Abstract

We describe an extension of multi-speckle diffusing wave spectroscopy adapted to follow the non-stationary microscopic dynamics in drying films and coatings in a very reactive way and with a high dynamic range. We call this technique “Adaptive Speckle Imaging Interferometry”. We introduce an efficient tool, the inter-image distance, to evaluate the speckle dynamics, and the concept of “speckle rate” (SR, in Hz) to quantify this dynamics. The adaptive algorithm plots a simple kinetics, the time evolution of the SR, providing a non-invasive characterization of drying phenomena. A new commercial instrument, called HORUS®, based on ASII and specialized in the analysis of film formation and drying processes is presented.

© 2007 Optical Society of America

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  1. N. A. Clark, J. H. Lunacek, and G. B. Benedek, "A Study of Brownian Motion Using Light Scattering," Am. J. Phys. 38, 5 (1970).
    [CrossRef]
  2. B. J. Berne, and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  3. P. E. Wolf and G. Maret, "Multiple Light Scattering from Disordered Media. The Effect of Brownian Motion of Scatterers," Z. Phy. B 65, 409 (1987).
    [CrossRef]
  4. D. J. Pine, D. A. Weitz, P. M. Chaikin and E. Herbolzeimer. "Diffusing Wave Spectroscopy," Phy Rev. Lett. 60, 1434 (1988).
    [CrossRef]
  5. D. A. Weitz and D. J. Pine, "Diffusing Wave Spectroscopy" in Dynamic Light Scattering, The Method and Some Applications, W. Brown, ed., (Clarendon, Oxford, 1993), p. 719.
  6. P. N. Pusey and W. van Megen, "Dynamic light scattering by non-ergodic media," Physica A 157, 705 (1989).
    [CrossRef]
  7. J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, and P. M. Chaikin, "Nonergodicity and Light-Scattering from Polymer Gels," Phys. Rev. A 46, 6550 (1992).
    [CrossRef] [PubMed]
  8. F. Scheffold, S.E. Skipetrov, S. Romer, and P. Schurtenberger, "Diffusing wave spectroscopy of non ergodic media," Phys. Rev. E 63, 061404 (2001).
    [CrossRef]
  9. V. Viasnoff, F. Lequeux, and D. J. Pine, "Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics," Rev. Sci. Instrum. 73, 2336 (2002).
    [CrossRef]
  10. J. D. Briers, "Speckle fluctuations and biomedical optics: implications and applications," Opt. Eng. 32, 277 (1993).
    [CrossRef]
  11. R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).
  12. G. Romero, E. E. Alanis, H. J. Rabal, "Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessement of paint drying," Opt. Eng. 39, 1652 (2000).
    [CrossRef]
  13. J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, "Application of dynamic speckle interferometry to the drying of coatings," Progress in Organic Coatings 42, 89 (2001).
    [CrossRef]
  14. A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547 (1993).
    [CrossRef]
  15. S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758 (1996).
    [CrossRef]
  16. L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214 (1999).
    [CrossRef]
  17. A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
    [CrossRef]
  18. L. Brunel, P. Snabre, Patent, "Method and device for the analysis of movement in a scattering medium," 25/09/2003, EP1664744, WO 2005/031324.
  19. K. Schätzel, "Noise in photon correlation and photon structure functions," Optica acta 30, 155 (1983).
    [CrossRef]
  20. A look up table can be also used for the multiplication, but its size would be the square of the size of the one used for computing the square. For 8-bit numbers, the LUT used for the square has 256 entries while the one used for the multiplication has 65536 entries.
  21. J. W. Goodman, in Laser speckles and related phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975) p. 9.
  22. L. Cipelletti, L. Ramos, "Slow dynamics in glassy soft matter," J. Phy.: Condens. Matter 17, R253 (2005).
    [CrossRef]
  23. L/l* is estimated by comparing measurements of the backscattered flux to results from Monte Carlo simulations of the photon propagation in a random scattering medium, where L/l* is tuned to reproduce the experimental measurements.

