## Nanoparticle characterization by using tilted laser microscopy: back scattering measurement in near field

Optics Express, Vol. 17, Issue 18, pp. 15431-15448 (2009)

http://dx.doi.org/10.1364/OE.17.015431

Acrobat PDF (449 KB)

### Abstract

By using scattering in near field techniques, a microscope can be easily turned into a device measuring static and dynamic light scattering, very useful for the characterization of nanoparticle dispersions. Up to now, microscopy based techniques have been limited to forward scattering, up to a maximum of 30°. In this paper we present a novel optical scheme that overcomes this limitation, extending the detection range to angles larger than 90° (back-scattering). Our optical scheme is based on a microscope, a wide numerical aperture objective, and a laser illumination, with the collimated beam positioned at a large angle with respect to the optical axis of the objective (Tilted Laser Microscopy, TLM). We present here an extension of the theory of near field scattering, which usually applies only to paraxial scattering, to our strongly out-of-axis situation. We tested our instrument and our calculations with calibrated spherical nanoparticles of several different diameters, performing static and dynamic scattering measurements up to 110°. The measured static spectra and decay times are compatible with the Mie theory and the diffusion coefficients provided by the Stokes-Einstein equation. The ability of performing backscattering measurements with this modified microscope opens the way to new applications of scattering in near field techniques to the measurement of systems with strongly angle dependent scattering.

© 2009 Optical Society of America

## 1. Introduction

^{1}. Conversely light scattering devices measure statistical properties, detecting the light scattered in the far field [6, 7, 8, 9, 10]. Accordingly, traditional light scattering methods can be conveniently renamed as Scattering In the Far Field (SIFF) techniques.

12. 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).
[PubMed]

13. 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).
[PubMed]

16. D. Brogioli, “Near field speckles,” Ph.D. thesis, Università degli Studi di Cagliari (2002). Available at the http://arxiv.org/abs/0907.3376

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

22. M. Lesaffre, M. Atlan, and M. Gross, “Effect of the photon’s Brownian Doppler shift on the weak-localization coherent-backscattering cone,” Phys. Rev. Lett.97 (2006). [PubMed]

25. R. Dzakpasu and D. Axelrod, “Dynamic light scattering microscopy. A novel optical technique to image submicroscopic motions. II: experimental applications,” Biophys. J. **87**, 1288–1297 (2004).
[PubMed]

13. 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).
[PubMed]

32. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of non equilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. **1077**, 365–379 (2006).
[PubMed]

33. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic Schlieren to study fluctuations during free diffusion,” Appl. Opt. **45**, 2166–2173 (2006).
[PubMed]

## 2. Scattering In the Near Field tutorial

13. 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).
[PubMed]

*I*(ϑ,

*φ*) is measured at a given scattering angle ϑ and azimuthal angle j. Then, for example, the scattering intensity from spherical colloids

*I*(ϑ,φ) can be compared with the outcome of the exact Mie algorithm for determining the particle size.

*in silico*by means of a 2D Fast Fourier Transform software. The obtained IPS is very similar to the far field image obtained in the SIFF experiment: essentially the same information is obtained by means of a software elaboration on the SINF image, instead of the optical Fourier transform given by the SIFF image.

## 3. Tilted laser methods

*q*⃗ with the transferred wave vector

*Q*⃗, which have to be taken into account when performing a TLM measurement. Fig. 3, upper panels, shows a schematic drawing of the geometrical arrangement of the wave vectors, for the two cases of collinear (left panels) and out-of-axis (right panels) illumination with tilt angle α. The picture helps understand the physical mechanism by which TLM increases the range of collected scattering angles.

*S*(ϑ,φ), that is the near field Image Power Spectrum, obtained, through a FFT algorithm, as the mean square of the Fourier transform of the images [15].

*S*(

*q*⃗) represents the amplitude of the Fourier mode with wave vector

*q*⃗ of the near field images; or equivalently, it represents the light intensity

*I*(ϑ,φ) at a given scattering angle ϑ and azimuthal angle φ.

*q*⃗ and (ϑ,φ), which is essential to relate the obtained IPS

*S*(

*q*⃗) to the scattered intensity

*I*(ϑ,φ):

*T*(ϑ,φ) is the tranfer function of the optical system.

