Abstract

A technique is presented which uses a laser beam to measure both vector components of the transverse velocity of a diffuse target. It is shown that the derivative of the spatio-temporal cross-correlation function of laser speckle intensity fluctuations, taken with respect to the time delay and evaluated at zero time delay, is directly proportional to the component of target velocitythat is parallel to the spatial separation. Experimental results are presented which verify this linearity.

© 1981 Optical Society of America

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References

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  1. G. Stavis, Instrum. Control Syst. 39, 99 (1966).
  2. B. E. A. Saleh, Appl. Opt. 14, 2344 (1975).
    [CrossRef] [PubMed]
  3. A. F. Fercher, Opt. Commun. 33, 129 (1980).
    [CrossRef]
  4. J. Ohtsubo, T. Asakura, Opt. Quantum Electron. 8, 523 (1976).
    [CrossRef]
  5. N. Takai, T. Iwai, T. Ushizaka, T. Asakura, Opt. Commun. 30, 287 (1979).
    [CrossRef]
  6. N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
    [CrossRef]
  7. S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
    [CrossRef]
  8. L. Z. Kennedy, J. W. Bilbro, Appl. Opt. 15, 2008 (1976).
    [CrossRef] [PubMed]
  9. L. Z. Kennedy, J. W. Bilbro, Appl. Opt. 18, 3010 (1979).
    [CrossRef] [PubMed]
  10. J. O’Shaughnessy, W. R. M. Pomeroy, Opt. Quantum Electron. 10, 270 (1978).
    [CrossRef]
  11. J. Ohtsubo, T. Asakura, Optik 52, 413 (1978/79).
  12. J. Ohtsubo, Opt. Commun. 34, 147 (1980).
    [CrossRef]
  13. J. C. Dainty, Ed., Laser Speckle and Related Phenomena (Springer, New York, 1975).
  14. J. W. Goodman, J. Opt. Soc. Am. 66, 1145 (1976).
    [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  16. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
    [CrossRef]
  17. Myung Hun Lee, J. F. Holmes, J. R. Kerr, J. Opt. Soc. Am. 66, 1164 (1976).
    [CrossRef]
  18. H. W. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]

1980 (3)

A. F. Fercher, Opt. Commun. 33, 129 (1980).
[CrossRef]

N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
[CrossRef]

J. Ohtsubo, Opt. Commun. 34, 147 (1980).
[CrossRef]

1979 (2)

N. Takai, T. Iwai, T. Ushizaka, T. Asakura, Opt. Commun. 30, 287 (1979).
[CrossRef]

L. Z. Kennedy, J. W. Bilbro, Appl. Opt. 18, 3010 (1979).
[CrossRef] [PubMed]

1978 (1)

J. O’Shaughnessy, W. R. M. Pomeroy, Opt. Quantum Electron. 10, 270 (1978).
[CrossRef]

1976 (5)

1975 (1)

1966 (2)

G. Stavis, Instrum. Control Syst. 39, 99 (1966).

H. W. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

1965 (1)

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

Asakura, T.

N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
[CrossRef]

N. Takai, T. Iwai, T. Ushizaka, T. Asakura, Opt. Commun. 30, 287 (1979).
[CrossRef]

J. Ohtsubo, T. Asakura, Optik 52, 413 (1978/79).

J. Ohtsubo, T. Asakura, Opt. Quantum Electron. 8, 523 (1976).
[CrossRef]

Bilbro, J. W.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Fercher, A. F.

A. F. Fercher, Opt. Commun. 33, 129 (1980).
[CrossRef]

Goodman, J. W.

Holmes, J. F.

Hun Lee, Myung

Iwai, T.

N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
[CrossRef]

N. Takai, T. Iwai, T. Ushizaka, T. Asakura, Opt. Commun. 30, 287 (1979).
[CrossRef]

Kennedy, L. Z.

Kerr, J. R.

Kogelnik, H. W.

Komatsu, S.

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

Li, T.

O’Shaughnessy, J.

J. O’Shaughnessy, W. R. M. Pomeroy, Opt. Quantum Electron. 10, 270 (1978).
[CrossRef]

Ohtsubo, J.

J. Ohtsubo, Opt. Commun. 34, 147 (1980).
[CrossRef]

J. Ohtsubo, T. Asakura, Optik 52, 413 (1978/79).

J. Ohtsubo, T. Asakura, Opt. Quantum Electron. 8, 523 (1976).
[CrossRef]

Pomeroy, W. R. M.

J. O’Shaughnessy, W. R. M. Pomeroy, Opt. Quantum Electron. 10, 270 (1978).
[CrossRef]

Saito, H.

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

Saleh, B. E. A.

Stavis, G.

G. Stavis, Instrum. Control Syst. 39, 99 (1966).

Takai, N.

N. Takai, T. Iwai, T. Asakura, J. Opt. Soc. Am. 70, 450 (1980).
[CrossRef]

N. Takai, T. Iwai, T. Ushizaka, T. Asakura, Opt. Commun. 30, 287 (1979).
[CrossRef]

Ushizaka, T.