2006

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

2005

L. Cipelletti, L. Ramos, "Slow dynamics in glassy soft matter," J. Phy.: Condens. Matter 17, R253 (2005).
[CrossRef]

2002

V. Viasnoff, F. Lequeux, and D. J. Pine, "Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics," Rev. Sci. Instrum. 73, 2336 (2002).
[CrossRef]

2001

F. Scheffold, S.E. Skipetrov, S. Romer, and P. Schurtenberger, "Diffusing wave spectroscopy of non ergodic media," Phys. Rev. E 63, 061404 (2001).
[CrossRef]

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, "Application of dynamic speckle interferometry to the drying of coatings," Progress in Organic Coatings 42, 89 (2001).
[CrossRef]

2000

G. Romero, E. E. Alanis, H. J. Rabal, "Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessement of paint drying," Opt. Eng. 39, 1652 (2000).
[CrossRef]

A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
[CrossRef]

1999

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214 (1999).
[CrossRef]

1996

S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758 (1996).
[CrossRef]

1993

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547 (1993).
[CrossRef]

J. D. Briers, "Speckle fluctuations and biomedical optics: implications and applications," Opt. Eng. 32, 277 (1993).
[CrossRef]

1992

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, and P. M. Chaikin, "Nonergodicity and Light-Scattering from Polymer Gels," Phys. Rev. A 46, 6550 (1992).
[CrossRef] [PubMed]

1989

P. N. Pusey and W. van Megen, "Dynamic light scattering by non-ergodic media," Physica A 157, 705 (1989).
[CrossRef]

1988

D. J. Pine, D. A. Weitz, P. M. Chaikin and E. Herbolzeimer. "Diffusing Wave Spectroscopy," Phy Rev. Lett. 60, 1434 (1988).
[CrossRef]

1987

P. E. Wolf and G. Maret, "Multiple Light Scattering from Disordered Media. The Effect of Brownian Motion of Scatterers," Z. Phy. B 65, 409 (1987).
[CrossRef]

1983

K. Schätzel, "Noise in photon correlation and photon structure functions," Optica acta 30, 155 (1983).
[CrossRef]

1970

N. A. Clark, J. H. Lunacek, and G. B. Benedek, "A Study of Brownian Motion Using Light Scattering," Am. J. Phys. 38, 5 (1970).
[CrossRef]

Alanis, E. E.

G. Romero, E. E. Alanis, H. J. Rabal, "Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessement of paint drying," Opt. Eng. 39, 1652 (2000).
[CrossRef]

Amalvy, J. I.

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, "Application of dynamic speckle interferometry to the drying of coatings," Progress in Organic Coatings 42, 89 (2001).
[CrossRef]

Arizaga, R.

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, "Application of dynamic speckle interferometry to the drying of coatings," Progress in Organic Coatings 42, 89 (2001).
[CrossRef]

Bartsch, E.

S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758 (1996).
[CrossRef]

Bellour, M.

A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
[CrossRef]

Benedek, G. B.

N. A. Clark, J. H. Lunacek, and G. B. Benedek, "A Study of Brownian Motion Using Light Scattering," Am. J. Phys. 38, 5 (1970).
[CrossRef]

Briers, J. D.

J. D. Briers, "Speckle fluctuations and biomedical optics: implications and applications," Opt. Eng. 32, 277 (1993).
[CrossRef]

Brunel, L.

L. Brunel, P. Snabre, Patent, "Method and device for the analysis of movement in a scattering medium," 25/09/2003, EP1664744, WO 2005/031324.

Cap, N.

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

Chaikin, P. M.

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, and P. M. Chaikin, "Nonergodicity and Light-Scattering from Polymer Gels," Phys. Rev. A 46, 6550 (1992).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin and E. Herbolzeimer. "Diffusing Wave Spectroscopy," Phy Rev. Lett. 60, 1434 (1988).
[CrossRef]

Cipelletti, L.

