Abstract

We show that the two-point correlation function in the near field of scattered light is simply related to the scattered intensity distribution. We present a new, to our knowledge, optical scheme to measure the correlation function in the near field, and we describe a processing technique that permits the subtraction of stray light on a statistical basis. We present experimental data for solutions of latex spheres, and we show that this novel technique is a powerful alternative to static light scattering.

© 2001 Optical Society of America

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References

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  1. See, for example, J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975).
  2. For an early account of intensity-fluctuation spectroscopy, see G. B. Benedek, “Optical mixing spectroscopy, with applications to problems in physics, chemistry, biology, and engineering,” in Polarization, Matter and Radiation, G. B. Benedek, ed. (Jubilee Volume in honor of Alfred Kastler) (Presses Universitaire de France, Paris, 1969).
  3. B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1974).
  4. M. Giglio, M. Carpineti, 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]
  5. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  6. A discussion of the effects on JA(r) of finite correlation at the source can be found in J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), Part 2, pp. 9–75.
  7. By this we mean that the intensity correlation obtained with a δ-correlated sample is quite narrow.
  8. The back focal plane of the entrance block of lenses of the microscope objective lens is inside it; therefore the beam stop was inserted into the objective itself. As a beam stop, we used a piece of a razor blade cut at 45° and lapped accurately. The transmitted beam is reflected and passes through a hole made in the microscope objective.
  9. L. Cipelletti, D. A. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. 70, 3214–3221 (1999).
    [CrossRef]
  10. M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
    [CrossRef] [PubMed]
  11. F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265–2274 (1997).
    [CrossRef]

2000 (1)

M. Giglio, M. Carpineti, 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]

1999 (1)

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

1997 (1)

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

1990 (1)

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Benedek, G. B.

For an early account of intensity-fluctuation spectroscopy, see G. B. Benedek, “Optical mixing spectroscopy, with applications to problems in physics, chemistry, biology, and engineering,” in Polarization, Matter and Radiation, G. B. Benedek, ed. (Jubilee Volume in honor of Alfred Kastler) (Presses Universitaire de France, Paris, 1969).

Berne, B.

B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1974).

Carpineti, M.

M. Giglio, M. Carpineti, 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. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Cipelletti, L.

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

Ferri, F.

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

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Giglio, M.

M. Giglio, M. Carpineti, 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. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

A discussion of the effects on JA(r) of finite correlation at the source can be found in J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), Part 2, pp. 9–75.

Paganini, E.

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Pecora, R.

B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1974).

Perini, U.

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Vailati, A.

M. Giglio, M. Carpineti, 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]

Weitz, D. A.

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

Phys. Rev. A (1)

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

M. Giglio, M. Carpineti, 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]

Rev. Sci. Instrum. (2)

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

Other (7)

See, for example, J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1975).

For an early account of intensity-fluctuation spectroscopy, see G. B. Benedek, “Optical mixing spectroscopy, with applications to problems in physics, chemistry, biology, and engineering,” in Polarization, Matter and Radiation, G. B. Benedek, ed. (Jubilee Volume in honor of Alfred Kastler) (Presses Universitaire de France, Paris, 1969).

B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1974).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

A discussion of the effects on JA(r) of finite correlation at the source can be found in J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), Part 2, pp. 9–75.

By this we mean that the intensity correlation obtained with a δ-correlated sample is quite narrow.

The back focal plane of the entrance block of lenses of the microscope objective lens is inside it; therefore the beam stop was inserted into the objective itself. As a beam stop, we used a piece of a razor blade cut at 45° and lapped accurately. The transmitted beam is reflected and passes through a hole made in the microscope objective.

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Figures (4)

Fig. 1
Fig. 1

(a) A beam of diameter D impinges upon a cell containing particles of diameter d > λ. Any zone within D scatters light into a lobe of angular width Θ = λ/d. (b) The same sample shown in (a) is viewed by a sensor S placed very close to it. S receives light from only a portion of the sample of diameter D* < D. Regions outside D do not feed light to S, although they are illuminated by the incident beam. Again, Θ = λ/d.

Fig. 2
Fig. 2

Optical layout: A lens (a microscope objective) images a plane immediately after the cell onto a CCD camera. The transmitted beam is removed through a beam stop that is placed in the focal plane of the lens.8 The lens magnification is the ratio q/p (not in scale in the figure).

Fig. 3
Fig. 3

(a) Near-field speckles produced by a sample of latex spheres of 5 µm in diameter. (b) Near-field speckles produced by a sample of latex spheres of 10 µm in diameter. Note the difference in the size of the speckles.

Fig. 4
Fig. 4

Intensity distributions obtained with the near-field speckle technique (triangles) from samples of latex spheres of (a) 10 and (b) 5 µm. The data are compared with light-scattering data (solid curves) obtained from the same samples.

Equations (6)

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JAΔx, Δy=Ex1, y1E*x2, y2=Iξ, ηexpi2πλzξΔx+ηΔydξdη,
RIΔx, Δy=I2+|JAΔx, Δy|2,
JAr   Iqexpiq·rdq,
JTOTr=RITOTr-Ī21/2
JSLr=RIMr-Ī21/2.
JAr=JTOTr-JSLr.

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