Abstract

We develop an analytical expression for the homodyne autocorrelation function of laser light scattered by a laminar flow of a polydisperse particle-fluid system. In contrast to the already existing literature on the development of autocorrelation functions, we explicitly begin with the effects of the finite linewidth of the light source, the spatial and temporal intensity averaging that is due to the detection process, the Brownian particle movement on the amplitudes of the scattered light waves as well as on the degree of resolution that we introduce in this paper, and a general system velocity v= (v x, v y, v z). One main result is a new physical interpretation of the well-known, generally empirically introduced coherence factor. Quantities that are comparable to the well-known degree of coherence, coherence area, and number of coherence areas have also been obtained. Finally the investigations are simplified to an autocorrelation function that can be used for the analysis of fluid-particle systems in the low Knudsen number regime. It is shown that in this case particle size or size distribution, system velocity, and particle concentration can be obtained simultaneously. The developed autocorrelation function is related to frequently analyzed special cases and compared with expressions from the literature.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. C. Y. She, J. A. Lucero, “Simultaneous determination of velocity, turbulence and particle concentration of a turbulent flow using laser cross-beam photon-correlation spectroscopy,” Opt. Commun. 9, 300–303 (1973).
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  16. J. B. Abbiss, T. W. Chubb, E. R. Pike, “Laser Doppler anemometry,” Opt. Laser Technol. 6, 249–261 (1974).
    [CrossRef]
  17. A. D. Birch, D. R. Brown, J. R. Thomas, “Photon correlation spectroscopy and its application to the measurement of turbulence parameters in fluid flows,” J. Phys. D 8, 438–447 (1975).
    [CrossRef]
  18. B. M. Ikegami, M. Shioji, D.-Y. Wei, “Measurement of turbulence by laser homodyne technique,” Bull. JSME 29, 2036–2041 (1986).
    [CrossRef]
  19. P. H. P. Chang, S. S. Penner, “Determinations of turbulent velocity fluctuations and mean particle radii in flames using scattered laser-power spectra,” J. Quant. Spectrosc. Radiat. Transfer 25, 97–104 (1981).
    [CrossRef]
  20. E. Jakeman, “Theory of optical spectroscopy by digital autocorrelation of photon-counting fluctuations,” J. Phys. A 3, 201–215 (1970).
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  21. E. Jakeman, C. J. Oliver, E. R. Pike, “Clipped correlation of integrated intensity fluctuations of Gaussian light,” J. Phys. A 4, 827–835 (1971).
    [CrossRef]
  22. E. Jakeman, “Photon correlation,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974), pp. 75–150.
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  24. R. V. Edwards, J. C. Angus, M. J. French, J. W. Duinning, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. 42, 837–850 (1971).
    [CrossRef]
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    [CrossRef]
  26. R. Weber, G. Schweiger, “Determination of particle size distribution in flowing aerosols by photon correlation spectroscopy,” J. Aerosol Sci. 26, S29–S30 (1995).
    [CrossRef]
  27. E. R. Pike, “Photon statistics,” Riv. Nuovo Cimento 1, 277–314 (1969).
  28. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965).
  29. E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).
  30. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
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    [CrossRef]
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  35. J. Rička, “Dynamic light scattering with single-mode and multimode receivers,” Appl. Opt. 32, 2860–2875 (1993).
    [CrossRef] [PubMed]
  36. G. Schweiger, “Application of photon correlation techniques to ultrafine particle analysis,” in Synthesis and Measurement of Ultrafine Particles, J. C. M. Marijnissen, S. Pratsinis, eds. (Delft U. Press, Delft, The Netherlands, 1993).
  37. D. K. Hutchins, M. H. Harper, R. L. Felder, “Slip correction measurement for solid spherical particles by modulated dynamic light scattering,” Aerosol Sci. Technol. 22, 202–218 (1995).
    [CrossRef]
  38. K. Schätzel, “Noise on photon correlation data: I. Autocorrelation functions,” Quantum Opt. 2, 287–305 (1990); erratum 2, 467–468 (1990).

