## Characterization of anisotropic nano-particles by using depolarized dynamic light scattering in the near field

Optics Express, Vol. 17, Issue 3, pp. 1222-1233 (2009)

http://dx.doi.org/10.1364/OE.17.001222

Acrobat PDF (168 KB)

### Abstract

Light scattering techniques are widely used in many fields of condensed and soft matter physics. Usually these methods are based on the study of the scattered light in the far field. Recently, a new family of near field detection schemes has been developed, mainly for the study of small angle light scattering. These techniques are based on the detection of the light intensity near to the sample, where light scattered at different directions overlaps but can be distinguished by Fourier transform analysis. Here we report for the first time data obtained with a dynamic near field scattering instrument, measuring both polarized and depolarized scattered light. Advantages of this procedure over the traditional far field detection include the immunity to stray light problems and the possibility to obtain a large number of statistical samples for many different wave vectors in a single instantaneous measurement. By using the proposed technique we have measured the translational and rotational diffusion coefficients of rod-like colloidal particles. The obtained data are in very good agreement with the data acquired with a traditional light scattering apparatus.

© 2009 Optical Society of America

## 1. Introduction

1. F. Scheffold and R. Cerbino, “New trends in light scattering,” Curr. Opin. Colloid Interface Sci. **12**(1), 50–57 (2007). [CrossRef]

2. F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. **68**, 2265–2274 (1997). [CrossRef]

3. L. Cipelletti and D. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. **70**, 3214–3221 (1999). [CrossRef]

4. K. Schatzel, “Suppression of multiple-scattering by photon cross-correlation techniques,” J. Mod. Opt. **38**(9), 1849–1865 (1991). [CrossRef]

5. P. N. Pusey, “Suppression of multiple scattering by photon cross-correlation techniques,” Curr. Opin. Colloid Interface Sci. **4**(3), 177–185 (1999). [CrossRef]

6. J. C. Thomas and S. Tjin, “Fiber optics dynamic light-scattering (FODLS) from moderately concentrated suspensions,” J. Colloid Interface Sci. **129**, 15–31 (1989). [CrossRef]

7. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. **60**(12), 1134–1137 (1988). [CrossRef] [PubMed]

3. L. Cipelletti and D. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. **70**, 3214–3221 (1999). [CrossRef]

9. D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. **81**, 4109–4111 (2002). [CrossRef]

10. D. Brogioli, “Near Field Speckles,” Ph.D. thesis, Università degli Studi di Cagliari (2002). Available at the url: www.geocities.com/dbrogioli/nfs_phd.

11. M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function *g*(*r*),” Phys. Rev. Lett. **85**, 1416–1419 (2000). [CrossRef] [PubMed]

10. D. Brogioli, “Near Field Speckles,” Ph.D. thesis, Università degli Studi di Cagliari (2002). Available at the url: www.geocities.com/dbrogioli/nfs_phd.

13. M. Wu, G. Ahlers, and D. Cannell, “Thermally induced fluctuations below the onset of Reyleight-Benard convection,” Phys. Rev. Lett. **75**, 1743–1746 (1995). [CrossRef] [PubMed]

14. S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids **14**, 1340–1363 (2002). [CrossRef]

15. D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. **63**, 220–225 (2003). [CrossRef]

23. G. H. Koenderink, H. Y. Zhang, D. G. A. L. Aarts, M. P. Lettinga, A. P. Philipse, and G. Nagele, “On the validity of Stokes-Einstein-Debye relations for rotational diffusion in colloidal suspensions,” Faraday Discuss. **123**, 335–354 (2003). [CrossRef] [PubMed]

## 2. Experimental set-up

17. D. Brogioli, F. Croccolo, V. Cassina, D. Salerno, and F. Mantegazza, “Nano-particle characterization by using Exposure Time Dependent Spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera.” Opt. Express **16**(25), 20,272–20,282 (2008). [CrossRef]

*e*by a negative lens. The laser intensity is attenuated by a neutral filter, selected by a filter wheel.