*K*⃗

*, the impinging beam wave vector*

_{s}*K*⃗

*, the transferred wave vector*

_{i}*Q*⃗=

*K*⃗

*-*

_{s}*K*⃗

*and the 2D image wave vector*

_{i}*q*⃗. The image wave vector

*q*⃗ is actually the 2D projection of the transferred wave vector

*Q*⃗ on the plane perpendicular to the optical axis, i.e. the sensor plane. Therefore the

*x*and

*y*components of the two vectors

*Q*⃗ and

*q*⃗ are the same.

*Q*⃗ is known, then the wave vector

*q*⃗ on the image can be directly obtained:

*q*⃗ can also be expressed in terms of the scattering angle ϑ, azimuthal angle φ and the tilt angle α as:

*q*⃗ is given, that is the actual experimental situation, then a third equation is necessary to get the third z component of the transferred wave vector

*Q*⃗. This can be obtained from the condition |

*Q*⃗+

*K*⃗

*|=|*

_{i}*K*⃗

*|=*

_{s}*K*, plus the condition

*K*⃗

*·*

_{s}*z*̂>0 which allows choosing one of the two solutions of the quadratic equation. The relationship between the image and the transferred vector is therefore:

*q*⃗ for values of scattering angle

*ϑ*from 20° up to 120° and azimuthal angle

*φ*in steps of 30° are shown in Fig. 3, lower panels, for collinear and tilted illumination. They represent the mapping of

*ϑ,φ*on IPS images. It’s worth noting that each scattered beam at

*ϑ,φ*corresponds to

*two*points,

*q*⃗ and -

*q*⃗, in the IPS. The mapping -

*q*⃗(

*ϑ,φ*) is also shown in Fig. 3, represented by thin lines. It is evident that the out-of-axis illumination allows mapping of angles larger than 90° in the IPS.

*ϑ*are accessible only for azimuthal angles

*φ*nearly aligned with the illumination tilt plane, that is

*φ*≈0°. In the following, the mapping

*q*⃗(

*ϑ,φ*) will be used mainly to get the value of

*I*(

*ϑ*), that is, the average value of

*I*(

*ϑ*) over a small range of

*φ*around 0. If the polarization of the main beam is

*φ*=0°, the measured scattering component will be called “parallel”. In the opposite case, that is

*φ*=90°, we measure the “perpendicular” component.

## 4. Data processing

*S*(

*q*) to the scattering intensity

*I*(

*Q*). In order to evaluate the sample dynamics, further analysis can be implemented by using the so called Exposure-Time-Dependent Spectrum (ETDS) processing, which we recently reported in [11]. Essentially, the IPS is evaluated by taking images at various exposure times, thus actually obtaining the Exposure-Time-Dependent Spectrum

*S*(

*q*,Δ

*t*) [35]. As Δ

*t*is increased, the fluctuations average out, leading to a decrease in the ETDS signal. For example, for Brownian colloidal particles, the ETDS decreases strongly at large scattering angles

*ϑ*. For very long Δ

*t*, all the fluctuations are washed out, and the resulting images contain only the optical background plus the fluctuating instrumental noise

*B*(

*q*). In this way, the ETDS gives access to a quantitative measurement of the system dynamics. Indeed, it is possible to analytically derive a theoretical expression for the

*S*(

*q*,Δ

*t*), and thus to get the diffusion coefficient of the particles by using a fitting procedure [35, 11]. When a negligible Δ

*t*is considered, the “instantaneous” IPS

*S*(

*q*) is obtained, as described by Eq. 1. When Δ

*t*is not negligible with respect to the sample dynamics, the ETDS is accordingly modified [11]. For colloidal samples, the time correlation function is a decreasing exponential with decay time

*τ*=1=(

*DQ*

^{2}), where

*D*is the translational diffusion coefficient of the nanoparticles. In this case the ETDS is expressed as [11, 35]:

*S*[

*q*(

*ϑ,φ*),Δ

*t*] for each scattering angle as a function of the exposure time, and finally in fitting it with Eq. 5, keeping τ as free parameter. By using this procedure, a direct measurement of the time constants for all the measured wave vectors is simultaneously achieved. Moreover, the static scattered intensity

*I*(

*ϑ,φ*), multiplied by the transfer function

*T*(

*ϑ,φ*) is obtained, in analogy with the procedure developed for the calculation of the structure function in [32

32. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of non equilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. **1077**, 365–379 (2006).
[PubMed]

33. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic Schlieren to study fluctuations during free diffusion,” Appl. Opt. **45**, 2166–2173 (2006).
[PubMed]

*T*(

*ϑ,φ*) can significantly depend on the wave vector, such as in the shadowgraph [39]. On the contrary, in the near field scattering regime, the transfer function is slowly varying within the accessible scattering range [17]. The transfer function was actually evaluated by performing calibration measurements on known samples, so that a direct access to the static scattered intensity of our sample can be obtained.