1995 (2)

R. Weber, G. Schweiger, “Determination of particle size distribution in flowing aerosols by photon correlation spectroscopy,” J. Aerosol Sci. 26, S29–S30 (1995).
[CrossRef]

D. K. Hutchins, M. H. Harper, R. L. Felder, “Slip correction measurement for solid spherical particles by modulated dynamic light scattering,” Aerosol Sci. Technol. 22, 202–218 (1995).
[CrossRef]

1993 (2)

J. Rička, “Dynamic light scattering with single-mode and multimode receivers,” Appl. Opt. 32, 2860–2875 (1993).
[CrossRef] [PubMed]

R. Weber, R. Rambau, G. Schweiger, K. Lucas, “Analysis of a flowing aerosol by correlation spectroscopy: concentration, aperture, velocity and particle size effects,” J. Aerosol Sci. 24, 485–499 (1993).
[CrossRef]

1991 (1)

A. J. Hurd, P. Ho, “In situ light scattering study of particles synthesized in a RF silane-ammonia glow discharge,” J. Aerosol Sci. 22, 617–635 (1991).
[CrossRef]

1990 (1)

K. Schätzel, “Noise on photon correlation data: I. Autocorrelation functions,” Quantum Opt. 2, 287–305 (1990); erratum 2, 467–468 (1990).

1989 (1)

N. Lhuissier, G. Gouesbet, M. E. Weill, “Extensive measurements on soot particles in laminar premixed flames by quasi elastic light scattering spectroscopy,” Combust. Sci. Technol. 67, 17–36 (1989).
[CrossRef]

1986 (1)

B. M. Ikegami, M. Shioji, D.-Y. Wei, “Measurement of turbulence by laser homodyne technique,” Bull. JSME 29, 2036–2041 (1986).
[CrossRef]

1984 (1)

1982 (1)

1981 (1)

P. H. P. Chang, S. S. Penner, “Determinations of turbulent velocity fluctuations and mean particle radii in flames using scattered laser-power spectra,” J. Quant. Spectrosc. Radiat. Transfer 25, 97–104 (1981).
[CrossRef]

1975 (1)

A. D. Birch, D. R. Brown, J. R. Thomas, “Photon correlation spectroscopy and its application to the measurement of turbulence parameters in fluid flows,” J. Phys. D 8, 438–447 (1975).
[CrossRef]

1974 (1)

J. B. Abbiss, T. W. Chubb, E. R. Pike, “Laser Doppler anemometry,” Opt. Laser Technol. 6, 249–261 (1974).
[CrossRef]

1973 (2)

A. D. Birch, D. R. Brown, J. R. Thomas, E. R. Pike, “The application of photon correlation spectroscopy to the measurement of turbulent flows,” J. Phys. D 6, L71–L73 (1973).
[CrossRef]

C. Y. She, J. A. Lucero, “Simultaneous determination of velocity, turbulence and particle concentration of a turbulent flow using laser cross-beam photon-correlation spectroscopy,” Opt. Commun. 9, 300–303 (1973).
[CrossRef]

1972 (1)

C. T. Meneely, C. Y. She, D. F. Edwards, “Measurement of flow and turbulence distribution of a free jet by laser photon correlation spectroscopy,” Opt. Commun. 6, 380–382 (1972).
[CrossRef]

1971 (2)

E. Jakeman, C. J. Oliver, E. R. Pike, “Clipped correlation of integrated intensity fluctuations of Gaussian light,” J. Phys. A 4, 827–835 (1971).
[CrossRef]

R. V. Edwards, J. C. Angus, M. J. French, J. W. Duinning, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. 42, 837–850 (1971).
[CrossRef]

1970 (2)

E. Jakeman, “Theory of optical spectroscopy by digital autocorrelation of photon-counting fluctuations,” J. Phys. A 3, 201–215 (1970).
[CrossRef]

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

1969 (1)

E. R. Pike, “Photon statistics,” Riv. Nuovo Cimento 1, 277–314 (1969).

1905 (1)

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. (Paris) 17, 549–560 (1905).

Abbiss, J. B.

J. B. Abbiss, T. W. Chubb, E. R. Pike, “Laser Doppler anemometry,” Opt. Laser Technol. 6, 249–261 (1974).
[CrossRef]

Angus, J. C.

R. V. Edwards, J. C. Angus, M. J. French, J. W. Duinning, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. 42, 837–850 (1971).
[CrossRef]

Berne, J. B.

J. B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Birch, A. D.

A. D. Birch, D. R. Brown, J. R. Thomas, “Photon correlation spectroscopy and its application to the measurement of turbulence parameters in fluid flows,” J. Phys. D 8, 438–447 (1975).
[CrossRef]

A. D. Birch, D. R. Brown, J. R. Thomas, E. R. Pike, “The application of photon correlation spectroscopy to the measurement of turbulent flows,” J. Phys. D 6, L71–L73 (1973).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Bourke, P. J.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Brown, D. R.

