## Simultaneous measurement of the microscopic dynamics and the mesoscopic displacement field in soft systems by speckle imaging |

Optics Express, Vol. 21, Issue 19, pp. 22353-22366 (2013)

http://dx.doi.org/10.1364/OE.21.022353

Acrobat PDF (1762 KB)

### Abstract

The constituents of soft matter systems such as colloidal suspensions, emulsions, polymers, and biological tissues undergo microscopic random motion, due to thermal energy. They may also experience drift motion correlated over mesoscopic or macroscopic length scales, *e.g.* in response to an internal or applied stress or during flow. We present a new method for measuring simultaneously both the microscopic motion and the mesoscopic or macroscopic drift. The method is based on the analysis of spatio-temporal cross-correlation functions of speckle patterns taken in an imaging configuration. The method is tested on a translating Brownian suspension and a sheared colloidal glass.

© 2013 Optical Society of America

## 1. Introduction

*e.g.*from a laser. By analyzing a time sequence of speckle patterns, valuable information can be retrieved on the sample evolution. Broadly speaking, one may distinguish between “static” speckle patterns generated by solid objects and “dynamic” speckles formed by soft matter systems (

*e.g.*colloidal suspensions, emulsions, polymer solutions, biological tissues), whose components undergo Brownian motion, thereby continuously reconfiguring the scattered speckle pattern. In the former case, relevant to metrology and interferometry [2], a rigid displacement or a long wavelength deformation is often measured,

*e.g.*in response to vibrations, applied load, or a change of temperature; speckle patterns are recorded onto a 2D detector such as a CCD or CMOS camera, using an imaging optics. By contrast, the microscopic (

*e.g.*Brownian) dynamics of soft systems is quantified by

*g*

_{2}(

*τ*) − 1, the autocorrelation function of the temporal fluctuations of the scattered intensity. In these dynamic light scattering measurements (DLS, a.k.a. photon correlation spectroscopy [3]) a point-like detector (

*e.g.*a phototube) is placed in the far field, where it collects light within a few speckles.

*τ*exhibits a peak, whose position and height yield the sample rigid shift and its internal dynamics over the time

*τ*, respectively. Applications of this method to gels submitted to gravitational [18

18. G. Brambilla, S. Buzzaccaro, R. Piazza, L. Berthier, and L. Cipelletti, “Highly nonlinear dynamics in a slowly sedimenting colloidal gel,” Phys. Rev. Lett. **106**, 118302 (2011). [CrossRef] [PubMed]

19. O. Lieleg, J. Kayser, G. Brambilla, L. Cipelletti, and A. R. Bausch, “Slow dynamics and internal stress relaxation in bundled cytoskeletal networks,” Nature Materials **10**, 236–242 (2011). [CrossRef] [PubMed]

## 2. Sub-pixel digital imaging correlation algorithm

*k̄*,

*l̄*) of the global maximum of corr[

*J*,

*I*] yields the desired displacement along the direction of columns (

*x*axis) and rows (

*y*axis), Δ

*x*=

*l̄*and Δ

*y*=

*k̄*respectively, with pixel resolution. Several schemes have been proposed to improve this resolution,

*e.g.*by calculating the centroid of corr[

*J*,

*I*], or by fitting its peak to a 2-dimensional analytical function such as a Gaussian. While both methods work well for broad, circularly symmetric peaks, they tend to be less robust when the peak is sharp or it has an asymmetric shape. The shape of the peak is determined by the spatial autocorrelation of the intensity pattern; for our speckle images, it depends on the shape and size of the speckles, which may not be symmetrical, depending on the shape of the illuminated sample volume and the imaging optics [1]. Moreover, the peak usually extends over just a few pixels, because one minimizes the speckle size in order to maximize the information content in the image. To overcome the limitations inherent to peak-based schemes, we use an alternative approach based on a least-square method that allows us to obtain the displacement field with a typical resolution of a few hundredths of a pixel, with no requirements on the shape or broadness of the peak and without using any fitting function.