## 5. Experimental set up

## 6. Materials

## 7. Results and discussion

*α*=0), the IPS shows a bright, nearly uniform circle at the center, corresponding to the nearly isotropically scattered light, clipped by the angular acceptance of the objective. The beams scattered at small angle ϑ are represented by the points close to the center of the IPS image. In general, the optical collecting system determines the scattering angle range which can be measured. In SIFF, this angular limitation produces a vignetting visible in the far field image. By comparison, as shown in Fig. 5, in SINF set up the acceptance angle of the microscope generates a vignetting in the near field IPS (Fourier space). On the other hand, the intensity distribution in the near field image (real space) shows a speckle pattern, superimposed on an average uniform intensity distribution with no intensity fading in the periphery of the image.

*α*.

*K*⃗

*=(*

_{s}*K*) satisfies the condition:

_{x},K_{y},K_{z}*K*⃗

*=*

_{i}*K*(sinα,0,cos α), the transferred wave vector

*Q*⃗=

*K*⃗

*-*

_{s}*K*⃗

*satisfies:*

_{i}*q*⃗=(

*K*sin

*α*,0) with radius

*K*sin Θ.

*K*⃗

*=(*

_{s}*K*) and

_{x},K_{y},K_{z}*K*⃗′

*=(*

_{s}*K*′

*,*

_{x}*K*′

*,*

_{y}*K*′

*z*), they both satisfy Eq. (7). The interference pattern is again a Fourier mode with wave vector

*q*⃗=(

*K*-

_{x}*K*′

*,*

_{x}*K*-

_{y}*K*′

_{y}, 0). In this case, the condition on

*q*⃗ becomes:

*q*⃗=(0,0) and with radius 2

*K*sin Θ, twice than in the heterodyne case.

*α*=0. In Fig. 6, right column, the laser enters the sample tilted of about α=45°. In this second case, the CCD sensor is also rotated by 45° around the axis, perpendicularly to the sensor plane, so that it is possible to achieve the largest scattering vectors up to 110° along the IPS diagonal. In Fig. 6, lower panels, we show the IPS as obtained by averaging over the colored lines which correspond to to data with the same

*ϑ*or with the same |

*q*⃗|. Actually the data are also averaged on the region of small φ in order to avoid mixing of the perpendicular and parallel scattering contributions and to achieve larger scattering angle

*ϑ*.

*N*=100 images have been taken at different exposure times Δ

*t*(0.55ms, 1.8ms, 5.5ms, 18ms, 55ms, 180ms, and 550ms), and we evaluated the static and dynamic power spectra of the sample.

*S*(

*ϑ*) with two different polarizations of the impinging laser beam, i.e. parallel and perpendicular to the azimuthal angle

*φ*=0°. Fig. 8 shows the results obtained for the colloidal sample B, for both parallel (right panels) and perpendicular (left panels) components of the scattered light. The IPS are shown in the upper panels, while the corresponding

*I*(

*ϑ*) are shown in the lower panels. For the parallel case shown in the upper right panel, the dark bands in the corners represent the minimum of scattering intensity at 90° along the polarization direction, a consequence of the dipolar radiation of the scatterers, showing the usual factor cos2(ϑ). The same feature can be observed in the corresponding

*I*(

*ϑ*) spectrum (lower right panel).

*I*(

*ϑ*), for two colloids B and C. Also in this case the data are compatible with the Mie theory, and one can easily detect the 90° drop in the scattered intensity of the parallel component (blue dots in Fig. 9).

*t*, for

*ϑ*=90°, for the different samples A, B, C, D, E. Fitting lines are theoretical ETDS functions (see Eq. 6), with decay time

*τ*=1/

*DQ*

^{2}, and

*D*calculated with Stokes Einstein formula. The data have been normalized so that the asymptotic value at short time is equal to 1. We have used in the ETDS function a value of the nanoparticle diameter as measured with dynamic SIFF and reported in Tab. 1. The expected dependence

*f*(Δ

*t*/τ) is recognized. Also this experiment confirms that TLM allows detection of the scattered light at 90°.