A. D. Birch, D. R. Brown, J. R. Thomas, “Photon correlation spectroscopy and its application to the measurement of turbulence parameters in fluid flows,” J. Phys. D 8, 438–447 (1975).
[CrossRef]

A. D. Birch, D. R. Brown, J. R. Thomas, E. R. Pike, “The application of photon correlation spectroscopy to the measurement of turbulent flows,” J. Phys. D 6, L71–L73 (1973).
[CrossRef]

Butterworth, J.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Chang, P. H. P.

P. H. P. Chang, S. S. Penner, “Determinations of turbulent velocity fluctuations and mean particle radii in flames using scattered laser-power spectra,” J. Quant. Spectrosc. Radiat. Transfer 25, 97–104 (1981).
[CrossRef]

Chowdhury, D. P.

Chu, B.

B. Chu, Laser Light Scattering (Academic, New York, 1991).

Chubb, T. W.

J. B. Abbiss, T. W. Chubb, E. R. Pike, “Laser Doppler anemometry,” Opt. Laser Technol. 6, 249–261 (1974).
[CrossRef]

Drain, L. E.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Duinning, J. W.

R. V. Edwards, J. C. Angus, M. J. French, J. W. Duinning, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. 42, 837–850 (1971).
[CrossRef]

Edwards, D. F.

C. T. Meneely, C. Y. She, D. F. Edwards, “Measurement of flow and turbulence distribution of a free jet by laser photon correlation spectroscopy,” Opt. Commun. 6, 380–382 (1972).
[CrossRef]

Edwards, R. V.

R. V. Edwards, J. C. Angus, M. J. French, J. W. Duinning, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. 42, 837–850 (1971).
[CrossRef]

Egelstaff, P. A.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Einstein, A.

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. (Paris) 17, 549–560 (1905).

Felder, R. L.

D. K. Hutchins, M. H. Harper, R. L. Felder, “Slip correction measurement for solid spherical particles by modulated dynamic light scattering,” Aerosol Sci. Technol. 22, 202–218 (1995).
[CrossRef]

French, M. J.

R. V. Edwards, J. C. Angus, M. J. French, J. W. Duinning, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. 42, 837–850 (1971).
[CrossRef]

Gouesbet, G.

N. Lhuissier, G. Gouesbet, M. E. Weill, “Extensive measurements on soot particles in laminar premixed flames by quasi elastic light scattering spectroscopy,” Combust. Sci. Technol. 67, 17–36 (1989).
[CrossRef]

Harper, M. H.

D. K. Hutchins, M. H. Harper, R. L. Felder, “Slip correction measurement for solid spherical particles by modulated dynamic light scattering,” Aerosol Sci. Technol. 22, 202–218 (1995).
[CrossRef]

Hecht, E.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).

Ho, P.

A. J. Hurd, P. Ho, “In situ light scattering study of particles synthesized in a RF silane-ammonia glow discharge,” J. Aerosol Sci. 22, 617–635 (1991).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hughes, A. J.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Hurd, A. J.

A. J. Hurd, P. Ho, “In situ light scattering study of particles synthesized in a RF silane-ammonia glow discharge,” J. Aerosol Sci. 22, 617–635 (1991).
[CrossRef]

Hutchins, D. K.

D. K. Hutchins, M. H. Harper, R. L. Felder, “Slip correction measurement for solid spherical particles by modulated dynamic light scattering,” Aerosol Sci. Technol. 22, 202–218 (1995).
[CrossRef]

Hutchinson, P.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Ikegami, B. M.

B. M. Ikegami, M. Shioji, D.-Y. Wei, “Measurement of turbulence by laser homodyne technique,” Bull. JSME 29, 2036–2041 (1986).
[CrossRef]

Jackson, D. A.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Jakeman, E.

E. Jakeman, C. J. Oliver, E. R. Pike, “Clipped correlation of integrated intensity fluctuations of Gaussian light,” J. Phys. A 4, 827–835 (1971).
[CrossRef]

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

E. Jakeman, “Theory of optical spectroscopy by digital autocorrelation of photon-counting fluctuations,” J. Phys. A 3, 201–215 (1970).
[CrossRef]

E. Jakeman, “Photon correlation,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974), pp. 75–150.

King, G. B.