**3. Dynamic light scattering: corrections to***g*_{2}(*τ*) − 1 **for drifting samples**

*g*

_{2}− 1 between image

*J*and a shifted version of

*I*, so as to avoid any artifact due to the rigid shift of the speckles. Denoting by

*I′*the image

*I*shifted by (Δ

*x*, Δ

*y*), the (un-normalized) intensity correlation function corrected for the shift contribution is The shifted image

*I′*may be constructed using an interpolation method. Tests on real speckle images show that linear interpolation, although suitable for determining the shift with good accuracy, is not precise enough to reconstruct a shifted version of

*I*suitable for the calculation of

*g*

_{2}− 1. Higher-order interpolation schemes are thus required. As shown in [21

21. T. M. Lehmann, C. Gonner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” Ieee Transactions on Medical Imaging **18**, 1049–1075 (1999). [CrossRef]

_{2D}

*h*(

*x*,

*y*)=

*h*(

*x*)

*h*(

*y*). Unfortunately, in our case this approach would be too time-consuming, because it requires a convolution operation, Eq. (12), in addition to the calculation of the correlation function, Eq. (11).

*j*= floor(Δ

_{x}*x*),

*i*= floor(Δ

_{y}*y*), where floor(

*x*) is the largest integer ≤

*x*. As we shall discuss it below, the choice of the kernel is not crucial; a good choice is a truncated, windowed sinc function with an even number,

*M*, of supporting points: where we choose the three-term Blackman-Harris window function [21

21. T. M. Lehmann, C. Gonner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” Ieee Transactions on Medical Imaging **18**, 1049–1075 (1999). [CrossRef]

22. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier-transform,” Proc. IEEE **66**, 5183 (1978). [CrossRef]

21. T. M. Lehmann, C. Gonner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” Ieee Transactions on Medical Imaging **18**, 1049–1075 (1999). [CrossRef]

22. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier-transform,” Proc. IEEE **66**, 5183 (1978). [CrossRef]

*J*and

*I*, Eq. (3), and using the fact that the kernel is DC-constant, Eq. (17), one obtains or, equivalently, where

*Ī*=

*N*

^{−1}∑

_{r,c}*I*and similarly for

_{r,c}*J̄*.

*J*,

*I*], weighted by the kernel. Since covar[

*J*,

*I*] has already been calculated to determine the shift, the extra cost is essentially limited to the evaluation of

*M*

^{2}values of the kernel, which is typically negligible. Finally, we note that covar[

*J*,

*I*] vanishes on the length scale of the speckle size as its argument departs from (

*i*,

_{y}*j*), which is close to the location of the peak of the covariance. Hence, it is sufficient to take

_{x}*M*on the order of a few speckle sizes (in units of pixels), because in Eq. (21) the contribution of the kernel for larger lags would be multiplied by a vanishingly small quantity. For example, we find that for images with a speckle size of about 5 pixels, the correction is virtually independent of

*M*for

*M*≥ 8.

## 4. Experimental tests

*R*= 0.265

*μ*m) in an aqueous solution of fructose at 75% weight fraction. The particle volume fraction is 10

^{−5}and the sample is kept at a temperature

*T*= 9 °C. The setup is described in [23

23. D. El Masri, M. Pierno, L. Berthier, and L. Cipelletti, “Aging and ultra-slow equilibration in concentrated colloidal hard spheres,” J. Phys.: Condens. Matter **17**, S3543 (2005). [CrossRef]

13. A. Duri, D. A. Sessoms, V. Trappe, and L. Cipelletti, “Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging,” Phys. Rev. Lett. **102**, 085702 (2009). [CrossRef] [PubMed]

*θ*= 90 deg, corresponding to a scattering vector

*q*= 2.46

*μ*m

^{−1}. The field of view is 1820×364

*μ*m

^{2}and images are acquired at a rate of 10 Hz, with an exposure time of 5 msec. To avoid any spurious increase of the base line of

*g*

_{2}− 1, the speckle images are corrected for non-uniform illumination as detailed in [24

24. A. Duri, H. Bissig, V. Trappe, and L. Cipelletti, “Time-resolved-correlation measurements of temporally heterogeneous dynamics,” Phys. Rev. E **72**, 051401 (2005). [CrossRef]

*y*direction at a controlled speed,

*v*= 10

_{y}*μ*ms

^{−1}.