## 8. Conclusions

12. 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).
[PubMed]

## Acknowledgements

## Footnotes

1 | The term “near field” refers to the Fresnel region, as opposed to the far field Fraunhofer region, as classically reported in classical optics textbook [1]. It is also worth underlining that, in the present paper, the name “near field” in conjunction with “microscopy” has no relation with evanescent-wave based techniques like Scanning Near-Field Optical Microscopy (SNOM) [2], Total Internal Reflection Fluorescent Microscopy (TIRFM) [3 3. D. Axelrod, “Total internal reflection fluorescence microscopy in cell biology,” Traffic |

## References and links

1. | E. Hecht, |

2. | D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution lambda/20,” Appl. Phys. Lett. |

3. | D. Axelrod, “Total internal reflection fluorescence microscopy in cell biology,” Traffic |

4. | M. A. C. Potenza, D. Brogioli, and M. Giglio, “Total internal reflection scattering,” Appl. Phys. Lett. |

5. | D. C. Prieve, “Measurement of colloidal forces with TIRM,” Adv. Colloid Interface Sci. |

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

7. | H. C. van de Hulst, |

8. | B. Chu, |

9. | P. N. Pusey and R. J. A. Tough, |

10. | V. Degiorgio and M. Corti, |

11. | 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 |

12. | 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 |

13. | 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 |

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

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

16. | D. Brogioli, “Near field speckles,” Ph.D. thesis, Università degli Studi di Cagliari (2002). Available at the http://arxiv.org/abs/0907.3376 |

17. | F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: A technique for complex fluids,” Phys. Rev. E |

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

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

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

21. | L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, “Gabor’s hologram in a modern perspective,” Am. J. Phys. |

22. | M. Lesaffre, M. Atlan, and M. Gross, “Effect of the photon’s Brownian Doppler shift on the weak-localization coherent-backscattering cone,” Phys. Rev. Lett.97 (2006). [PubMed] |

23. | H. F. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett. |

24. | R. Cerbino and V. Trappe, “Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope,” Phys. Rev. Lett. |

25. | R. Dzakpasu and D. Axelrod, “Dynamic light scattering microscopy. A novel optical technique to image submicroscopic motions. II: experimental applications,” Biophys. J. |

26. | P. D. Kaplan, V. Trappe, and D. A. Weitz, “Light-scattering microscope,” Appl. Opt. |

27. | A. K. Popp, P. D. Kaplan, and D. A. Weitz, “Microscope-based static light-scattering instrument,” Opt. Lett. |

28. | M. S. Amin, Y. Park, N. Lue, R. R. Dasari, K. Badizadegan, M. S. Feld, and G. Popescu, “Microrheology of red blood cell membranes using dynamic scattering microscopy,” Opt. Express |

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

30. | F. Croccolo, “Non diffusive decay of non equilibrium fluctuations in free diffusion processes.” in |

31. | F. Croccolo, D. Brogioli, A. Vailati, D. S. Cannell, and M. Giglio, “Dynamics of gradient driven fluctuations in a free diffusion process,” in |

32. | F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of non equilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. |

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

34. | R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. |

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

36. | F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in |

37. | J. W. Goodman, |

38. | D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. |

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

40. | A practical interactive program to calculate Mie scattering can be found at the following address: http://omlc.ogi.edu/calc/mie calc.html. |

**OCIS Codes**

(100.2960) Image processing : Image analysis

(120.5820) Instrumentation, measurement, and metrology : Scattering measurements

(290.5820) Scattering : Scattering measurements

(290.5850) Scattering : Scattering, particles

**ToC Category:**

Scattering

**History**

Original Manuscript: May 28, 2009

Revised Manuscript: July 1, 2009

Manuscript Accepted: August 3, 2009

Published: August 17, 2009

**Citation**

D. Brogioli, D. Salerno, V. Cassina, and F. Mantegazza, "Nanoparticle characterization by using tilted laser microscopy: back scattering measurement in near field," Opt. Express **17**, 15431-15448 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-18-15431