Lester, T. W.

Lhuissier, N.

N. Lhuissier, G. Gouesbet, M. E. Weill, “Extensive measurements on soot particles in laminar premixed flames by quasi elastic light scattering spectroscopy,” Combust. Sci. Technol. 67, 17–36 (1989).
[CrossRef]

Lucas, K.

R. Weber, R. Rambau, G. Schweiger, K. Lucas, “Analysis of a flowing aerosol by correlation spectroscopy: concentration, aperture, velocity and particle size effects,” J. Aerosol Sci. 24, 485–499 (1993).
[CrossRef]

Lucero, J. A.

C. Y. She, J. A. Lucero, “Simultaneous determination of velocity, turbulence and particle concentration of a turbulent flow using laser cross-beam photon-correlation spectroscopy,” Opt. Commun. 9, 300–303 (1973).
[CrossRef]

Meneely, C. T.

C. T. Meneely, C. Y. She, D. F. Edwards, “Measurement of flow and turbulence distribution of a free jet by laser photon correlation spectroscopy,” Opt. Commun. 6, 380–382 (1972).
[CrossRef]

Merklin, J. F.

Moss, B.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

O’Shaughnessy, J.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Oliver, C. J.

E. Jakeman, C. J. Oliver, E. R. Pike, “Clipped correlation of integrated intensity fluctuations of Gaussian light,” J. Phys. A 4, 827–835 (1971).
[CrossRef]

Pecora, R.

J. B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Penner, S. S.

P. H. P. Chang, S. S. Penner, “Determinations of turbulent velocity fluctuations and mean particle radii in flames using scattered laser-power spectra,” J. Quant. Spectrosc. Radiat. Transfer 25, 97–104 (1981).
[CrossRef]

Pike, E. R.

J. B. Abbiss, T. W. Chubb, E. R. Pike, “Laser Doppler anemometry,” Opt. Laser Technol. 6, 249–261 (1974).
[CrossRef]

A. D. Birch, D. R. Brown, J. R. Thomas, E. R. Pike, “The application of photon correlation spectroscopy to the measurement of turbulent flows,” J. Phys. D 6, L71–L73 (1973).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “Clipped correlation of integrated intensity fluctuations of Gaussian light,” J. Phys. A 4, 827–835 (1971).
[CrossRef]

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

E. R. Pike, “Photon statistics,” Riv. Nuovo Cimento 1, 277–314 (1969).

Pusey, P. N.

P. N. Pusey, “Statistical properties of scattered radiation,” in Photon Correlation Spectroscopy and Velocimetry, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1977), pp. 45–141.

Rambau, R.

R. Weber, R. Rambau, G. Schweiger, K. Lucas, “Analysis of a flowing aerosol by correlation spectroscopy: concentration, aperture, velocity and particle size effects,” J. Aerosol Sci. 24, 485–499 (1993).
[CrossRef]

Reif, F.

F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965).

Ricka, J.

Schätzel, K.

K. Schätzel, “Noise on photon correlation data: I. Autocorrelation functions,” Quantum Opt. 2, 287–305 (1990); erratum 2, 467–468 (1990).

Schmitz, K. S.

K. S. Schmitz, Dynamic Light Scattering by Macromolecules (Academic, Boston, 1990).

Schofield, P.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Schweiger, G.

R. Weber, G. Schweiger, “Determination of particle size distribution in flowing aerosols by photon correlation spectroscopy,” J. Aerosol Sci. 26, S29–S30 (1995).
[CrossRef]

R. Weber, R. Rambau, G. Schweiger, K. Lucas, “Analysis of a flowing aerosol by correlation spectroscopy: concentration, aperture, velocity and particle size effects,” J. Aerosol Sci. 24, 485–499 (1993).
[CrossRef]

G. Schweiger, “Application of photon correlation techniques to ultrafine particle analysis,” in Synthesis and Measurement of Ultrafine Particles, J. C. M. Marijnissen, S. Pratsinis, eds. (Delft U. Press, Delft, The Netherlands, 1993).

She, C. Y.

C. Y. She, J. A. Lucero, “Simultaneous determination of velocity, turbulence and particle concentration of a turbulent flow using laser cross-beam photon-correlation spectroscopy,” Opt. Commun. 9, 300–303 (1973).
[CrossRef]

C. T. Meneely, C. Y. She, D. F. Edwards, “Measurement of flow and turbulence distribution of a free jet by laser photon correlation spectroscopy,” Opt. Commun. 6, 380–382 (1972).
[CrossRef]

Shioji, M.

