Abstract

Diffraction-limited accuracy is estimated for measuring systems exploiting dynamic speckles. Statistical properties of the signal in the systems with spatial filtering are used to evaluate the signal frequency with precision sufficient to achieve the diffraction-limited accuracy. The results of the analysis allow for designing an optimal measuring system in which components are matched with each other to provide the highest accuracy. Experiments carried out with a range sensor using spatially filtered dynamic speckles are in good agreement with theory.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  8. Y. Aizu and T. Asakura, Spatial Filtering Velocimetry. Fundamentals and Applications (Springer, 2006).
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2008 (1)

2007 (1)

2006 (1)

2005 (2)

1998 (1)

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

1997 (1)

1986 (1)

1981 (1)

1980 (1)

1977 (1)

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 (1)

P. N. Pusey, “Photon correlation study of laser speckle produced by a moving rough surface,” J. Phys. D 9, 1399-1409 (1976).
[CrossRef]

1963 (1)

Aizu, Y.

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

Asakura, T.

Ator, J. T.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1958).

Giglio, M.

Horváth, P.

Hrabovsky, M.

Iwai, T.

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]

Miridonov, S. V.

Musazzi, S.

Nippolainen, E.

Perini, U.

Popov, I. A.

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

Pusey, P. N.

P. N. Pusey, “Photon correlation study of laser speckle produced by a moving rough surface,” J. Phys. D 9, 1399-1409 (1976).
[CrossRef]

Semenov, D. V.

Sjödahl, M.

Smíd, P.

Takai, N.

Veselov, L. M.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1958).

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]

Yoshimura, T.

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Phys. D (1)

P. N. Pusey, “Photon correlation study of laser speckle produced by a moving rough surface,” J. Phys. D 9, 1399-1409 (1976).
[CrossRef]

Opt. Acta (1)

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. Express (1)

Opt. Lett. (2)

Opt. Spectrosc. (1)

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

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1958).

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

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Figures (7)

Fig. 1
Fig. 1

Two configurations for the formation of dynamic speckles: (a) moving object and (b) scanning laser beam.

Fig. 2
Fig. 2

Schematic layout of the dynamic-speckle range sensor, which was used for the estimation of the accuracy of distance measurements.

Fig. 3
Fig. 3

Typical oscilloscope trace of a segment of the photodiode signal.

Fig. 4
Fig. 4

Spectral power densities of the recorded signals from the photodiode for different distances between the beam waist and the moving surface: (a) 2.5, (b) 2, and (c) 1.5 mm .

Fig. 5
Fig. 5

Mean signal frequency versus the distance between the Gaussian beam waist and the object surface moving at a speed of 30.5 m s . The solid curve is the theoretical curve given by Eq. (17). Squares and crosses are experimental points averaged for 25 and 100 μ s fragments, respectively.

Fig. 6
Fig. 6

Standard deviation of the modulation frequency as a function of the distance to the object surface for segments of the photodiode signal with (a) T = 25 and (b) T = 100 μ s . Solid and dashed curves are theoretical estimations of Eq. (20) while squares and circles are the experimental data for 25 and 100 μ s fragments, respectively.

Fig. 7
Fig. 7

Relative accuracy of the mean frequency measurement as a function of the distance to the object surface. Squares and circles are the experimental data for the fragments lengths of (a) 25 and (b) 100 μ s , respectively. Solid curves are the theoretical curves calculated using Eq. (21) with T = 25 and T = 100 μ s , respectively. The dashed curves are the diffraction-limited accuracy estimated by Eq. (8).

Equations (23)

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G ( r , r 0 ) = S I ( r r , r 0 ) I ( r , r 0 ) d S .
g ( r , r 0 ) 1 = exp ( r A r 0 2 r S 2 ) exp ( r 0 2 w 2 ) .
γ r 0 = δ r 0 r 0 = δ r r .
γ A = δ A A = δ r r .
δ A A δ ρ ρ .
γ = δ L T L T = r S r T L T .
γ = r S A w L S .
γ = λ π NA 3 2 ρ L S .
δ ρ = λ π NA 3 2 ρ L S .
δ V = λ π NA 3 2 V ρ T .
1 τ C = V ( A 2 r S 2 + 1 w 2 ) 1 2 .
f S = ( π τ C ) 1 = V NA λ .
γ = τ C τ L T T = 1 π f S τ L T T .
G ( f ) = exp ( f 2 f D 2 ) + 1 4 exp ( π 2 r S 2 Λ 2 ) exp [ ( f f 0 ) 2 f D 2 ] .
τ C D = 1 V S ( 1 r T 2 + 1 D 2 ) 1 2 ,
G ( f ) = exp ( f 2 f D 2 ) + 1 4 exp ( f 0 2 f S 2 ) exp [ ( f f 0 ) 2 f D 2 ] .
f 0 = V S Λ .
γ = f D f 0 π T 0.56 f 0 f D T .
σ Δ f = σ Δ ϕ 2 π τ C D = 1 τ C D 12 = π f D 12 .
σ Δ f , T = σ Δ f N = π f D 12 T .
γ SF = 1 f 0 π f D 12 T 0.51 f 0 f D T .
γ SF = γ ρ ρ 0 ,
f 0 = k f k S k 2 k S k 2 ,

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