*τ*= 0 s, Eq. (2) yields the spatial autocorrelation of the speckle pattern: accordingly, a sharp peak of height one and centered at Δ

*x*= Δ

*y*= 0 is visible, whose FWHM ≈ 2.9 pixels provides the speckle size. As the lag increases, the peak position drifts in the

*y*direction, due to the translation motion imposed by the motor. Additionally, its height decreases, due to the relative motion of the Brownian particles that reconfigure the speckle pattern. Figure 2(d) shows a cut of the cross-correlation peak along the Δ

*x*= 0 direction, for four values of

*τ*. From this plot, it is clear that if

*g*

_{2}(

*τ*) − 1 was to be computed from a purely temporal cross-correlation, as in Eq. (1), one would observe a spurious, fast decay, essentially due to the rigid shift only. This would correspond to follow corr[

*I*(

*t*),

*I*(

*t*+

*τ*)] at Δ

*x*= Δ

*y*= 0, as a function of

*τ*. By contrast, if the relative motion of the Brownian particles is to be obtained, one has to measure the height of the peak as it drifts, as in the method proposed here. The inset of Fig. 2(d) shows the same data, plotted as a function of distance along

*y*with respect to the (subpixel) peak position. It is worth noting that the peak width remains constant, in contrast to what suggested (but not demonstrated, to our knowledge) in patent literature [25], where it was proposed that the peak would broaden with

*τ*as a result of the internal motion of the scatterers. Thus, the relevant parameter for extracting the relative motion is indeed the peak height, not its width.

*static*sample undergoing translational motion. These works typically focussed on the far field speckle pattern, for which a loss of correlation is observed even in the absence of any internal dynamics (see [27

27. T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” App. Physics **25**, 179–194 (1981). [CrossRef]

27. T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” App. Physics **25**, 179–194 (1981). [CrossRef]

*τ*, obtained from the sub-pixel peak position averaged over 200 pairs of images (

*i.e.*20 s), taken while translating the sample. The data are very well fitted by a linear law (red line) as expected for motion at constant speed, thus indicating that our algorithm captures very well the drift component of the speckle pattern, from a fraction of a pixel up to tens of pixels. The error bars represent

*σ*, the standard deviation of the temporal fluctuations of the peak position detected for a fixed lag time

_{y}*τ*.For

*τ*≤ 4.2s,

*σ*/Δ

_{y}*y*< 4% and the error bars are smaller than the symbol size, indicating that the detection of the peak position is consistently reliable, even when the peak height is as low as 0.1 or the displacement is just a fraction of a pixel. For

*τ*= 5.6 s, the error bar is significantly larger, because the peak height is typically of order 0.05 − 0.06, comparable to the noise level. As a consequence, the detected peak position departs erratically from its true value for a significant fraction of the 200 pairs of images, leading to a large value of

*σ*. Beyond

_{y}*τ*= 5.6 s, no peak can be reliably found, thus preventing the displacement to be measured. The slope of the linear fit to the data is 3.30 ± 0.03 pixel s

^{−1}. Recalling that the nominal speed of the motor is

*v*= 10

_{y}*μ*m s

^{−1}, this implies that 1 pixel corresponds to 3.03 ± 0.03

*μ*m in the sample, in excellent agreement with 3.15 ± 0.15

*μ*m/pixel as obtained from the magnification of the imaging system, evaluated using geometrical optics. Figure 3(b) shows the intensity correlation function