B. M. Ikegami, M. Shioji, D.-Y. Wei, “Measurement of turbulence by laser homodyne technique,” Bull. JSME 29, 2036–2041 (1986).
[CrossRef]

Sorensen, C. M.

Sorensen, T. W.

Štepánek, P.

P. Štěpánek, “Data analysis in dynamic light scattering,” in Dynamic Light Scattering, W. Brown, ed. (Clarendon, Oxford, 1993).

Taylor, T. W.

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[CrossRef]

A. D. Birch, D. R. Brown, J. R. Thomas, E. R. Pike, “The application of photon correlation spectroscopy to the measurement of turbulent flows,” J. Phys. D 6, L71–L73 (1973).
[CrossRef]

Weber, R.

R. Weber, G. Schweiger, “Determination of particle size distribution in flowing aerosols by photon correlation spectroscopy,” J. Aerosol Sci. 26, S29–S30 (1995).
[CrossRef]

R. Weber, R. Rambau, G. Schweiger, K. Lucas, “Analysis of a flowing aerosol by correlation spectroscopy: concentration, aperture, velocity and particle size effects,” J. Aerosol Sci. 24, 485–499 (1993).
[CrossRef]

R. Weber, “Charakterisierung von Aerosolen mit der Photonen-Korrelationsspektroskopie,” Thesis (Ruhr-Universität Bochum, Bochum, Germany, 1997).

Wei, D.-Y.

B. M. Ikegami, M. Shioji, D.-Y. Wei, “Measurement of turbulence by laser homodyne technique,” Bull. JSME 29, 2036–2041 (1986).
[CrossRef]

Weill, M. E.

N. Lhuissier, G. Gouesbet, M. E. Weill, “Extensive measurements on soot particles in laminar premixed flames by quasi elastic light scattering spectroscopy,” Combust. Sci. Technol. 67, 17–36 (1989).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Zajac, A.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).

Aerosol Sci. Technol. (1)

D. K. Hutchins, M. H. Harper, R. L. Felder, “Slip correction measurement for solid spherical particles by modulated dynamic light scattering,” Aerosol Sci. Technol. 22, 202–218 (1995).
[CrossRef]

Ann. Phys. (Paris) (1)

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. (Paris) 17, 549–560 (1905).

Appl. Opt. (3)

Bull. JSME (1)

B. M. Ikegami, M. Shioji, D.-Y. Wei, “Measurement of turbulence by laser homodyne technique,” Bull. JSME 29, 2036–2041 (1986).
[CrossRef]

Combust. Sci. Technol. (1)

N. Lhuissier, G. Gouesbet, M. E. Weill, “Extensive measurements on soot particles in laminar premixed flames by quasi elastic light scattering spectroscopy,” Combust. Sci. Technol. 67, 17–36 (1989).
[CrossRef]

J. Aerosol Sci. (3)

R. Weber, G. Schweiger, “Determination of particle size distribution in flowing aerosols by photon correlation spectroscopy,” J. Aerosol Sci. 26, S29–S30 (1995).
[CrossRef]

R. Weber, R. Rambau, G. Schweiger, K. Lucas, “Analysis of a flowing aerosol by correlation spectroscopy: concentration, aperture, velocity and particle size effects,” J. Aerosol Sci. 24, 485–499 (1993).
[CrossRef]

A. J. Hurd, P. Ho, “In situ light scattering study of particles synthesized in a RF silane-ammonia glow discharge,” J. Aerosol Sci. 22, 617–635 (1991).
[CrossRef]

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R. V. Edwards, J. C. Angus, M. J. French, J. W. Duinning, “Spectral analysis of the signal from the laser Doppler flowmeter: time-independent systems,” J. Appl. Phys. 42, 837–850 (1971).
[CrossRef]

J. Phys. A (3)

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, A. J. Hughes, P. Hutchinson, D. A. Jackson, E. Jakeman, B. Moss, J. O’Shaughnessy, E. R. Pike, P. Schofield, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

E. Jakeman, “Theory of optical spectroscopy by digital autocorrelation of photon-counting fluctuations,” J. Phys. A 3, 201–215 (1970).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “Clipped correlation of integrated intensity fluctuations of Gaussian light,” J. Phys. A 4, 827–835 (1971).
[CrossRef]

