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

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    [PubMed]
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  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]
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    [PubMed]
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  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 70, 41,405-1-9 (2004).
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  20. D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. 63, 220–225 (2003).
  21. L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, “Gabor’s hologram in a modern perspective,” Am. J. Phys. 72, 964–967 (2004).
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  24. 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).
  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]
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  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 15, 17,001–17,009 (2007).
  29. 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).
  30. F. Croccolo, “Non diffusive decay of non equilibrium fluctuations in free diffusion processes.” in Proceedings of INFMeeting, pp. I-166 (INFM, Genova, 2003).
  31. 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).
  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]
  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. 4, 238–243 (2008).
  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 69, 21,106-1-13 (2004).
  36. F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C. Riccardi and H. E. Roman, eds. (Research Signpost, Trivandrum, 2008).
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  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 76, 41,112-1-9 (2007).
  40. A practical interactive program to calculate Mie scattering can be found at the following address: http://omlc.ogi.edu/calc/mie calc.html.

2009 (1)

2008 (5)

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, 20,272–20,282 (2008).

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, 238,102-1-4 (2008).

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).

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).

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).

2007 (2)

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).

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 76, 41,112-1-9 (2007).

2006 (3)

D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88, 191,101-1-3 (2006).

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]

2004 (5)

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 69, 21,106-1-13 (2004).

L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, “Gabor’s hologram in a modern perspective,” Am. J. Phys. 72, 964–967 (2004).

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]

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, 41,405-1-9 (2004).

M. A. C. Potenza, D. Brogioli, and M. Giglio, “Total internal reflection scattering,” Appl. Phys. Lett. 85, 2730–2732 (2004).

2003 (1)

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

2002 (2)

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

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

2001 (3)

2000 (1)

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]

1999 (2)

D. C. Prieve, “Measurement of colloidal forces with TIRM,” Adv. Colloid Interface Sci. 82, 93–125 (1999).

P. D. Kaplan, V. Trappe, and D. A. Weitz, “Light-scattering microscope,” Appl. Opt. 38, 4151–4157 (1999).

1995 (1)

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]

1984 (1)

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution lambda/20,” Appl. Phys. Lett. 44, 651–3 (1984).

Ahlers, G.

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 69, 21,106-1-13 (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]

Alaimo, D.

D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88, 191,101-1-3 (2006).

Alaimo, M. D.

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).

Amin, M. S.

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).

Atlan, M.

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]

Axelrod, D.

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]

D. Axelrod, “Total internal reflection fluorescence microscopy in cell biology,” Traffic 2, 764–774 (2001).
[PubMed]

Badizadegan, K.

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).

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Dover, New York, 2000).

Boppart, S. A.

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, 238,102-1-4 (2008).

Bösecke, P.

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).

Brogioli, D.

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]

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, 20,272–20,282 (2008).

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 76, 41,112-1-9 (2007).

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]

M. A. C. Potenza, D. Brogioli, and M. Giglio, “Total internal reflection scattering,” Appl. Phys. Lett. 85, 2730–2732 (2004).

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

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

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40, 4036–4040 (2001).

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

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).

Cannell, D. S.

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 76, 41,112-1-9 (2007).

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]

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

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]

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).

Carpineti, M.

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40, 4036–4040 (2001).

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]

Cassina, V.

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]

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, 20,272–20,282 (2008).

Cerbino, R.

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).

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).

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C. Riccardi and H. E. Roman, eds. (Research Signpost, Trivandrum, 2008).

Chu, B.

B. Chu, Laser Light Scattering: Basic Principles and Practice (Dover, New York, 2007).

Corti, M.

V. Degiorgio and M. Corti, Light scattering in liquids and macromolecular solutions (Plenum, New York, 1980).

Croccolo, F.

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]

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, 20,272–20,282 (2008).

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 76, 41,112-1-9 (2007).

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]

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C. Riccardi and H. E. Roman, eds. (Research Signpost, Trivandrum, 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).

Dasari, R. R.

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).

de Zárate, J. M. O.

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 69, 21,106-1-13 (2004).

Degiorgio, V.

V. Degiorgio and M. Corti, Light scattering in liquids and macromolecular solutions (Plenum, New York, 1980).

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution lambda/20,” Appl. Phys. Lett. 44, 651–3 (1984).