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### References

- E. Hecht, Optics (Addison Wesley, San Francisco, 2002).
- D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: Image recording with resolution lambda/20," Appl. Phys. Lett. 44, 651-3 (1984).
- D. Axelrod, "Total internal reflection fluorescence microscopy in cell biology," Traffic 2, 764-774 (2001). [PubMed]
- M. A. C. Potenza, D. Brogioli, and M. Giglio, "Total internal reflection scattering," Appl. Phys. Lett. 85, 2730-2732 (2004).
- D. C. Prieve, "Measurement of colloidal forces with TIRM," Adv. Colloid Interface Sci. 82, 93-125 (1999).
- B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Dover, New York, 2000).
- H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
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- V. Degiorgio and M. Corti, Light scattering in liquids and macromolecular solutions (Plenum, New York, 1980).
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- 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). [PubMed]
- 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). [PubMed]
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- D. Brogioli, A. Vailati, and M. Giglio, "Heterodyne near-field scattering," Appl. Phys. Lett. 81, 4109-4111 (2002).
- D. Brogioli, "Near field speckles," Ph.D. thesis, Universit`a degli Studi di Cagliari (2002). Available at the http://arxiv.org/abs/0907.3376
- F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, "Heterodyne near-field scattering: A technique for complex fluids," Phys. Rev. E 70, 41405 (2004).
- M. Wu, G. Ahlers, and D. S. Cannell, "Thermally induced fluctuations below the onset of Reyleight-Benard convection," Phys. Rev. Lett. 75, 1743-1746 (1995). [PubMed]
- S. P. Trainoff and D. S. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002).
- D. Brogioli, A. Vailati, and M. Giglio, "A schlieren method for ultra-low angle light scattering measurements," Europhys. Lett. 63, 220-225 (2003).
- L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, "Gabor’s hologram in a modern perspective," Am. J. Phys. 72, 964-967 (2004).
- M. Lesaffre, M. Atlan, and M. Gross, "Effect of the photon’s Brownian Doppler shift on the weak-localization coherent-backscattering cone," Phys. Rev. Lett.97 (2006). [PubMed]
- H. F. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, "Fourier transform light scattering of inhomogeneous and dynamic structures," Phys. Rev. Lett. 101, 238102 (2008).
- R. Cerbino and V. Trappe, "Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope," Phys. Rev. Lett. 100, 188102 (2008).
- R. Dzakpasu and D. Axelrod, "Dynamic light scattering microscopy. A novel optical technique to image submicroscopic motions. II: experimental applications," Biophys. J. 87, 1288-1297 (2004). [PubMed]
- P. D. Kaplan, V. Trappe, and D. A. Weitz, "Light-scattering microscope," Appl. Opt. 38, 4151-4157 (1999).
- A. K. Popp, P. D. Kaplan, and D. A. Weitz, "Microscope-based static light-scattering instrument," Opt. Lett. 26, 890-892 (2001).
- M. S. Amin, Y. Park, N. Lue, R. R. Dasari, K. Badizadegan, M. S. Feld, and G. Popescu, "Microrheology of red blood cell membranes using dynamic scattering microscopy," Opt. Express 15, 17,001-17,009 (2007).
- D. Magatti, M. D. Alaimo, M. A. C. Potenza, and F. Ferri, "Dynamic heterodyne near field scattering," Appl. Phys. Lett. 92, 241101 (2008).
- F. Croccolo, "Non diffusive decay of non equilibrium fluctuations in free diffusion processes." in Proceedings of INFMeeting, pp. I-166 (INFM, Genova, 2003).
- F. Croccolo, D. Brogioli, A. Vailati, D. S. Cannell, and M. Giglio, "Dynamics of gradient driven fluctuations in a free diffusion process," in 2004 Photon Correlation and Scattering Conference, p. 52, NASA (OSA, Amsterdam, 2004).
- F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, "Effect of gravity on the dynamics of non equilibrium fluctuations in a free diffusion experiment," Ann. N.Y. Acad. Sci. 1077, 365-379 (2006). [PubMed]
- F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, "Use of dynamic Schlieren to study fluctuations during free diffusion," Appl. Opt. 45, 2166-2173 (2006). [PubMed]
- R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, "X-ray-scattering information obtained from near-field speckle," Nat. Phys. 4, 238-243 (2008).
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- A practical interactive program to calculate Mie scattering can be found at the following address: http://omlc.ogi.edu/calc/mie calc.html.

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