*x*150

*μ*m

^{2}. The diameter of the illuminated area of the sample is about 4mm; the imaged area sees a region of illuminated sample for every direction inside the numerical aperture of the objective; this ensures that near field detection of the light can be performed over the whole accepted scattering angles [15

15. D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. **63**, 220–225 (2003). [CrossRef]

21. D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. **92**, 241,101-1-3 (2008). [CrossRef]

## 3. Materials and sample characterization

24. T. Bellini, V. Degiorgio, F. Mantegazza, F. Ajmone-Marsan, and C. Scarnecchia, “Electrokinetic properties of colloids of variable charge. 1. Electrophoretic and electrooptic characterization,” J. Chem. Phys. **103**, 8228–8237 (1995). [CrossRef]

25. V. Degiorgio, R. Piazza, T. Bellini, and M. Visca, “Static and dynamic light scattering study of fluorinated polymer colloids with a crystalline internal structure,” Adv. Colloid Interface Sci. **48**, 61–91 (1994). [CrossRef]

26. R. Piazza, J. Stavans, T. Bellini, and V. Degiorgio, “Light scattering study of crystalline latex particles,” Opt. Commun. **73**(4), 263–267 (1989). [CrossRef]

24. T. Bellini, V. Degiorgio, F. Mantegazza, F. Ajmone-Marsan, and C. Scarnecchia, “Electrokinetic properties of colloids of variable charge. 1. Electrophoretic and electrooptic characterization,” J. Chem. Phys. **103**, 8228–8237 (1995). [CrossRef]

25. V. Degiorgio, R. Piazza, T. Bellini, and M. Visca, “Static and dynamic light scattering study of fluorinated polymer colloids with a crystalline internal structure,” Adv. Colloid Interface Sci. **48**, 61–91 (1994). [CrossRef]

27. T. Bellini, R. Piazza, C. Sozzi, and V. Degiorgio, “Electric Birefringence of a Dispersion of Electrically Charged Anisotropic Particles,” Europhys. Lett. **7**(6), 561–565 (1988). [CrossRef]

*n*= 0.04, and their average refractive index is

*n*= 1.37.

**Q**=

**K**-

_{S}**K**

_{I},

**K**

_{S}and

**K**

_{I}being the wave vectors of the scattered and incident beams, respectively. Characterization measurements have been performed at scattering angles of 15° and 90° using a 659nm diode laser. The measured intensity autocorrelation functions for both the VV and VH components are with a good approximation monoexponential. Indeed, the field autocorrelation functions

*C*and

^{VV}_{E}*C*expected for scattering of a monodisperse, anisotropic colloidal sample are monoexponential [28]:

^{VH}_{E}*D*is the translational diffusion coefficient, and Θ is the rotational diffusion coefficient of the scattering objects. It is worth pointing out that while the translational time constant changes with the wave vector, the rotational one is independent of it. The predicted intensity autocorrelation functions can be simply obtained by the Siegert relation [29] as follows:

_{T}*β*is a constant depending on the detector geometry. Fitting the above formulae to our experimentally measured autocorrelation functions allows the evaluation of the translational and rotational diffusion coefficients of PTFE:

*D*= 1.5 · 10

_{T}^{-12}m

^{2}/s; Θ = 24.5s

^{-1}. In turn, from these values, under the hypothesis that the particles are prolate ellipsoids, the particle size can be estimated. Accordingly the obtained major axis is 640nm; while the minor one is 150nm, thus providing a form factor of about 4,3:1. The PTFE sample was diluted to a 0.25% volume fraction, but in order to exclude artifacts due to multiple scattering, we tested also the 0.1% concentration, obtaining similar results.

*β*- FeOOH) rods were prepared following a modified synthesis originally developed by Sugimoro et al. [30

30. T. Sugimoto and K. Sakata, “Preparation of monodisperse pseudocubic *α* - Fe_{2}O_{3} particles from condensed ferric hydroxide gel,” J. Colloid Interface Sci. **152**(2), 587–590 (1992). [CrossRef]

_{3}) was aged at 100°C for 48 hours inside a sealed Pyrex bottle. The resulting precipitate was then quenched at room temperature, washed and resuspended in deionized water. This yielded a stable suspension of akaganeite needle-like particles with a polydispersity, determined by TEM analysis, of about 30% (more details can be found in [31]). The VV and VH intensity autocorrelation functions obtained with traditional SIFF apparatus on the DR1 sample are monoexponential for the VV component, but stretched exponential for the VH component:

*D*= 2.1·10

_{T}^{-12}m

^{2}/s; Θ = 27.8s

^{-1};

*α*= 0.523. Such a value of the stretching exponent a confirms that the sample has a large degree of polydispersity as observed in [31]. Given the non exponential decay of the correlation functions, it is difficult to have a precise evaluation of the size of the DR1 rods which have to be compared with average values obtained by TEM: major axis 150nm, minor axis 10nm.

