Abstract

Optical vortex analysis has become an important tool in optical metrology. It has been shown to be able to measure small displacements with up to nanometric precision. We analyze optical vortex behavior in dynamic speckle patterns with the boiling phenomenon. We first study translational patterns with boiling and we find the limitations of the optical vortex metrology. Pure boiling patterns are also evaluated and we find a quantitative descriptor for the activity. We also observe that vortices exhibit a Brownian motion in pure boiling patterns. Numerical and experimental results are shown.

© 2009 Optical Society of America

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References

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  1. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165-190 (1974).
    [CrossRef]
  2. W. Wang, T. Yokozeki, R. Ishijima, M. Takeda, and S. G. Hanson, “Optical vortex metrology based on the core structures of phase singularities in Laguerre-Gauss transform of a speckle pattern,” Opt. Express 14, 10195-10206 (2006).
    [CrossRef] [PubMed]
  3. W. Wang, T. Yokozeki, R. Ishijima, A. Wada, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Optical vortex metrology for nanometric speckle displacement measurement,” Opt. Express 14, 120-127 (2006).
    [CrossRef] [PubMed]
  4. H. J. Rabal and R. A. Braga, Dynamic Laser Speckle and Applications, Optical Science and Engineering (CRC Press, 2009), p. 272.
  5. W. Wang, M. R. Dennis, R. Ishijima, T. Yokozeki, A. Matsuda, S. G. Hanson, and M. Takeda, “Poincaré sphere representation for the anisotropy of phase singularities and its applications to optical vortex metrology for fluid mechanical analysis,” Opt. Express 15, 11008-11019 (2007).
    [CrossRef] [PubMed]
  6. G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693-3700 (2009).
    [CrossRef]
  7. T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” Prog. Opt. 34, 183-248 (1995).
    [CrossRef]
  8. B. D. Hughes, Random Walks and Random Environments, Vol. 1 (Clarendon, 1995).

2009 (1)

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693-3700 (2009).
[CrossRef]

2007 (1)

2006 (2)

1995 (1)

T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” Prog. Opt. 34, 183-248 (1995).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165-190 (1974).
[CrossRef]

Arizaga, R.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693-3700 (2009).
[CrossRef]

Asakura, T.

T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” Prog. Opt. 34, 183-248 (1995).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165-190 (1974).
[CrossRef]

Braga, R. A.

H. J. Rabal and R. A. Braga, Dynamic Laser Speckle and Applications, Optical Science and Engineering (CRC Press, 2009), p. 272.

Dennis, M. R.

Hanson, S. G.

Hughes, B. D.

B. D. Hughes, Random Walks and Random Environments, Vol. 1 (Clarendon, 1995).

Ishijima, R.

Matsuda, A.

Miyamoto, Y.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165-190 (1974).
[CrossRef]

Okamoto, T.

T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” Prog. Opt. 34, 183-248 (1995).
[CrossRef]

Rabal, H.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693-3700 (2009).
[CrossRef]

Rabal, H. J.

H. J. Rabal and R. A. Braga, Dynamic Laser Speckle and Applications, Optical Science and Engineering (CRC Press, 2009), p. 272.

Sendra, G.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693-3700 (2009).
[CrossRef]

Takeda, M.

Trivi, M.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693-3700 (2009).
[CrossRef]

Wada, A.

Wang, W.

Yokozeki, T.

Opt. Commun. (1)

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693-3700 (2009).
[CrossRef]

Opt. Express (3)

Proc. R. Soc. London, Ser. A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165-190 (1974).
[CrossRef]

Prog. Opt. (1)

T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” Prog. Opt. 34, 183-248 (1995).
[CrossRef]

Other (2)

B. D. Hughes, Random Walks and Random Environments, Vol. 1 (Clarendon, 1995).

H. J. Rabal and R. A. Braga, Dynamic Laser Speckle and Applications, Optical Science and Engineering (CRC Press, 2009), p. 272.

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Figures (4)

Fig. 1
Fig. 1

Setup scheme for simulation and experiment. The object plane is a moving diffuser.

Fig. 2
Fig. 2

Vortex displacement analysis as a function of the diffuser velocity for simulated and experimental translational speckle patterns with boiling: (a) Proportion of identified vortices, (b) mean horizontal displacement, (c) mean vertical displacement.

Fig. 3
Fig. 3

Vortex displacement analysis as a function of the diffuser velocity for simulated and experimental pure boiling speckle patterns: (a) Proportion of identified vortices, (b) average Euclidean distance between homologous vortices.

Fig. 4
Fig. 4

Product of the averaged Euclidean distance and the square root of the diffuser velocity as a function of the diffuser velocity.

Tables (1)

Tables Icon

Table 1 Vortices' Behavior in Uncorrelated Speckle Patterns

Equations (13)

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( 1 d o + 1 d i 1 f ) ( 1 + d o ρ ) 1 d o = 0 ,
g ̃ ( x , y ) = H LG ( ξ , η ) G ( ξ , η ) exp [ j 2 π ( x ξ + y η ) ] d ξ d η ,
H LG ( ξ , η ) = ( ξ + j η ) exp ( ξ 2 + η 2 ω 2 ) .
Re [ g ̃ ( x , y ) ] = 0 , Im [ g ̃ ( x , y ) ] = 0
Re [ g ̃ ( x , y ) ] = a r x + b r y + c r , Im [ g ̃ ( x , y ) ] = a i x + b i y + c i ,
x = c i b r c r b i a r b i a i b r , y = a i c r a r c i a r b i a i b r .
S 0 = a r 2 + b r 2 + a i 2 + b i 2 ,
S 1 = a r 2 + a i 2 b r 2 b i 2 ,
S 2 = 2 ( a r b r + a i b i ) ,
S 3 = 2 ( a r b i a i b r ) ,
q = sgn ( Ω k ̂ ) = sgn ( a r b i a i b r ) ,
| Δ S | = | arccos ( S S ) | ,
d T = l N l .

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