J. Phys. D (2)

A. D. Birch, D. R. Brown, J. R. Thomas, E. R. Pike, “The application of photon correlation spectroscopy to the measurement of turbulent flows,” J. Phys. D 6, L71–L73 (1973).
[CrossRef]

A. D. Birch, D. R. Brown, J. R. Thomas, “Photon correlation spectroscopy and its application to the measurement of turbulence parameters in fluid flows,” J. Phys. D 8, 438–447 (1975).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

P. H. P. Chang, S. S. Penner, “Determinations of turbulent velocity fluctuations and mean particle radii in flames using scattered laser-power spectra,” J. Quant. Spectrosc. Radiat. Transfer 25, 97–104 (1981).
[CrossRef]

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C. Y. She, J. A. Lucero, “Simultaneous determination of velocity, turbulence and particle concentration of a turbulent flow using laser cross-beam photon-correlation spectroscopy,” Opt. Commun. 9, 300–303 (1973).
[CrossRef]

C. T. Meneely, C. Y. She, D. F. Edwards, “Measurement of flow and turbulence distribution of a free jet by laser photon correlation spectroscopy,” Opt. Commun. 6, 380–382 (1972).
[CrossRef]

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[CrossRef]

Quantum Opt. (1)

K. Schätzel, “Noise on photon correlation data: I. Autocorrelation functions,” Quantum Opt. 2, 287–305 (1990); erratum 2, 467–468 (1990).

Riv. Nuovo Cimento (1)

E. R. Pike, “Photon statistics,” Riv. Nuovo Cimento 1, 277–314 (1969).

Other (16)

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E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

R. Weber, “Charakterisierung von Aerosolen mit der Photonen-Korrelationsspektroskopie,” Thesis (Ruhr-Universität Bochum, Bochum, Germany, 1997).

E. Jakeman, “Photon correlation,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974), pp. 75–150.

P. N. Pusey, “Statistical properties of scattered radiation,” in Photon Correlation Spectroscopy and Velocimetry, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1977), pp. 45–141.

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

H. Z. Cummins, E. R. Pike, eds. Photon Correlation Spectroscopy and Velocimetry (Plenum, New York, 1977).

E. O. Schulz-Du Bois, ed. Photon Correlation Techniques in Fluid Mechanics (Springer-Verlag, Berlin, 1983).

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B. Chu, Laser Light Scattering (Academic, New York, 1991).

K. S. Schmitz, Dynamic Light Scattering by Macromolecules (Academic, Boston, 1990).

W. Brown, ed. Dynamic Light Scattering (Clarendon, Oxford, 1993).

P. Štěpánek, “Data analysis in dynamic light scattering,” in Dynamic Light Scattering, W. Brown, ed. (Clarendon, Oxford, 1993).

G. Schweiger, “Application of photon correlation techniques to ultrafine particle analysis,” in Synthesis and Measurement of Ultrafine Particles, J. C. M. Marijnissen, S. Pratsinis, eds. (Delft U. Press, Delft, The Netherlands, 1993).

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Figures (7)

Fig. 1
Fig. 1

Geometry of light scattering from a particle.

Fig. 2
Fig. 2

Definition of the scattering vector.

Fig. 3
Fig. 3

Scattering geometry in the direction of detection.

Fig. 4
Fig. 4

Time delay of light waves scattered by two particles because of path difference Δl.

Fig. 5
Fig. 5

Degree of resolution as a function of geometric parameter s.

Fig. 6
Fig. 6

Arrangement of the slit (field stop) in the detector optics with respect to the laser beam.

Fig. 7
Fig. 7

Comparison between the Fraunhofer diffraction profile L(y′) of a slit and a Gaussian approximation.

Equations (70)