L. Cipelletti, L. Ramos, "Slow dynamics in glassy soft matter," J. Phy.: Condens. Matter 17, R253 (2005).
[CrossRef]

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214 (1999).
[CrossRef]

Clark, N. A.

N. A. Clark, J. H. Lunacek, and G. B. Benedek, "A Study of Brownian Motion Using Light Scattering," Am. J. Phys. 38, 5 (1970).
[CrossRef]

Frenz, V.

S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758 (1996).
[CrossRef]

Grumel, E. E.

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

Harden, J. L.

A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
[CrossRef]

Herbolzeimer, E.

D. J. Pine, D. A. Weitz, P. M. Chaikin and E. Herbolzeimer. "Diffusing Wave Spectroscopy," Phy Rev. Lett. 60, 1434 (1988).
[CrossRef]

Kirsch, S.

S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758 (1996).
[CrossRef]

Knaebel, A.

A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
[CrossRef]

Lasquibar, C. A.

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, "Application of dynamic speckle interferometry to the drying of coatings," Progress in Organic Coatings 42, 89 (2001).
[CrossRef]

Lequeux, F.

V. Viasnoff, F. Lequeux, and D. J. Pine, "Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics," Rev. Sci. Instrum. 73, 2336 (2002).
[CrossRef]

A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
[CrossRef]

Lunacek, J. H.

N. A. Clark, J. H. Lunacek, and G. B. Benedek, "A Study of Brownian Motion Using Light Scattering," Am. J. Phys. 38, 5 (1970).
[CrossRef]

Maret, G.

P. E. Wolf and G. Maret, "Multiple Light Scattering from Disordered Media. The Effect of Brownian Motion of Scatterers," Z. Phy. B 65, 409 (1987).
[CrossRef]

Milner, S. T.

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, and P. M. Chaikin, "Nonergodicity and Light-Scattering from Polymer Gels," Phys. Rev. A 46, 6550 (1992).
[CrossRef] [PubMed]

Munch, J.-P.

A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
[CrossRef]

Pine, D. J.

V. Viasnoff, F. Lequeux, and D. J. Pine, "Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics," Rev. Sci. Instrum. 73, 2336 (2002).
[CrossRef]

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, and P. M. Chaikin, "Nonergodicity and Light-Scattering from Polymer Gels," Phys. Rev. A 46, 6550 (1992).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin and E. Herbolzeimer. "Diffusing Wave Spectroscopy," Phy Rev. Lett. 60, 1434 (1988).
[CrossRef]

Pusey, P. N.

P. N. Pusey and W. van Megen, "Dynamic light scattering by non-ergodic media," Physica A 157, 705 (1989).
[CrossRef]

Rabal, H.

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, "Application of dynamic speckle interferometry to the drying of coatings," Progress in Organic Coatings 42, 89 (2001).
[CrossRef]

Rabal, H. J.

G. Romero, E. E. Alanis, H. J. Rabal, "Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessement of paint drying," Opt. Eng. 39, 1652 (2000).
[CrossRef]

Ramos, L.

L. Cipelletti, L. Ramos, "Slow dynamics in glassy soft matter," J. Phy.: Condens. Matter 17, R253 (2005).
[CrossRef]

Ricaurte, G.

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

Romer, S.

F. Scheffold, S.E. Skipetrov, S. Romer, and P. Schurtenberger, "Diffusing wave spectroscopy of non ergodic media," Phys. Rev. E 63, 061404 (2001).
[CrossRef]

Romero, G.

G. Romero, E. E. Alanis, H. J. Rabal, "Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessement of paint drying," Opt. Eng. 39, 1652 (2000).
[CrossRef]

Schartl, W.

S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758 (1996).
[CrossRef]

Schätzel, K.