N. Takai, T. Iwai, T. Ushizaka, T. Asakura, Opt. Commun. 30, 287 (1979).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Yamaguchi, I.

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

Appl. Opt. (4)

Instrum. Control Syst. (1)

G. Stavis, Instrum. Control Syst. 39, 99 (1966).

J. Opt. Soc. Am. (3)

Jpn. J. Appl. Phys. (1)

S. Komatsu, I. Yamaguchi, H. Saito, Jpn. J. Appl. Phys. 15, 1715 (1976).
[CrossRef]

Opt. Commun. (3)

J. Ohtsubo, Opt. Commun. 34, 147 (1980).
[CrossRef]

N. Takai, T. Iwai, T. Ushizaka, T. Asakura, Opt. Commun. 30, 287 (1979).
[CrossRef]

A. F. Fercher, Opt. Commun. 33, 129 (1980).
[CrossRef]

Opt. Quantum Electron. (2)

J. Ohtsubo, T. Asakura, Opt. Quantum Electron. 8, 523 (1976).
[CrossRef]

J. O’Shaughnessy, W. R. M. Pomeroy, Opt. Quantum Electron. 10, 270 (1978).
[CrossRef]

Optik (1)

J. Ohtsubo, T. Asakura, Optik 52, 413 (1978/79).

Proc. IEEE (1)

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

J. C. Dainty, Ed., Laser Speckle and Related Phenomena (Springer, New York, 1975).

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Figures (2)

Fig. 1
Fig. 1

Scattering geometry used for laser speckle velocity measurements.

Fig. 2
Fig. 2

Measured values (circles) and theoretical relationship (line) for change in correlation function ΔCI vs x component of target velocity Vx.

Equations (19)

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C I ( p 1 , p 2 , τ ) = I ( p 1 , t ) I ( p 2 , t + τ ) - I ( p 1 , t ) I ( p 2 , t + τ ) [ I 2 ( p 1 , t ) - I ( p 1 , t ) 2 ] 1 / 2 [ I 2 ( p 2 , t + τ ) - I ( p 2 , t + τ ) 2 ] 1 / 2 ,
I ( p 1 , t ) I ( p 2 , t + τ ) = U ( p 1 , t ) U * ( p 1 , t ) U ( p 2 , t + τ ) U * ( p 2 , t + τ ) = Γ ( p 1 , p 2 , τ ) 2 + I ( p 1 , t ) I ( p 2 , t + τ ) ,
Γ ( p 1 , p 2 , τ ) = U ( p 1 , t ) U * ( p 2 , t + τ ) .
C I ( p 1 , p 2 , τ ) = Γ ( p 1 , p 2 , τ ) 2 Γ ( p 1 , p 1 , 0 ) Γ ( p 2 , p 2 , 0 ) .
U ( p , t ) = k exp ( i k z ) 2 π i z U ( ρ , t ) exp [ i k 2 z ( p - ρ ) 2 ] d 2 ρ ,
Γ ( p 1 , p 2 , τ ) = ( k 2 π z ) 2 Γ ( ρ 1 , ρ 2 , τ ) × exp { i k 2 z [ ( p 1 - ρ 1 ) 2 - ( p 2 - ρ 2 ) 2 ] } d 2 ρ 1 d 2 ρ 2 .
Γ ( ρ 1 , ρ 2 , τ ) = U I ( ρ 1 , t ) U I * ( ρ 2 , t + τ ) δ ( ρ 2 - ρ 1 - V τ ) ,
U T ( r , t ) = exp [ - r 2 2 ( 2 a 2 + i k f ) ] ,
U I ( ρ , t ) = exp [ - ρ 2 2 ( 2 b 2 + i k R ) ] ,
C I ( p , τ ) = exp { - [ 1 b 2 + ( k b 2 R ) 2 ( 1 - R z ) ] V 2 τ 2 - k 2 b 2 4 R z p 2 - ( k b 2 z ) 2 ( 1 - z R ) ( p - V τ ) 2 } .
C ˙ I ( p , 0 ) = 2 ( k b 2 z ) 2 ( 1 - z R ) exp [ - ( k b p 2 z ) 2 ] p · V ,
C ˙ I ( p , 0 ) = 2 ( k b 2 z ) 2 exp [ - ( k b p 2 z ) 2 ] p · V .
b 2 f k a ,
f z = 1 + ( 2 f k a 2 ) 2 1 ,
C ˙ I ( p , 0 ) = 2 a 2 ( 2 z k a 2 ) 2 exp ( - p 2 a 2 ) p · V .
C ˙ I ( p , 0 ) = 2 ( k a 2 z ) 2 exp { - [ 1 + ( k a 2 z ) 2 ] p 2 a 2 } p · V ,
C ˙ I ( p , 0 ) = 2 ( k a 2 z ) 2 exp ( - p 2 a 2 ) p · V
C ˙ I ( p , 0 ) Δ C I Δ τ = 1 2 τ [ C I ( p 1 , p 2 , τ ) - C I ( p 1 , p 2 , - τ ) ] ,
V x = 53 Δ C I cm / sec

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