## 4. Methods

9. D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. **81**, 4109–4111 (2002). [CrossRef]

9. D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. **81**, 4109–4111 (2002). [CrossRef]

*Q*. The obtained image is recorded with a pixelated sensor, digitalized and then Fourier transformed by standard software packages. The power spectrum

*S*(

*Q*) is then obtained as the mean square modulus of the Fourier transform of the image. The fundamental idea underlying SINF techniques is that each scattered beam, with transferred wave vector

**Q**, generates exactly one Fourier mode of the image, with two-dimensional wave vector

**q**. Thus a Fourier transform of the image readily gives the scattered fields, and the power spectrum gives the scattered intensities. The quantitative relation between the magnitudes of the scattering wave vector

**Q**and the image wave vector

**q**is:

*K*=

*K*=

_{I}*K*is the light wave vector in the medium. The approximation

_{S}*Q*≈

*q*holds in our case, since scattering angles and therefore image wave vectors

*q*are small. The relation between image power spectrum

*S*(

*q*) and scattered intensity

*I*(

*Q*) is:

*T*(

*Q*) is a transfer function heavily depending on the instrumental setup (see for example [14

14. S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids **14**, 1340–1363 (2002). [CrossRef]

**81**, 4109–4111 (2002). [CrossRef]

*B*(

*Q*) is the instrumental noise mainly due to the electronics. We abuse the notation by using

*S*(

*Q*) for

*S*[

*q*(

*Q*)], that is, we express the image power spectra

*S*(

*q*) as a function of the corresponding transferred wave vector

*Q*, which holds only if

*q*<<

*k*.

17. D. Brogioli, F. Croccolo, V. Cassina, D. Salerno, and F. Mantegazza, “Nano-particle characterization by using Exposure Time Dependent Spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera.” Opt. Express **16**(25), 20,272–20,282 (2008). [CrossRef]

## 5. PTFE experimental results

*t*= 48ms is nearly freezed; on the contrary, the image at Δ

*t*= 497ms is blurred by the averaging of the speckle motion. Sets of images taken at different exposure times Δ

*t*contain information on the dynamics of the scattering objects.

*S*(

*Q*) of the speckle images are also shown in Fig. 2, where the graphs represent the angular average of the spectra. The image blurring, due to large exposure time, appears as a depression, which is more evident at large wave vectors. Actually, all the information on the dynamics of the image Fourier modes, and hence of the scattered fields, is contained in the ETDS

*S*(

*Q*,Δ

*t*), that is, in the image power spectra taken at several different exposure times [17

17. D. Brogioli, F. Croccolo, V. Cassina, D. Salerno, and F. Mantegazza, “Nano-particle characterization by using Exposure Time Dependent Spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera.” Opt. Express **16**(25), 20,272–20,282 (2008). [CrossRef]

*t*increases, the power spectra

*S*

^{ϑ=0}(

*Q*,Δ

*t*) taken at ϑ = 0 decrease. Moreover, the decrease is stronger at large wave vectors. This can be qualitatively interpreted as a consequence of the translational diffusion of the colloidal particles: light scattered at the transferred wave vector

*Q*has a characteristic time τ

_{VV}, decreasing as

*Q*increases, see Eq. (3). For large

*Q*values, the corresponding Fourier modes oscillate faster, and hence the averaging cancels them at shorter exposure times. The graph on the right in Fig. 3 refers to data measured at nearly crossed polarizers, namely ϑ = 82.0°. As apparent from the graph, as the exposure time Δ

*t*increases, the ETDS decreases approximately at the same rate for all wave vector. This fact is explained if we recall that the power spectra

*S*

^{ϑ}=82.0° [

*Q*, Δ

*t*) mainly reflects the VH scattering dynamics. For small wave vectors

*Q*,

*τ*scales with the rotational diffusion of the anisotropic colloidal particles, thus being basically constant, see Eq. (4).

_{VH}*t*, at two fixed

*Q*vectors:

*Q*= 1.23·10

^{6}m

^{-1}and 4.42·10

^{6}m

^{-1}, for two different angles between the polarizer and the analyzer ϑ = 0 and ϑ = 82.0°. The data in Fig. 4 are obtained from the data in Fig. 3, and reflect the different blurring of the images at two values of ϑ and two values of

*Q*. It is apparent that the four curves show four different decay behaviors. At small

*Q*the

*S*(

*Q*,Δ

*t*) is larger than at large

*Q*. Moreover, the scattering at nearly crossed polarizers (ϑ = 82.0°) approximates the ϑ = 0 scattering at large exposure times. This is due to the fact that the rotational time constant is always smaller than the translational one.