Ding, H. F.

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, 238,102-1-4 (2008).

Dzakpasu, R.

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]

Feld, M. S.

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).

Ferri, F.

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).

D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88, 191,101-1-3 (2006).

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, 41,405-1-9 (2004).

Giglio, M.

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).

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 76, 41,112-1-9 (2007).

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]

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, 41,405-1-9 (2004).

M. A. C. Potenza, D. Brogioli, and M. Giglio, “Total internal reflection scattering,” Appl. Phys. Lett. 85, 2730–2732 (2004).

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

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

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40, 4036–4040 (2001).

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]

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C. Riccardi and H. E. Roman, eds. (Research Signpost, Trivandrum, 2008).

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).

Goodman, J. W.

J. W. Goodman, Statistical Optics, Wiley series in pure and applied optics (J. Wiley, New York, 1985).

Gross, M.

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]

Hecht, E.

E. Hecht, Optics (Addison Wesley, San Francisco, 2002).

Kaplan, P. D.

Lanz, M.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution lambda/20,” Appl. Phys. Lett. 44, 651–3 (1984).

Lesaffre, M.

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]

Lue, N.

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).

Magatti, D.

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).

D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88, 191,101-1-3 (2006).

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, 41,405-1-9 (2004).

Mantegazza, F.

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]

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, 20,272–20,282 (2008).

Nguyen, F.

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, 238,102-1-4 (2008).

Oh, J.

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 69, 21,106-1-13 (2004).

Park, Y.

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).

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Dover, New York, 2000).

Pellistri, F.

L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, “Gabor’s hologram in a modern perspective,” Am. J. Phys. 72, 964–967 (2004).

Pescini, D.

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, 41,405-1-9 (2004).

Peverini, L.

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).

Philipse, A. P.

Piano, E.

L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, “Gabor’s hologram in a modern perspective,” Am. J. Phys. 72, 964–967 (2004).

Pohl, D. W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution lambda/20,” Appl. Phys. Lett. 44, 651–3 (1984).

Pontiggia, C.

L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, “Gabor’s hologram in a modern perspective,” Am. J. Phys. 72, 964–967 (2004).

Popescu, G.

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, 238,102-1-4 (2008).

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).

Popp, A. K.

Potenza, M. A. C.

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).

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).

D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88, 191,101-1-3 (2006).

M. A. C. Potenza, D. Brogioli, and M. Giglio, “Total internal reflection scattering,” Appl. Phys. Lett. 85, 2730–2732 (2004).

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, 41,405-1-9 (2004).

Prieve, D. C.

D. C. Prieve, “Measurement of colloidal forces with TIRM,” Adv. Colloid Interface Sci. 82, 93–125 (1999).

Pusey, P. N.

P. N. Pusey and R. J. A. Tough, Dynamic Light Scattering, pp. 85–171 (Plenum, New York, 1985).

Repetto, L.

L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, “Gabor’s hologram in a modern perspective,” Am. J. Phys. 72, 964–967 (2004).

Robert, A.

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).

Sacanna, S.

Salerno, D.

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]

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, 20,272–20,282 (2008).

Sengers, J. V.

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 69, 21,106-1-13 (2004).

Tough, R. J. A.

P. N. Pusey and R. J. A. Tough, Dynamic Light Scattering, pp. 85–171 (Plenum, New York, 1985).

Trainoff, S. P.

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

Trappe, V.

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).

P. D. Kaplan, V. Trappe, and D. A. Weitz, “Light-scattering microscope,” Appl. Opt. 38, 4151–4157 (1999).

Vailati, A.

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 76, 41,112-1-9 (2007).

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]

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

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

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40, 4036–4040 (2001).

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]

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C. Riccardi and H. E. Roman, eds. (Research Signpost, Trivandrum, 2008).

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).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Wang, Z.

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, 238,102-1-4 (2008).

Weitz, D. A.

Wu, M.

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]

Adv. Colloid Interface Sci. (1)

D. C. Prieve, “Measurement of colloidal forces with TIRM,” Adv. Colloid Interface Sci. 82, 93–125 (1999).

Am. J. Phys. (1)

L. Repetto, F. Pellistri, E. Piano, and C. Pontiggia, “Gabor’s hologram in a modern perspective,” Am. J. Phys. 72, 964–967 (2004).