*g*

_{2}(

*τ*)−1, averaged over 20 s. Data are normalized such that

*g*

_{2}(

*τ*→ 0)−1 = 1. If the sample is kept at rest during the measurement (black squares), the intensity correlation function exhibits an exponential decay, as expected for diluted Brownian suspensions [3], as better seen in the inset that shows the same data in a semilog plot. When the sample is translated at constant speed, the uncorrected

*g*

_{2}− 1 decays on a much shorter time scale (blue circles) and its shape departs from a simple exponential. Clearly, no information on the microscopic dynamics can be obtained from the uncorrected data. The red crosses are the data corrected according to Eq. (21): for

*τ*≤ 4.2 s the corrected

*g*

_{2}− 1 is very close to that measured for the stationary sample, thereby demonstrating the effectiveness of our correction scheme. For larger lags, the corrected data tend to overestimate

*g*

_{2}− 1: this is consistent with the fact that the displacement cannot be reliably measured, as discussed in relation to Fig. 3(a). Indeed, in this case the peak-finding algorithm spuriously interprets the highest level in the noisy base line of corr[

*I*(

*t*),

*I*(

*t*+

*τ*)] as the (higher-than-expected) degree of correlation.

29. P. N. Pusey and W. van Megen, “Observation of a glass-transition in suspensions of spherical colloidal particles,” Phys. Rev. Lett. **59**, 2083 (1987). [CrossRef] [PubMed]

28. G. Brambilla, D. El Masri, M. Pierno, L. Berthier, L. Cipelletti, G. Petekidis, and A. B. Schofield, “Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition,” Phys. Rev. Lett. **102**, 085703 (2009). [CrossRef] [PubMed]

^{2}, in which a glass bead of diameter

*D*= 5 mm is inserted. The bead is attached to a motor that displaces it in the

_{b}*y*(vertical) direction, parallel to the cell wall, at a speed

*v*= 0.1

_{y}*μ*ms

^{−1}. The minimum gap

*e*between the wall and the bead surface is 1280 ± 90

*μ*m. For the small displacements studied here (≤ 850

*μ*m) and given that

*e*≪

*D*, the deformation is close to a simple shear. The sample is illuminated by a laser sheet in the vertical (

_{b}*x*,

*y*) plane, of thickness ≈ 100

*μ*m. We image a region of size 710 × 530

*μ*m

^{2}using light scattered at

*θ*= 90 deg, corresponding to

*q*= 20.6

*μ*m

^{−1}. The CCD acquisition rate and exposure time are 1 Hz and 10 msec, respectively. To obtain space-resolved information on the mesoscopic displacement and the microscopic dynamics, we run our algorithm on ten ROIs of size 40 × 340

*μ*m

^{2}regularly spaced at a growing distance

*x*from the moving wall. As for the previous experiment, speckle images are corrected for non-uniform illumination.

*t*after starting shearing the sample. In this representation, the slope of the data is the local shear rate

*γ̇*. The solid line shows the velocity profile expected for homogeneous shear, corresponding to an average shear rate across the whole gap of

*γ̇*= 7.9 × 10

^{−5}s

^{−1}. It is clear that already at

*t*= 120 s

*γ̇*is non-uniform across the gap, with a highly-sheared band close to the moving surface (

*x*≥−164

*μ*m,

*γ̇*≈ 1.4 × 10

^{−4}s

^{−1}), followed by a low shear region (

*x*≤−220

*μ*m,

*γ̇*≈ 6.0 × 10

^{−5}s

^{−1}). Similar shear banding has been reported for other colloidal glasses [30

30. V. Chikkadi, G. Wegdam, D. Bonn, B. Nienhuis, and P. Schall, “Long-range strain correlations in sheared colloidal glasses,” Phys. Rev. Lett. **107**, 198303 (2011). [CrossRef] [PubMed]