## 6. PTFE discussion

*S*(

*Q*) of PTFE colloidal particles. We consider the image field as the superposition of three fields:

*E*

_{0}, the transmitted beam, and the scattered fields

*E*and

_{VV}*E*, parallel and perpendicular to

_{VH}*E*

_{0}:

*E*

_{VV}^{2}and

*E*

_{VH}^{2}can be neglected because we consider the transmitted beam much stronger than scattered ones (heterodyne condition). All the data processing is performed after normalization of the images’ intensities at a given average intensity. Changing ϑ modifies only the relative amplitude of the VH contribution to the image, while the VV term is left constant. For our samples, which scatter almost isotropically, the cross correlations between

*E*and

_{VV}*E*are negligible. Hence the power spectra is the sum of the VV and VH power spectra:

_{VH}*C*(

_{E}*Q*,

*t*) and the ETDS

*S*(

*Q*,Δ

*t*) is [17

**16**(25), 20,272–20,282 (2008). [CrossRef]

*C*(

_{E}*q*,

*t*) ∝ exp[−

*t*/

*t*], we have [16

16. J. Oh, J. O. de Zárate, J. Sengers, and G. Ahlers, “Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection,” Phys. Rev. E **69**, 21,106-1-13 (2004). [CrossRef]

18. 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. **76**(9), 093,110–11 (2005). [CrossRef]

**16**(25), 20,272–20,282 (2008). [CrossRef]

*τ*as fitting parameter (see filled symbols in Fig. 4 and the fitting curves).

_{VV}*τ*as fitting parameter. The obtained values are then used in the ETDS at ϑ = 82.0°, shown in Fig. 4 (see open symbols and their fitting curves). It is worth noting that, given its rotational diffusive behavior, the VH component has a constant characteristic decay time, for both wave vectors

_{VH}*Q*(see Eq. (4)). By contrast, the VV component shows a faster decay at larger wave vectors

*Q*, reflecting its translational diffusive behavior (see Eq. (3)).

*τ*and

_{VV}*τ*, obtained by the fitting procedure described above, are shown for several wave vectors

_{VH}*Q*in Fig. 5. At the end, by fitting the resulting data with Eq. (3) and Eq. (4), the translational and rotational diffusion coefficients of the sample are obtained. The outcomes of this fitting procedure for PTFE sample are

*D*= 1.4 · 10

_{T}^{12}m

^{2}/s; Θ = 23.8s

^{-1}, in very good agreement with the values obtained with the traditional dynamic SIFF apparatus.

## 7. DR1 experimental results and discussion

*S*(

*q*, Δ

*t*) at different exposure times Δ

*t*.

*S*(

^{VV}*q*,Δ

*t*) are simply fitted with Eq. (17). The characteristic times

*τ*obtained with the fitting procedure are shown in Fig. 6.

_{VV}*γ*(

*a*,

*x*) is the lower incomplete gamma function:

*τ*, obtained by fitting

_{VH}*S*(

^{VH}*Q*, Δ

*t*) with Eq. (19), are shown in Fig. 6.

*D*= 2.3·10

_{T}^{-12}m/s. From the VH term, we get Θ = 28.2s

^{-1}; α= 0.477. All the SINF fitting results are very close to the SIFF results.

## 8. Conclusions

## Acknowledgments

## Footnotes

1 | The scattered beams generate a speckle field. The intensity distribution of an homodyne image has an exponential decay; if the speckle field interfere with a much stronger transmitted beam, the image is heterodyne, and the intensity approaches a gaussian distribution, centered at the intensity of the transmitted beam. We use the intensity distribution of the images to check if we are working in heterodyne regime. |

## References and links

1. | F. Scheffold and R. Cerbino, “New trends in light scattering,” Curr. Opin. Colloid Interface Sci. |

2. | F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. |

3. | L. Cipelletti and D. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. |

4. | K. Schatzel, “Suppression of multiple-scattering by photon cross-correlation techniques,” J. Mod. Opt. |

5. | P. N. Pusey, “Suppression of multiple scattering by photon cross-correlation techniques,” Curr. Opin. Colloid Interface Sci. |

6. | J. C. Thomas and S. Tjin, “Fiber optics dynamic light-scattering (FODLS) from moderately concentrated suspensions,” J. Colloid Interface Sci. |

7. | D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. |

8. | S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Y. A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. express |