K. Schätzel, "Noise in photon correlation and photon structure functions," Optica acta 30, 155 (1983).
[CrossRef]

Scheffold, F.

F. Scheffold, S.E. Skipetrov, S. Romer, and P. Schurtenberger, "Diffusing wave spectroscopy of non ergodic media," Phys. Rev. E 63, 061404 (2001).
[CrossRef]

Schurtenberger, P.

F. Scheffold, S.E. Skipetrov, S. Romer, and P. Schurtenberger, "Diffusing wave spectroscopy of non ergodic media," Phys. Rev. E 63, 061404 (2001).
[CrossRef]

Sillescu, H.

S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758 (1996).
[CrossRef]

Skipetrov, S.E.

F. Scheffold, S.E. Skipetrov, S. Romer, and P. Schurtenberger, "Diffusing wave spectroscopy of non ergodic media," Phys. Rev. E 63, 061404 (2001).
[CrossRef]

Snabre, P.

L. Brunel, P. Snabre, Patent, "Method and device for the analysis of movement in a scattering medium," 25/09/2003, EP1664744, WO 2005/031324.

Trivi, M.

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, "Application of dynamic speckle interferometry to the drying of coatings," Progress in Organic Coatings 42, 89 (2001).
[CrossRef]

van Megen, W.

P. N. Pusey and W. van Megen, "Dynamic light scattering by non-ergodic media," Physica A 157, 705 (1989).
[CrossRef]

Viasnoff, V.

V. Viasnoff, F. Lequeux, and D. J. Pine, "Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics," Rev. Sci. Instrum. 73, 2336 (2002).
[CrossRef]

A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
[CrossRef]

Weitz, D. A.

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214 (1999).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin and E. Herbolzeimer. "Diffusing Wave Spectroscopy," Phy Rev. Lett. 60, 1434 (1988).
[CrossRef]

Wiltzius, P.

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547 (1993).
[CrossRef]

Wolf, P. E.

P. E. Wolf and G. Maret, "Multiple Light Scattering from Disordered Media. The Effect of Brownian Motion of Scatterers," Z. Phy. B 65, 409 (1987).
[CrossRef]

Wong, A. P. Y.

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547 (1993).
[CrossRef]

Wu, X. L.

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, and P. M. Chaikin, "Nonergodicity and Light-Scattering from Polymer Gels," Phys. Rev. A 46, 6550 (1992).
[CrossRef] [PubMed]

Xue, J. Z.

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, and P. M. Chaikin, "Nonergodicity and Light-Scattering from Polymer Gels," Phys. Rev. A 46, 6550 (1992).
[CrossRef] [PubMed]

Yepes, B.

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

Am. J. Phys.

N. A. Clark, J. H. Lunacek, and G. B. Benedek, "A Study of Brownian Motion Using Light Scattering," Am. J. Phys. 38, 5 (1970).
[CrossRef]

Europhys. Lett.

A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. L. Harden, "Aging behavior of Laponite clay particle supensions," Europhys. Lett. 52, 73 (2000).
[CrossRef]

J. Chem. Phys.

S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, H. Sillescu, "Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes," J. Chem. Phys. 104, 1758 (1996).
[CrossRef]

J. Phy.: Condens. Matter

L. Cipelletti, L. Ramos, "Slow dynamics in glassy soft matter," J. Phy.: Condens. Matter 17, R253 (2005).
[CrossRef]

JCT Research

R. Arizaga, E. E. Grumel, N. Cap, M. Trivi, J. I. Amalvy, B. Yepes, G. Ricaurte, "Following the drying of spray paints using space and time contrast of dynamic speckle," JCT Research 3, 295 (2006).

Opt. Eng.

G. Romero, E. E. Alanis, H. J. Rabal, "Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessement of paint drying," Opt. Eng. 39, 1652 (2000).
[CrossRef]

J. D. Briers, "Speckle fluctuations and biomedical optics: implications and applications," Opt. Eng. 32, 277 (1993).
[CrossRef]

Optica acta

K. Schätzel, "Noise in photon correlation and photon structure functions," Optica acta 30, 155 (1983).
[CrossRef]

Phy Rev. Lett.