*t*= 820 s, the shear rate for the high- and low-shear bands is comparable to that at

*t*= 120 s (

*γ̇*≈ 1.3 × 10

^{−4}s

^{−1}and

*γ̇*≈ 6.1 × 10

^{−5}s

^{−1}, respectively), but the boundary between the two zones has moved from

*x*= −190

*μ*m to

*x*= −240

*μ*m. Additionally, the occurrence of a marked drop of

*v*close to the moving surface suggests slipping. This behavior is reminiscent of that reported for a variety of jammed or glassy soft materials, see

_{y}*e.g.*[31

31. T. Divoux, D. Tamarii, C. Barentin, and S. Manneville, “Transient shear banding in a simple yield stress fluid,” Phys. Rev. Lett. **104**, 208301 (2010). [CrossRef] [PubMed]

*s*, about 2000 times the Brownian time for the same particles in the diluted regime. This is consistent with the notion that the microscopic dynamics of a sample at rest is slowed down by orders of magnitude on approaching the glass transition. The open symbols show the uncorrected

*g*

_{2}− 1: a fast decay is observed, essentially due to the translation of the speckle pattern due to the imposed shear. Once corrected, the data still show a decay of

*g*

_{2}− 1 (albeit a slower one), thus indicating that particles move with respect to each other, in addition to be advected by the shear deformation. We emphasize that the corrected

*g*

_{2}− 1 is sensitive to the component of the particle displacement along the direction of

**q**, which lays in the horizontal plane, perpendicular to the shear direction. Therefore, the decay of

*g*

_{2}− 1 is not due to the affine component of the particle displacement along

*y*, but rather to irreversible rearrangements associated with flow in glassy systems [32]. Interestingly, we find that the decay of

*g*

_{2}− 1 is faster at

*t*= 820 s, when both the local

*γ̇*and its gradient are larger. This suggest a direct relation between (local) shear rate and plastic rearrangements, as proposed for granular materials [16

16. A. Amon, V. B. Nguyen, A. Bruand, J. Crassous, and E. Clement, “Hot spots in an athermal system,” Phys. Rev. Lett. **108**, 135502 (2012). [CrossRef] [PubMed]

33. P. Jop, V. Mansard, P. Chaudhuri, L. Bocquet, and A. Colin, “Microscale rheology of a soft glassy material close to yielding,” Phys. Rev. Lett. **108**, 148301 (2012) [CrossRef] [PubMed]

## 5. Conclusions

*g*

_{2}− 1 does not requires any significant computational extra cost, besides that necessary to determine the displacement field. The method has been successfully tested on a Brownian suspension and a colloidal glass. Although similar information may be in principle obtained using confocal or optical microscopy, our method allows one to investigate samples that are difficult or impossible to visualize in real space, such as the very small particles of our colloidal glass. A generalization to speckle patterns obtained under multiple scattering conditions or for partially coherent illumination, such as in recent microscopy developments [34

34. R. Cerbino and A. Vailati, “Near-field scattering techniques: Novel instrumentation and results from time and spatially resolved investigations of soft matter systems,” Current Opinion in Colloid & Interface Science **14**, 416 (2009). [CrossRef]

35. F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: Differential dynamic microscopy and beyond,” Phys. Rev. E **80**, 031403 (2009). [CrossRef]

36. S. Buzzaccaro, E. Secchi, and R. Piazza, “Ghost particle velocimetry: accurate 3D flow visualization using standard lab equipment,” Phys. Rev. Lett. **111**048101 (2013). [CrossRef] [PubMed]

18. G. Brambilla, S. Buzzaccaro, R. Piazza, L. Berthier, and L. Cipelletti, “Highly nonlinear dynamics in a slowly sedimenting colloidal gel,” Phys. Rev. Lett. **106**, 118302 (2011). [CrossRef] [PubMed]