Ann. N.Y. Acad. Sci. (1)

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]

Appl. Opt. (3)

Appl. Phys. Lett. (5)

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

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution lambda/20,” Appl. Phys. Lett. 44, 651–3 (1984).

M. A. C. Potenza, D. Brogioli, and M. Giglio, “Total internal reflection scattering,” Appl. Phys. Lett. 85, 2730–2732 (2004).

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).

D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88, 191,101-1-3 (2006).

Biophys. J. (1)

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]

Europhys. Lett. (1)

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

Nat. Phys. (1)

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).

Opt. Express (3)

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. 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, 20,272–20,282 (2008).

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]

Opt. Lett. (1)

Phys. Fluids (1)

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

Phys. Rev. E (3)

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, 41,405-1-9 (2004).

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 69, 21,106-1-13 (2004).

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 76, 41,112-1-9 (2007).

Phys. Rev. Lett. (4)

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, 238,102-1-4 (2008).

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).

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]

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]

Traffic (1)

D. Axelrod, “Total internal reflection fluorescence microscopy in cell biology,” Traffic 2, 764–774 (2001).
[PubMed]

Other (13)

E. Hecht, Optics (Addison Wesley, San Francisco, 2002).

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).

B. Chu, Laser Light Scattering: Basic Principles and Practice (Dover, New York, 2007).

P. N. Pusey and R. J. A. Tough, Dynamic Light Scattering, pp. 85–171 (Plenum, New York, 1985).

V. Degiorgio and M. Corti, Light scattering in liquids and macromolecular solutions (Plenum, New York, 1980).

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

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]

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

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, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C. Riccardi and H. E. Roman, eds. (Research Signpost, Trivandrum, 2008).

J. W. Goodman, Statistical Optics, Wiley series in pure and applied optics (J. Wiley, New York, 1985).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic description of scattering detection techniques. The red, yellow, and magenta beams represent the impinging, scattered and transmitted beams respectively. Panel a: traditional Scattering In Far Field (SIFF) technique. The scheme refers to a typical small angle light scattering; other SIFF techniques are based on the same principle. The beam scattered at a given angle is focused by the lens into one point (yellow dot) on the observation plane, where the far field image is collected. Panel b: Scattering In Near Field (SINF) technique. The reported scheme refers to shadowgraph technique, and is quite similar to HNFS configuration; other SINF techniques are based on the same principle, with slightly different schemes. A near field image of a plane close to the sample is formed on the observation plane. The scattered and the transmitted beams are both interfering on the observation plane. The near field Image Power Spectrum (IPS) is then evaluated through a Fourier transform. The yellow beam generates two points (yellow dots) on the IPS

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Fig. 2.
Fig. 2.

Schematic description of Tilted Laser Microscopy technique. The red, yellow, and magenta beams represent the impinging, scattered and transmitted beams respectively. The impinging beam falls on the sample at angle α with respect to the optical axis of the system. A near field image of a plane close to the sample is formed on the observation plane. The near field Image Power Spectrum (IPS) is then evaluated through a Fourier transform. The yellow beam generates two points (yellow dots) on the IPS.

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Fig. 3.
Fig. 3.

Upper panels: schematic view of the geometry of the wave vectors corresponding to the incoming light (K⃗ i ), the scattered light (K⃗ s ), the transferred wave vector (Q⃗), and the 2D image wave vector (q⃗). 2Θ is the maximum acceptance angle of the objective and α is the tilted angle. Lower panels: mapping of the IPS wave vector q⃗ as a function of scattering angle ϑ and azimuthal angle φ. Acceptance angle Θ=80°. Left panels: collinear illumination. Right panels: out-of-axis illumination.

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Fig. 4.
Fig. 4.

Sketch of the optical set-up. The He-Ne laser generates a collimated laser beam, which is attenuated by a neutral filter. A half-wave plate and a polarizer control the beam polarization. A mirror bends and adjusts the beam direction. The beam is then expanded by means of a negative focal-length lens, making it slightly divergent. The beam goes through a 45° prism, and enters the sample cell with about a α=45° angle with respect to the vertical. Scattered light is acquired in the near field, together with transmitted light, through a vertical microscope objective, which conjugates a plane close to the sample onto the CCD sensor.

