini, U.

Popov, I. A.

L. M. Veselov and I. A. Popov, "Statistical properties of modulated dynamic speckles," Opt. Spectrosc. 84, 268-272 (1998).

Saito, H.

S. Komatsu, I. Yamaguchi, and H. Saito, "Velocity measurements using structural change of speckle," Opt. Commun. 18,314-316 (1976).
[CrossRef]

Semenov, D. V.

Stavis, G.

G. Stavis, "Optical diffraction velocimeter," Instrum. Control Syst. 39,99-102 (1966).

Veselov, L. M.

L. M. Veselov and I. A. Popov, "Statistical properties of modulated dynamic speckles," Opt. Spectrosc. 84, 268-272 (1998).

Yamaguchi, I.

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

S. Komatsu, I. Yamaguchi, and H. Saito, "Velocity measurements using structural change of speckle," Opt. Commun. 18,314-316 (1976).
[CrossRef]

Yoshimura, T.

Appl. Opt.

Appl. Phys. B

Y. Aizu and T. Asakura, "Principles and development of spatial filtering velocimetry," Appl. Phys. B 43, 209-224 (1987).
[CrossRef]

Instrum. Control Syst.

G. Stavis, "Optical diffraction velocimeter," Instrum. Control Syst. 39,99-102 (1966).

J. Opt. Soc. Am. A

Meas. Sci. Technol.

D. V. Semenov, E. Nippolainen, A. A. Kamshilin, A. V. Belyaev, S. V. Andreev, and B. S. Gurevich, "An ultra-fast distance sensor based on dynamic speckles generated by acousto-optic deflection," Meas. Sci. Technol. 17, 2906-2912 (2006).
[CrossRef]

Opt. Acta.

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

Opt. Commun.

S. Komatsu, I. Yamaguchi, and H. Saito, "Velocity measurements using structural change of speckle," Opt. Commun. 18,314-316 (1976).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

L. M. Veselov and I. A. Popov, "Statistical properties of modulated dynamic speckles," Opt. Spectrosc. 84, 268-272 (1998).

V. V. Anisimov, S. M. Kozel, and G. R. Lokshin, "Space-time statistical properties of coherent radiation scattered by a moving diffuse reflector," Opt. Spectrosc. 27,258-262 (1969).

Proc. IEEE

B. M. Oliver, "Sparkling spots and random diffraction," Proc. IEEE 51,220-221 (1963).
[CrossRef]

Other

J. D. Rigden and E. I. Gordon, "The granularity of scattered optical maser light," Proc. IRE 50, 2367-2368 (1962).

Supplementary Material (3)

» Media 1: MOV (729 KB)     
» Media 2: MOV (945 KB)     
» Media 3: MOV (1153 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Formation of dynamic speckles in the case of moving surface (left, 0.7 Mb) and laser-beam scanning (right, 0.9 Mb). [Media 1] [Media 2]

Fig. 2.
Fig. 2.

Schematic arrangement of the dynamic-speckle sensor for distance measurements. The chart on the left shows typical oscilloscope trace of the photodiode response (1.1 Mb).[Media 3]

Fig. 3.
Fig. 3.

Oscilloscope traces of the photocurrent for different displacement of the object surface perpendicular to the direction of the laser-beam scanning.

Fig. 4.
Fig. 4.

The maximum of cross-correlations calculated between a randomly selected scan and all others from the set of recorded data.

Fig. 5.
Fig. 5.

Instant frequency of the photodiode signal as a function of the current time and its variation for sequential scans recorded with longitudinal step of 3.5 μm. Right picture shows coding of the modulation frequency with pseudo-colors.

Fig. 6.
Fig. 6.

Experimental setup for measuring the correlation length in a multi-channel dynamicspeckles sensor. Numbers 1 and 2 indicate adjacent positions of the photodiode at which its responses are uncorrelated.

Fig. 7.
Fig. 7.

Correlation length LCP as a function of the reciprocal size (2rB )-1 of the scanning beam measured in the direction orthogonal to the scan. Red solid line is the average diameter of the speckles at the plane of the spatial filter.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

V SP = V BS D S R W .
V SP = V BS ( 1 + D S R W ) .
z = D 0 V BS V SP V BS .
z = D 0 V BS f SP Λ V BS .
g ( 2 ) ( r , τ ) 1 = exp ( r 2 r SP 2 + τ d 2 τ C 2 ) exp [ ( τ τ d ) 2 τ C 2 ] .
1 τ C 2 = V BS 2 [ 1 r SP 2 ( 1 + D s R W ) 2 + 1 r B 2 ] and τ d = τ C 2 r SP 2 ( 1 + D S R W ) V BS r .
1 τ C 2 = V BS 2 ( D S 2 r SP 2 R W 2 + 1 r B 2 ) ,
τ d = τ C 2 r SP 2 D S R W V BS r .
r SP = D S λ π r B .
g ( 2 ) ( r , r 0 ) 1 = exp ( r r 0 D S R W 2 r SP 2 ) exp ( r 0 2 r B 2 ) .
Δ f = V BS D S π R W R W 2 D S 2 r B 2 + 1 D F 2 ,
L CS = ( 1 r B 2 + D S 2 R W 2 D F 2 ) 1 2 .
z ¯ = V BS N i N C i D F i Λ i f PDi V BS .
z ¯ = V BS NM i N j M D F i Λ i f PD ij V BS .

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