19. O. Lieleg, J. Kayser, G. Brambilla, L. Cipelletti, and A. R. Bausch, “Slow dynamics and internal stress relaxation in bundled cytoskeletal networks,” Nature Materials **10**, 236–242 (2011). [CrossRef] [PubMed]

37. J.-P. Bouchaud and E. Pitard, “Anomalous dynamical light scattering in soft glassy gels,” Eur. Phys. J. E **6**, 231 (2001). [CrossRef]

## 6. APPENDIX A: Center-of-mass algorithm for determining the direction of shift

*J*,

*I*] extends over a few pixels at most. Accordingly, we calculate the center of mass of the peak based on the values of corr[

*J*,

*I*] at its maximum, located at (

*k̄*,

*l̄*), and in the eight neighboring pixels as showed in Fig. 1(b). Our aim is to determine in which of the four quadrants A, B, C, and D shown in Fig. 1(b) lays the center of mass of the correlation peak. To avoid any bias introduced by the square shape and the orientation of the pixels, we adopt a circular symmetry by considering only the contribution of the areas indicated by

*α*

_{1},

*α*

_{2},

*α*

_{3}in Fig. 1(b) (for clarity, only the overlap areas for quadrant B are shown in the figure). This is accomplished by weighting the contribution of each element of corr[

*J*,

*I*] by its overlap with the circle shown in the figure. The weights

*w*,

_{A}*w*,

_{B}*w*,

_{C}*w*associated with quadrants A, B, C, D respectively are then with

_{D}*α*

_{1}= 0.485869913,

*α*

_{2}= 0.545406041,

*α*

_{3}= 0.25. Once the weights of the four quadrants are determined, the indexes to be used in Eq. (6) and following are calculated from where δ

*r*and δ

*c*are obtained from

*w*,...,

_{A}*w*:

_{D}## Acknowledgments

## References and links

1. | J. W. Goodman, |

2. | R. K. Erf, |

3. | B. J. Berne and R. Pecora, |

4. | J. D. Briers, “Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging,” Physiological Measurement |

5. | M. Draijer, E. Hondebrink, T. Leeuwen, and W. Steenbergen, “Review of laser speckle contrast techniques for visualizing tissue perfusion,” Lasers in Medical Science |

6. | R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev. Sci. Instrum. |

7. | R. J. Adrian, “Scattering particle characteristics and their effect on pulsed laser measurements of fluid flow: speckle velocimetry vs particle image velocimetry,” Appl. Opt. |

8. | T. D. Dudderar, R. Meynart, and P. G. Simpkins, “Full-field laser metrology for fluid velocity measurement,” Optics and Lasers in Engineering |

9. | C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Experiments In Fluids |

10. | P. T. Tokumaru and P. E. Dimotakis, “Image correlation velocimetry,” Experiments In Fluids |

11. | A. P. Y. Wong and P. Wiltzius, “Dynamic light-scattering with a CCD camera,” Rev. Sci. Instrum. |

12. | S. Kirsch, V. Frenz, W. Schartl, E. Bartsch, and H. Sillescu, “Multispeckle autocorrelation spectroscopy and its application to the investigation of ultraslow dynamical processes,” J. Chem. Phys. |

13. | A. Duri, D. A. Sessoms, V. Trappe, and L. Cipelletti, “Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging,” Phys. Rev. Lett. |

14. | S. Maccarrone, G. Brambilla, O. Pravaz, A. Duri, M. Ciccotti, J. M. Fromental, E. Pashkovski, A. Lips, D. Sessoms, V. Trappe, and L. Cipelletti, “Ultra-long range correlations of the dynamics of jammed soft matter,” Soft Matter |

15. | P. Zakharov and F. Scheffold, “Monitoring spatially heterogeneous dynamics in a drying colloidal thin film,” Soft Matter |

16. | A. Amon, V. B. Nguyen, A. Bruand, J. Crassous, and E. Clement, “Hot spots in an athermal system,” Phys. Rev. Lett. |

