Abstract

Extraction of the mean number of foreground particles that evolve in the presence of an arbitrary background population is achieved by means of a comparative measurement of incoherent scattered intensity fluctuations. Photon-counting experiments are conducted on test particles (latex spheres) that appear in a background population of polydisperse sand particles (Arizona fine, International Organization for Standardization standard 12103). Measurements show recovery of the test particle concentration with an error of less than 10%, despite the presence of the background population that contributes more than 90% of the scattered intensity.

© 2000 Optical Society of America

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References

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  1. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  2. H. Z. Cummins and E. R. Pike, Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1974).
    [CrossRef]
  3. T. Allen, Particle Size Measurement, 4th ed. (Chapman & Hall, London, 1992).
  4. K.-Q. Xia, Y.-B. Xin, and P. Tong, J. Opt. Soc. Am. A 12, 1571 (1995).
    [CrossRef]
  5. P. R. Smith and R. Naimimohasses, Opt. Lett. 22, 1110 (1997).
    [CrossRef] [PubMed]
  6. A. P. Bates, K. I. Hopcraft, and E. Jakeman, J. Opt. Soc. Am. A 14, 3372 (1997).
    [CrossRef]
  7. International Organization for Standardization, “Road vehicles–test dust for filter evaluation. 1. Arizona test dust,” ISO Standard 12103–1 (ISO, Geneva, 1997).

1997

A. P. Bates, K. I. Hopcraft, and E. Jakeman, J. Opt. Soc. Am. A 14, 3372 (1997).
[CrossRef]

P. R. Smith and R. Naimimohasses, Opt. Lett. 22, 1110 (1997).
[CrossRef] [PubMed]

1995

Allen, T.

T. Allen, Particle Size Measurement, 4th ed. (Chapman & Hall, London, 1992).

Bates, A. P.

A. P. Bates, K. I. Hopcraft, and E. Jakeman, J. Opt. Soc. Am. A 14, 3372 (1997).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins and E. R. Pike, Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1974).
[CrossRef]

Goodman, J. W.

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

Hopcraft, K. I.

A. P. Bates, K. I. Hopcraft, and E. Jakeman, J. Opt. Soc. Am. A 14, 3372 (1997).
[CrossRef]

Jakeman, E.

A. P. Bates, K. I. Hopcraft, and E. Jakeman, J. Opt. Soc. Am. A 14, 3372 (1997).
[CrossRef]

Naimimohasses, R.

Pike, E. R.

H. Z. Cummins and E. R. Pike, Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1974).
[CrossRef]

Smith, P. R.

Tong, P.

Xia, K.-Q.

Xin, Y.-B.

J. Opt. Soc. Am. A

A. P. Bates, K. I. Hopcraft, and E. Jakeman, J. Opt. Soc. Am. A 14, 3372 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

International Organization for Standardization, “Road vehicles–test dust for filter evaluation. 1. Arizona test dust,” ISO Standard 12103–1 (ISO, Geneva, 1997).

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

H. Z. Cummins and E. R. Pike, Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1974).
[CrossRef]

T. Allen, Particle Size Measurement, 4th ed. (Chapman & Hall, London, 1992).

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Figures (3)

Fig. 1
Fig. 1

Schematic of experimental arrangement for measuring incoherent scattering fluctuations. A vertically polarized laser source is focused into the scattering chamber (25-mm diameter), and the scattered intensity is measured (at 45 deg) by use of photon-counting technology. The field of view of the detector is limited by a 1-mm aperture a=40 mm, and a photomultiplier tube b=335 mm detects the copolar scattered intensity by means of a polarizer.

Fig. 2
Fig. 2

Particle-number estimation without the presence of a background population. The mean number is recovered with Rij and instrument calibration factor α=4. The mean number NA is also estimated from the physical concentrations of suspensions used.

Fig. 3
Fig. 3

Particle-number estimation with the presence of a polydisperse background population (Arizona fine, filtered in the range 05 µm).

Equations (7)

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I=I0k=1Mj=1Nkqkxj.
I=I0k=1MNkqk,
I2=I02k=1MNkqk2+k=1MNkNk-1qk2+l=1Mk=1MNlNkqkql|kl,
σ2=I02k=1MNkqk2.
I=I0NAqA+kAMNkqk,
σ2=I02NAqA2+kAMNkqk2.
Rij=Ii-Ij2σi2-σj2=NAiqAi-NAjqAj2NAiqAi2-NAjqAj2.

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