9. | D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. |

10. | D. Brogioli, “Near Field Speckles,” Ph.D. thesis, Università degli Studi di Cagliari (2002). Available at the url: www.geocities.com/dbrogioli/nfs_phd. |

11. | M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function |

12. | M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. |

13. | M. Wu, G. Ahlers, and D. Cannell, “Thermally induced fluctuations below the onset of Reyleight-Benard convection,” Phys. Rev. Lett. |

14. | S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids |

15. | D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. |

16. | J. Oh, J. O. de Zárate, J. Sengers, and G. Ahlers, “Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection,” Phys. Rev. E |

17. | D. Brogioli, F. Croccolo, V. Cassina, D. Salerno, and F. Mantegazza, “Nano-particle characterization by using Exposure Time Dependent Spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera.” Opt. Express |

18. | 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. |

19. | F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. Cannell, “Use of dynamic Schlieren to study fluctuations during free diffusion,” Appl. Opt. |

20. | F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. Cannell, “Non-diffusive decay of gradient driven fluctuations in a free-diffusion process,” Phys. Rev. E |

21. | D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, “Dynamic heterodyne near field scattering,” Appl. Phys. Lett. |

22. | R. Cerbino and V. Trappe, “Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope,” Phys. Rev. Lett. |

23. | G. H. Koenderink, H. Y. Zhang, D. G. A. L. Aarts, M. P. Lettinga, A. P. Philipse, and G. Nagele, “On the validity of Stokes-Einstein-Debye relations for rotational diffusion in colloidal suspensions,” Faraday Discuss. |

24. | T. Bellini, V. Degiorgio, F. Mantegazza, F. Ajmone-Marsan, and C. Scarnecchia, “Electrokinetic properties of colloids of variable charge. 1. Electrophoretic and electrooptic characterization,” J. Chem. Phys. |

25. | V. Degiorgio, R. Piazza, T. Bellini, and M. Visca, “Static and dynamic light scattering study of fluorinated polymer colloids with a crystalline internal structure,” Adv. Colloid Interface Sci. |

26. | R. Piazza, J. Stavans, T. Bellini, and V. Degiorgio, “Light scattering study of crystalline latex particles,” Opt. Commun. |

27. | T. Bellini, R. Piazza, C. Sozzi, and V. Degiorgio, “Electric Birefringence of a Dispersion of Electrically Charged Anisotropic Particles,” Europhys. Lett. |

28. | B. Berne and R. Pecora, |

29. | J. Goodman, |

30. | T. Sugimoto and K. Sakata, “Preparation of monodisperse pseudocubic |

31. | S. Sacanna, “Novel Routes to Model Colloids: ellipsoids, lattices and stable meso-emulsions,” Ph.D. thesis, Utrecht University (2007). ISBN 978-90-393-4598-6. |

**OCIS Codes**

(100.2960) Image processing : Image analysis

(290.5855) Scattering : Scattering, polarization

**ToC Category:**

Scattering

**History**

Original Manuscript: December 3, 2008

Revised Manuscript: December 27, 2008

Manuscript Accepted: January 3, 2009

Published: January 21, 2009

**Virtual Issues**

Vol. 4, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

D. Brogioli, D. Salerno, V. Cassina, S. Sacanna, A. P. Philipse, F. Croccolo, and F. Mantegazza, "Characterization of anisotropic nano-particles by using depolarized dynamic light scattering in the near field," Opt. Express **17**, 1222-1233 (2009)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-3-1222

