Abstract

In this work we present a method to evaluate activity in low dynamic speckle patterns. It consists of binarizing the speckle image and analyzing the displacements and deformations of the resulting speckle grain regions, here called islands. Numerical simulations and controlled experiments were used to study the variations of the island features with the aim of finding a correlation with the activity of the speckle pattern. From the obtained results it was possible to conclude that the developed method can be useful for the analysis of low activity speckle patterns with the advantage of requiring only pairs of frames, thus permitting the assessment of nonstationary processes. In the case of stationary phenomena, so that stacks of frames registers are representative of them, dilute activity images can also be constructed.

© 2013 Optical Society of America

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References

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  1. H. J. Rabal and R. A. Braga, eds. Dynamic Laser Speckle and Applications (CRC Press, 2008).
  2. 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]
  3. W. Wang, T. Yokozeki, R. Ishijima, M. Takeda, and S. 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]
  4. K. R. Castleman, Digital Image Processing (Prentice Hall, 1996).
  5. T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” in Progress in Optics, E. Wolf, ed., Vol. 34 (North Holland, 1995).
  6. G. H. 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. G. H. Sendra, H. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
    [CrossRef]
  8. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  9. B. D. Hughes, Random Walks and Random Environments, Vol. 1 (Clarendon, 1995).
  10. J. M. Burch and J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101 (1968).
  11. S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
    [CrossRef]

2012 (1)

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

2009 (2)

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

G. H. Sendra, H. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
[CrossRef]

2006 (2)

1968 (1)

J. M. Burch and J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101 (1968).

Arizaga, R.

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

G. H. Sendra, H. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
[CrossRef]

Asakura, T.

T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” in Progress in Optics, E. Wolf, ed., Vol. 34 (North Holland, 1995).

Burch, J. M.

J. M. Burch and J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101 (1968).

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice Hall, 1996).

Gonzalez, J.

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Guzman, M.

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

Hanson, S.

Hanson, S. G.

Hughes, B. D.

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

Ishijima, R.

Miyamoto, Y.

Murialdo, S.

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

Okamoto, T.

T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” in Progress in Optics, E. Wolf, ed., Vol. 34 (North Holland, 1995).

Passoni, L.

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

Rabal, H.

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

G. H. Sendra, H. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
[CrossRef]

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

Sendra, G.

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

Sendra, G. H.

G. H. Sendra, H. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
[CrossRef]

G. H. 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.

Tokarski, J.

J. M. Burch and J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101 (1968).

Trivi, M.

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

G. H. Sendra, H. Rabal, R. Arizaga, and M. Trivi, “Vortex analysis in dynamic speckle images,” J. Opt. Soc. Am. A 26, 2634–2639 (2009).
[CrossRef]

G. H. 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.

J. Biomed. Opt. (1)

S. Murialdo, L. Passoni, M. Guzman, G. Sendra, H. Rabal, M. Trivi, and J. Gonzalez, “Discrimination of motile bacteria from filamentous fungi using dynamic speckle,” J. Biomed. Opt. 17, 056011 (2012).
[CrossRef]

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

Opt. Acta (1)

J. M. Burch and J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101 (1968).

Opt. Commun. (1)

G. H. 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 (2)

Other (5)

K. R. Castleman, Digital Image Processing (Prentice Hall, 1996).

T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” in Progress in Optics, E. Wolf, ed., Vol. 34 (North Holland, 1995).

H. J. Rabal and R. A. Braga, eds. Dynamic Laser Speckle and Applications (CRC Press, 2008).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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

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Figures (12)

Fig. 1.
Fig. 1.

Set-up employed to generate the speckle patterns: (a) Free-space propagation geometry and (b) propagation through a lens (focused or defocused).

Fig. 2.
Fig. 2.

(a) Speckle pattern and (b) resulting image after binarization.

Fig. 3.
Fig. 3.

Sample thresholded speckle grain (island) and its corresponding best fitting ellipse, where the mass center and the angle of inclination α can be appreciated.

Fig. 4.
Fig. 4.

Result of the application of the islands method for speckle translation with boiling displacements in (a) simulation and (b) controlled experiment. Figures show the average island displacement versus the diffuser displacement.

Fig. 5.
Fig. 5.

Average island displacement for subpixel simulated diffuser displacement, in pure translation condition.

Fig. 6.
Fig. 6.

Effect of Gaussian white noise variance on the translation of the islands, in pure translational condition.

Fig. 7.
Fig. 7.

Island method applied to a simulated (pure translation) in-plane rotational measurement with a rotation of 10° between initial (circle) and final (cross) positions.

Fig. 8.
Fig. 8.

(a) Averaged Euclidean distance of the islands displacements in pure boiling speckle for simulation (crosses) and experiment (dots) and (b) the corresponding number of identified islands.

Fig. 9.
Fig. 9.

(a) Product of the average Euclidean distance of displacement of the “islands” times the square root of the diffuser displacement versus the displacement of the diffuser. The graph (b) is an enlargement of (a) considering only experimental data. A linear regression was applied, and the dash lines shows the maximum deviation of the samples from the regression line.

Fig. 10.
Fig. 10.

Displacements measurements. Upper and lower halves of the figures were horizontally displaced in different amounts and opposite directions: (a) 10 and 20 μm and (b) 10 and 80 μm, respectively.

Fig. 11.
Fig. 11.

(a) Displacements of the islands shown as intensity levels. (b) Gaussian blurred version of (a).

Fig. 12.
Fig. 12.

Application of activity images in a Petri dish with two colonies of bacteria and a fungus: (a) Image obtained with the islands and (b) its Gaussian blurred version. The fungus exhibits lower activity (inside a red circle).

Equations (4)

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1+zρ=0,
(1dO+1di1f)(1+dOρ)1dO=0.
J=Δε2+(AAA+A)2+(2πΔα)2,
dT=lNl.

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