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I 2 τ lim T 1 T t 0 t 0 + T   I t I t + τ d t .
I 2 τ = I 0 I τ   I Γ 0 I Γ τ p Γ 0 d Γ 0 .
I t = j = 1 M   I j t + m n = 1 M   I mn t ,
I 2 τ = i = 1 M j = 1 M   I i 0 I j τ + k l = 1 M m n = 1 M   I kl 0 I mn τ + i = 1 M m n = 1 M   I i 0 I mn τ + k l = 1 M j = 1 M   I kl 0 I j τ .
I 2 τ = i j = 1 M   I i 0 I j 0 + i = 1 M   I i 0 I i τ + k l = 1 M   I kl 0 I lk τ .
I j τ = I j 0 ,
I r ˆ ,   t 0 = A   1 T t 0 t 0 + T   D r ,   t d t d A .
D r ,   t = 0 r c 2 E r ,   t · E * r ,   t .
E s = exp ik r - z - ikr X E i ,
X = S 2   cos   ϕ + S 3   sin   ϕ S 4   cos   ϕ + S 1   sin   ϕ .
E i r ,   t = ε 0 z ,   t P ρ exp i k ¯ i · r - ω ¯ t .
ε 0 z ,   t = e 0 z ,   t exp i ψ z ,   t
| ρ | 2 = x 2 + y 2 .
I j r ˆ = D j σ j Ω .
D j = D 0 P ρ j ,   D 0 0 r c 2 1 T t 0 t 0 + T   e 0 2 z j ,   t - t j d t
σ j | X | 2 k 2 ,
I mn r ˆ = 0 c 2 A   1 T t 0 t 0 + T   ε 0 z m ,   t - t m ε 0 * z n ,   t - t n d t × P ρ m P ρ n X m · X n * k ¯ 2 | r - r m | r - r n | exp i k ¯ | r - r m | - | r - r n | d A × exp i k ¯ i · r n - r m .
0 r c 2 1 T t 0 t 0 + T   ε 0 z m ,   t - t m ε 0 * z n ,   t - t n d t = γ mn D 0 ,
γ mn 1 T t 0 t 0 + T   ε 0 z m ,   t - t m ε 0 * z n ,   t - t n d t 1 T t 0 t 0 + T   e 0 2 t d t
| γ mn | 0 l c     Δ l if 1 l c     Δ l .
I mn r ˆ = D 0 Ω μ mn P ρ m P ρ n X m · X n * k ¯ 2 R 2 × exp i q ¯ · r n - r m exp i k ¯   ρ m 2 - ρ n 2 2 R .
μ mn = 1 A A   exp i k ¯ x n - x m R   ξ + y n - y m R   η d ξ d η = 2 J 1 s s ,
s = k ¯   κ R   Δ mn ,   Δ mn x n - x m 2 + y n - y m 2 1 / 2
P ρ = exp - ρ 2 w 0 2
L y = sin 2   α α 2 ,     α = k ¯ b 2 R   y ,
L y exp - y 2 w d 2 ,   w d = β   2 R k ¯ b ,   β = 2.29   m - 1 ,
μ mn = 2 J 1 s s exp - s 2 8 .
I 2 a i j = 1 M   I i 0 I j 0 = M M - 1 I 0 2 .
I 0 = D 0 Ω σ a P 2 ρ L y r 0 .
σ a = 0   n a σ a d a ,     0   n a d a = 1 ,
y = y   cos   θ - z   sin   θ ,
P 2 ρ L y r 0 = 1 V T V T   P 2 ρ L y d V = V S V T ,
V S = π 2 3 / 2 w 0 2 w d sin   θ .
I 2 a = D 0 2 Ω 2 N 2 σ 2 ,
N = M / V T V S
N N - 1 = N 2
I 2 b τ i = 1 M   I i 0 I i τ = M I 0 I τ .
r τ = r 0 + δ + v τ .
I 0 I τ = F 0 2 Ω 2 σ 2 a × P 2 ρ 0 P 2 ρ τ L y 0 L y τ r 0 .
σ 2 a 0   n a σ 2 a d a
P 2 y 0 P 2 y τ L y 0 L y τ r 0 = 2 - 3 / 2 V S V T × exp - v x 2 + v y 2 τ 2 w 0 2 - v z   sin   θ - v y   cos   θ 2 τ 2 w d 2 ,
I 2 b τ = N σ 2 F 0 2 Ω 2 2 - 3 / 2 × exp - v x 2 + v y 2 τ 2 w 0 2 - v z   sin   θ - v y   cos   θ 2 τ 2 w d 2 .