17. | L. Cipelletti, “Method and device for characterizing the internal dynamics of a sample of material in the presence of a rigid displacement,” Patent WO 2012/076826, 14June2012. |

18. | G. Brambilla, S. Buzzaccaro, R. Piazza, L. Berthier, and L. Cipelletti, “Highly nonlinear dynamics in a slowly sedimenting colloidal gel,” Phys. Rev. Lett. |

19. | O. Lieleg, J. Kayser, G. Brambilla, L. Cipelletti, and A. R. Bausch, “Slow dynamics and internal stress relaxation in bundled cytoskeletal networks,” Nature Materials |

20. | W. H. Press and S. A. Teukolsky, |

21. | T. M. Lehmann, C. Gonner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” Ieee Transactions on Medical Imaging |

22. | F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier-transform,” Proc. IEEE |

23. | D. El Masri, M. Pierno, L. Berthier, and L. Cipelletti, “Aging and ultra-slow equilibration in concentrated colloidal hard spheres,” J. Phys.: Condens. Matter |

24. | A. Duri, H. Bissig, V. Trappe, and L. Cipelletti, “Time-resolved-correlation measurements of temporally heterogeneous dynamics,” Phys. Rev. E |

25. | G. J. Tearney and E. B. Bouma, “Optical methods and systems for tissue analysis,” Patent US20020183601 A1, 5December2002. |

26. | D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: The method of cumulants,” J. Chem. Phys. |

27. | T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” App. Physics |

28. | G. Brambilla, D. El Masri, M. Pierno, L. Berthier, L. Cipelletti, G. Petekidis, and A. B. Schofield, “Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition,” Phys. Rev. Lett. |

29. | P. N. Pusey and W. van Megen, “Observation of a glass-transition in suspensions of spherical colloidal particles,” Phys. Rev. Lett. |

30. | V. Chikkadi, G. Wegdam, D. Bonn, B. Nienhuis, and P. Schall, “Long-range strain correlations in sheared colloidal glasses,” Phys. Rev. Lett. |

31. | T. Divoux, D. Tamarii, C. Barentin, and S. Manneville, “Transient shear banding in a simple yield stress fluid,” Phys. Rev. Lett. |

32. | P. Schall, D. A. Weitz, and F. Spaepen, “Structural rearrangements that govern flow in colloidal glasses,” Science |

33. | P. Jop, V. Mansard, P. Chaudhuri, L. Bocquet, and A. Colin, “Microscale rheology of a soft glassy material close to yielding,” Phys. Rev. Lett. |

34. | R. Cerbino and A. Vailati, “Near-field scattering techniques: Novel instrumentation and results from time and spatially resolved investigations of soft matter systems,” Current Opinion in Colloid & Interface Science |

35. | F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: Differential dynamic microscopy and beyond,” Phys. Rev. E |

36. | S. Buzzaccaro, E. Secchi, and R. Piazza, “Ghost particle velocimetry: accurate 3D flow visualization using standard lab equipment,” Phys. Rev. Lett. |

37. | J.-P. Bouchaud and E. Pitard, “Anomalous dynamical light scattering in soft glassy gels,” Eur. Phys. J. E |

**OCIS Codes**

(100.0100) Image processing : Image processing

(120.6150) Instrumentation, measurement, and metrology : Speckle imaging

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: June 18, 2013

Revised Manuscript: August 22, 2013

Manuscript Accepted: September 3, 2013

Published: September 16, 2013

**Virtual Issues**

Vol. 8, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

L. Cipelletti, G. Brambilla, S. Maccarrone, and S. Caroff, "Simultaneous measurement of the microscopic dynamics and the mesoscopic displacement field in soft systems by speckle imaging," Opt. Express **21**, 22353-22366 (2013)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-19-22353

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### References

- J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications(Roberts and Company, Englewood, 2007).
- R. K. Erf, Speckle Metrology(Academic, 1978).
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