D. J. Pine, D. A. Weitz, P. M. Chaikin and E. Herbolzeimer. "Diffusing Wave Spectroscopy," Phy Rev. Lett. 60, 1434 (1988).
[CrossRef]

Phys. Rev. A

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, and P. M. Chaikin, "Nonergodicity and Light-Scattering from Polymer Gels," Phys. Rev. A 46, 6550 (1992).
[CrossRef] [PubMed]

Phys. Rev. E

F. Scheffold, S.E. Skipetrov, S. Romer, and P. Schurtenberger, "Diffusing wave spectroscopy of non ergodic media," Phys. Rev. E 63, 061404 (2001).
[CrossRef]

Physica A

P. N. Pusey and W. van Megen, "Dynamic light scattering by non-ergodic media," Physica A 157, 705 (1989).
[CrossRef]

Progress in Organic Coatings

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, M. Trivi, "Application of dynamic speckle interferometry to the drying of coatings," Progress in Organic Coatings 42, 89 (2001).
[CrossRef]

Rev. Sci. Instrum.

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547 (1993).
[CrossRef]

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214 (1999).
[CrossRef]

V. Viasnoff, F. Lequeux, and D. J. Pine, "Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics," Rev. Sci. Instrum. 73, 2336 (2002).
[CrossRef]

Z. Phy. B

P. E. Wolf and G. Maret, "Multiple Light Scattering from Disordered Media. The Effect of Brownian Motion of Scatterers," Z. Phy. B 65, 409 (1987).
[CrossRef]

Other

D. A. Weitz and D. J. Pine, "Diffusing Wave Spectroscopy" in Dynamic Light Scattering, The Method and Some Applications, W. Brown, ed., (Clarendon, Oxford, 1993), p. 719.

B. J. Berne, and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

L. Brunel, P. Snabre, Patent, "Method and device for the analysis of movement in a scattering medium," 25/09/2003, EP1664744, WO 2005/031324.

A look up table can be also used for the multiplication, but its size would be the square of the size of the one used for computing the square. For 8-bit numbers, the LUT used for the square has 256 entries while the one used for the multiplication has 65536 entries.

J. W. Goodman, in Laser speckles and related phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975) p. 9.

L/l* is estimated by comparing measurements of the backscattered flux to results from Monte Carlo simulations of the photon propagation in a random scattering medium, where L/l* is tuned to reproduce the experimental measurements.

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Figures (4)

Fig. 1.
Fig. 1.

The HORUS® setup.

Fig. 2.
Fig. 2.

Normalized inter-image distance d2/dmax versus time for white corrector (blue line), acrylic paint (red line) and marker pen ink (green line). The black lines are fits according to Eq. (2).

Fig. 3.
Fig. 3.

Rate of change of the speckle pattern, SR, versus time in a double logarithmic graph. The fastest-drying curve (left, red) is for a commercial marker pen, the middle one is for a water-based paint (middle, orange) and the longest drying curve if for a organic solvent-based paint (right, blue).

Fig. 4.
Fig. 4.

Rate of change of the speckle pattern, SR, versus time in a semi logarithmic graph, for the drying of a 75μm layer of an acrylic paint. The blue curve (higher SR) corresponds to a white substrate and the red curve (lower SR) corresponds to a black substrate. There is a ratio of approximately 3 between the absolute magnitudes of the 2 curves, but the shape of SR vs t is insensitive to the substrate color.

Tables (1)

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Table 1. Computational cost of various correlation tools, including camera offset calibration

Equations (2)

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d n = [ 2 n I 2 g 2 I 2 ] 1 2
d 2 ( τ ) = d 2 0 + ( d 2 max d 2 0 ) [ 1 exp ( τ τ c ) ]

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