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### References

- F. Scheffold and R. Cerbino, "New trends in light scattering," Curr. Opin. Colloid Interface Sci. 12, 50-57 (2007). [CrossRef]
- F. Ferri, "Use of a charge coupled device camera for low-angle elastic light scattering," Rev. Sci. Instrum. 68, 2265-2274 (1997). [CrossRef]
- L. Cipelletti and D. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214-3221 (1999). [CrossRef]
- K. Schatzel, "Suppression of multiple-scattering by photon cross-correlation techniques," J. Mod. Opt. 38, 1849-1865 (1991). [CrossRef]
- P. N. Pusey, "Suppression of multiple scattering by photon cross-correlation techniques," Curr. Opin. Colloid Interface Sci. 4, 177-185 (1999). [CrossRef]
- J. C. Thomas and S. Tjin, "Fiber optics dynamic light-scattering (FODLS) from moderately concentrated suspensions," J. Colloid Interface Sci. 129, 15-31 (1989). [CrossRef]
- D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, "Diffusing-wave spectroscopy," Phys. Rev. Lett. 60, 1134-1137 (1988). [CrossRef] [PubMed]
- S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Y. A. van Blaaderen, P. van Oostrum, and D. G. Grier, "Characterizing and tracking single colloidal particles with video holographic microscopy," Opt. express 15, 275-282 (2007).
- D. Brogioli, A. Vailati, and M. Giglio, "Heterodyne near-field scattering," Appl. Phys. Lett. 81, 4109-4111 (2002). [CrossRef]
- D. Brogioli, "Near Field Speckles," Ph.D. thesis, Universit`a degli Studi di Cagliari (2002), www.geocities.com/dbrogioli/nfs phd.
- M. Giglio, M. Carpineti, and A. Vailati, "Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r)," Phys. Rev. Lett. 85, 1416-1419 (2000). [CrossRef] [PubMed]
- M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, "Near-field intensity correlations of scattered light," Appl. Opt. 40, 4036-4040 (2001). [CrossRef]
- M. Wu, G. Ahlers, and D. Cannell, "Thermally induced fluctuations below the onset of Reyleight-Benard convection," Phys. Rev. Lett. 75, 1743-1746 (1995). [CrossRef] [PubMed]
- S. P. Trainoff and D. S. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002). [CrossRef]
- D. Brogioli, A. Vailati, and M. Giglio, "A schlieren method for ultra-low angle light scattering measurements," Europhys. Lett. 63, 220-225 (2003). [CrossRef]
- J. Oh, J. O. de Z’arate, J. Sengers, and G. Ahlers, "Dynamics of fluctuations in a fluid below the onset of Rayleigh-B’enard convection," Phys. Rev. E 69, 1-13 (2004). [CrossRef]
- D. Brogioli, F. Croccolo, V. Cassina, D. Salerno, and F. Mantegazza, "Nano-particle characterization by using Exposure Time Dependent Spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera." Opt. Express 16, 272-282 (2008). [CrossRef]
- 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. 76, 110-111 (2005). [CrossRef]
- F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. Cannell, "Use of dynamic Schlieren to study fluctuations during free diffusion," Appl. Opt. 45, 2166-2173 (2006). [CrossRef] [PubMed]
- F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. Cannell, "Non-diffusive decay of gradient driven fluctuations in a free-diffusion process," Phys. Rev. E 76, 41,112-1-9 (2007). [CrossRef]
- D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, "Dynamic heterodyne near field scattering," Appl. Phys. Lett. 92, 241,101-1-3 (2008). [CrossRef]
- R. Cerbino and V. Trappe, "Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope," Phys. Rev. Lett. 100, 188,102-1-4 (2008). [CrossRef] [PubMed]
- G. H. Koenderink, H. Y. Zhang, D. G. A. L. Aarts, M. P. Lettinga, A. P. Philipse, and G. Nagele, "On the validity of Stokes-Einstein-Debye relations for rotational diffusion in colloidal suspensions," Faraday Discuss. 123, 335-354 (2003). [CrossRef] [PubMed]
- T. Bellini, V. Degiorgio, F. Mantegazza, F. Ajmone-Marsan, and C. Scarnecchia, "Electrokinetic properties of colloids of variable charge. 1. Electrophoretic and electrooptic characterization," J. Chem. Phys. 103, 8228-8237 (1995). [CrossRef]
- V. Degiorgio, R. Piazza, T. Bellini, and M. Visca, "Static and dynamic light scattering study of fluorinated polymer colloids with a crystalline internal structure," Adv. Colloid Interface Sci. 48, 61-91 (1994). [CrossRef]
- R. Piazza, J. Stavans, T. Bellini, and V. Degiorgio, "Light scattering study of crystalline latex particles," Opt. Commun. 73(4), 263-267 (1989). [CrossRef]
- T. Bellini, R. Piazza, C. Sozzi, and V. Degiorgio, "Electric Birefringence of a Dispersion of Electrically Charged Anisotropic Particles," Europhys. Lett. 7(6), 561-565 (1988). [CrossRef]
- B. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, New York, 2000).
- J. Goodman, Introduction to Fourier Optics (Roberts & Company, Englewood, 2005).
- T. Sugimoto and K. Sakata, "Preparation of monodisperse pseudocubic 〈-Fe2O3 particles from condensed ferric hydroxide gel," J. Colloid Interface Sci. 152587-590 (1992). [CrossRef]
- S. Sacanna, "Novel Routes to Model Colloids: ellipsoids, lattices and stable meso-emulsions," Ph.D. thesis, Utrecht University (2007). ISBN 978-90-393-4598-6.

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