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Fig. 5.
Fig. 5.

Upper panels: 2D images of the SINF speckle field, taken at different tilt angles α. The size of the images is 12.5µm in real space. After software magnification, finite-pixel-size effects have been removed by suitable image processing for an easier visualization. The contrast of the image with α=45° has been enhanced. Lower panels: power spectra of the same images, presented using a logarithmic intensity scale. The size of the image represents a wave vector q=12µm-1. The microscope objective is a 40X, 0.65 NA. The bright disks represent the heterodyne signal, given by the interference between the most intense transmitted beam and the scattered beam. The geometrical position of the disks depends on the tilt angle α. A faint circular halo, centered in the IPS, represents the negligible homodyne signal, due to self interference between different scattered beams. The disks are surrounded by very faint whiskers due to spurious reflections. In the last column on the right, the image shows the homodyne contribution only, since the transmitted beam is stopped by the objective diaphragm, by deliberately using a tilting angle higher than the objective maximum acceptance angle. This last configuration cannot be used in TLM setup. Data obtained with sample C.

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Fig. 6.
Fig. 6.

Upper panels: 2D representation of the Intensity Power Spectra IPS. Lower panels: spectrum intensity S(ϑ) as obtained by averaging on the lines having the same ϑ. Left column: in-axis configuration, 40X objective, Θ=30°. Right column: tilted configuration, 100X objective, Θ=70°, α=45° with a tube lens with half the nominal length. In the in-axis case, the power spectrum shows a dramatic drop around the angle 30°, corresponding to the clipping due to the acceptance angle Θ=30° of the 40X objective. On the contrary, the 100X objective, with tilted illumination, is able to collect light up to 110°. Colored lines: lines of constant ϑ as in Fig. 3. Data obtained with sample D.

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Fig. 7.
Fig. 7.

Scattered intensity I(ϑ) measured as a function of the scattering angle ϑ in the plane perpendicular to the impinging polarization. Experimental results for polystyrene colloids A, B, C, D, E. The lines represent the values calculated with Mie theory for diameter 23nm, 81nm, 149nm, 450nm, and 1700nm respectively. Left column graphs are in Cartesian coordinates, and right column graphs are in polar coordinates. Upper panels represent scattering intensity in linear scale, while in the lower panels the scale is logarithmic.

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Fig. 8.
Fig. 8.

Upper panels: Intensity Power Spectra IPS measured in two different polarization conditions. Lower panels: log-log polar plot of I(ϑ), along the diagonal (φ=0, red line). Left column: perpendicular component of scattering. Right column: parallel component of scattering. The spectra, for the parallel case, shows dark bands representing the minimum of scattering at 90° along the polarization direction, due the dipolar scattering. Data obtained with sample B.

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Fig. 9.
Fig. 9.

Polar plots of the perpendicular and parallel components of the scattering intensity I(θ) measured as a function of the scattering angle ϑ. Data obtained with colloidal samples B (left panel) and C (right panel). Intensity has been mapped as a square root, in order to emphasize the minima around 90° of the parallel component.

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Fig. 10.
Fig. 10.

Dynamic SINF measurements. Exposure-Time Dependent Spectra (ETDS), measured as a function of exposure time Δt, for ϑ=90°. Data obtained with 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, using the values of nanoparticle diameters measured with dynamic SIFF and reported in Tab. 1.

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Tables (1)

Tables Icon

Table 1. List of the analyzed samples.

View Table

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

s [q→(ϑ,φ)]=T(ϑ,φ) I (ϑ,φ)
q→(Q→)=(Qx,Qy,0)
q→(ϑ,φ)=K[cos(α)sin(ϑ)cos(φ)+sin(α)cos(ϑ)−sin(α),sin(ϑ)sin(φ),0]
Q→(q→)=(qx,qy,(ki→·ẑ)2−q→2−2q→· K→i −K→i·ẑ)
S=[q(ϑ,φ),Δt] =T(ϑ,φ) I (ϑ,φ)f(Δtτ)
f(x)=2e−x−1+xx2
Kx2+Ky2 < K sin Θ .
(Qx+Ksinα)2+Qy2 < K sin Θ ,
Qx2+Qy2 < 2 K sin Θ ,

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