I 2 c τ k l = 1 M   I kl 0 I lk τ = M M - 1 I 12 0 I 21 τ .
I 12 0 I 21 τ = D 0 2 Ω 2 P ρ 1 0 P ρ 1 τ L y 1 0 L y 1 τ × P ρ 2 0 P ρ 2 τ L y 2 0 × L y 2 τ μ 12 0 μ 21 τ × σ a 1 σ a 2 exp i q · r 1 τ - r 1 0 + r 2 0 - r 2 τ .
Δ r = r 2 0 - r 1 0
I 12 0 I 21 τ = D 0 2 Ω 2 P ρ 1 0 P ρ 1 τ L y 1 0 L y 1 τ × P ρ 2 0 P ρ 2 τ L y 2 0 × L y 2 τ μ 12 0 μ 21 τ r 1 0 , Δ r × exp i q · r 1 τ - r 1 0 δ 1 a 1 × exp - i q · r 2 τ - r 2 0 δ 2 a 2 .
P ρ 1 0 P ρ 1 τ L y 1 0 L y 1 τ P ρ 2 0 P ρ 2 τ L y 2 0 L y 2 τ μ 12 0 μ 21 τ r 1 0 , Δ r = V S 2 V T 2 1 + k ¯ 2 κ 2 w 0 2 4 R 2 1 + k ¯ 2 κ 2 w d 2 4 R 2 - 1 / 2 × exp - v x 2 + v y 2 τ 2 w 0 2 - v z   sin   θ - v y   cos   θ 2 τ 2 w d 2 .
p δ ,   τ = 4 π D τ - 3 / 2 exp - δ 2 4 D τ
exp i q · r 1 τ - r 1 0 δ 1 a 1 × exp - i q · r 2 τ - r 2 0 δ 2 a 2 = 0   n a σ a exp i q 2 D a τ d a 2 .
I 2 c τ = D 0 2 Ω 2 N 2 1 + k ¯ 2 κ 2 w 0 2 4 R 2 1 + k ¯ 2 κ 2 w d 2 4 R 2 - 1 / 2 × 0   n a σ a exp - q 2 D a τ d a 2 × exp - v x 2 + v y 2 τ 2 w 0 2 - v z   sin   θ - v y   cos   θ 2 τ 2 w d 2 .
exp i q · Δ v r τ Δ v = exp - 1 2 q 2 v T 2 τ 2 .
I 2 τ = D 0 2 Ω 2 N 2 σ 2 + f N 2 I 1 2 τ + 2 - 3 / 2 N σ 2 × exp - v ˜ 2 τ 2 w 0 2 ,
f = 1 + k ¯ 2 κ 2 w 0 2 4 R 2 1 + k ¯ 2 κ 2 w d 2 4 R 2 - 1 / 2 ,
I 1 τ = 0   n a σ a exp - q 2 D a τ d a ,
v ˜ 2 = v x 2 + v y 2 - w 0 2 w d 2 v z   sin   θ - v y   cos   θ 2 .
i 2 τ = 1 + fi 1 2 τ ,
i 1 τ E 0 E * τ E 0 2 = I 1 τ σ
A P = 4 w 0 2 ,
f = 1 1 + N C ,
N C = A P π 2.26   R k κ ¯ 2
A C = π 2.26   R k κ ¯ 2
I 2 τ = D 0 2 Ω 2 σ 2 N 2 + f N 2 exp - τ τ 1 + 2 - 3 / 2 N exp - τ 2 τ 2 2 ,
τ 1 = 2 q 2 D - 1 ,
τ 2 = w 0 v ,     v = v x 2 + v y 2 + v z 2 1 / 2
D = k B T 6 π η a   C a .
ξ = 1 2 3 / 2 f N σ 2 σ 2 .
var σ σ - σ 2 = σ 2 - σ 2 .
ξ = 1 2 3 / 2 f N 1 + var σ σ 2
I 0 I τ = F 0 2 Ω 2 σ 2 a P 2 ρ 0 P 2 ρ τ × L y 0 L y 0 L y τ r 0 δ × a .
I 0 I τ = N F 0 2 Ω 2 2 - 3 / 2 exp - v x 2 + v y 2 τ 2 w 0 2 × 0   n a σ 2 a 1 + 4 D a τ w 0 2 - 1 / 2 × 1 + 4 D a τ   sin 2   θ w d 2 - 1 / 2 × 1 + 4 D a τ w 0 2 - 4 D a τ   cos 2   θ w d 2 + 4 D a τ   sin 2   θ - 1 / 2 × exp - v z   sin   θ - v y   cos   θ 2 τ 2 w d 2 + 4 D a τ   sin 2   θ × exp v y τ w 0 2 - v y τ   cos 2   θ + v z τ   sin   θ   cos   θ w d 2 + 4 D a τ   sin 2   θ 2 × 1 w 0 2 + 1 4 D a τ - cos 2   θ w d 2 + 4 D a τ   sin 2   θ - 1 d a .

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