Abstract

In heterodyne detection (such as in coherent lidar) the optical local oscillator defines a single mode of the incoming-signal light field; this single-mode selectivity has been previously predicted to preserve the full fluctuation character of scattered light. This is in contrast with direct-detection schemes, as in photon-correlation spectroscopy, where aperture averaging usually reduces the range of fluctuations. Examples of Gaussian and non-Gaussian statistics in laser light scattered from a moving ground-glass screen have been studied. This simple laboratory experiment has several advantages over equivalent direct-detection schemes and has been shown to yield experimentally the theoretically predicted factorial intensity moments (up to the seventh order) that result from zero-mean, circulo-complex Gaussian statistics.

© 1994 Optical Society of America

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References

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  1. H. Z. Cummins, E. R. Pike, eds., Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1974); Photon Correlation and Velocimetry (Plenum, New York, 1977).
  2. P. N. Pusey, J. M. Vaughan, “Light scattering and intensity fluctuation spectroscopy,” in Dielectric and Related Molecular Processes, M. Davies, ed. (Chemical Society, London, 1976), Vol. 2, pp. 48–105.
    [CrossRef]
  3. A. V. Jelalian, Laser Radar Systems (Artech, Boston, Mass., 1992).
  4. E. V. Hoversten, “Optical communication theory,” in Laser Handbook, F. T. Arecchi, E. O. Schulz-DuBois, eds. (North-Holland, Amsterdam, 1972), pp. 1805–1862.
  5. R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976), Chap. 6.
  6. E. Jakeman, C. J. Oliver, E. R. Pike, “Measurements of the factorization properties of higher-order optical correlation functions,” J. Phys. A 1, 497–499 (1968).
    [CrossRef]
  7. E. Jakeman, C. J. Oliver, E. R. Pike, “A measurement of optical linewidth by photon-counting statistics,” J. Phys. A 1, 406–408 (1968).
    [CrossRef]
  8. D. L. Jordan, R. C. Hollins, “Measurements of Gaussian speckle statistics using both direct and heterodyne detection of CO2 laser radiation,” Opt. Acta 30, 417–423 (1983).
    [CrossRef]
  9. P. H. Flamant, R. T. Menzies, M. J. Kavaya, “Evidence for speckle effects on pulsed CO2 lidar signal returns from remote targets,” Appl. Opt. 23, 1412–1417 (1984).
    [CrossRef] [PubMed]
  10. D. Letalick, I. Renhorn, O. Steinvall, “Measured signal amplitude distributions for a coherent FM-cw CO2 laser radar,” Appl. Opt. 25, 3927–3938 (1986).
    [CrossRef] [PubMed]
  11. D. K. Killinger, N. Menyuk, W. E. DeFeo, “Experimental comparison of heterodyne and direct detection for pulsed differential absorption CO2 lidar,” Appl. Opt. 22, 682–689 (1983).
    [CrossRef] [PubMed]
  12. R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, “Characteristics of coherent lidar returns from calibration targets and aerosols,” Appl. Opt. 20, 3763–3769 (1981).
    [CrossRef] [PubMed]
  13. G. M. Ancellet, R. T. Menzies, “Atmospheric correlation time measurements and effects on coherent Doppler lidar,” J. Opt. Soc. Am. A 4, 367–373 (1987).
    [CrossRef]
  14. J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
    [CrossRef]
  15. J. H. Shapiro, “Correlation scales of laser speckle in heterodyne detection,” Appl. Opt. 24, 1883–1888 (1985).
    [CrossRef] [PubMed]
  16. R. G. Frehlich, J. J. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
    [CrossRef]
  17. G. Parry, P. N. Pusey, “K distributions in atmospheric propagation of light,” J. Opt. Soc. Am. 69, 796–798 (1979).
    [CrossRef]
  18. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
    [CrossRef]
  19. P. N. Pusey, E. Jakeman, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. II. Application to dynamic scattering in a liquid,” J. Phys. A 8, 392–410 (1975).
    [CrossRef]
  20. V. Bluemel, L. M. Narducci, R. A. Tuft, “Photon-count distributions and irradiance fluctuations of a log-normally distributed light field,” J. Opt. Soc. Am. 62, 1309–1314 (1972).
    [CrossRef]
  21. Strictly, this is true only for the simple classical picture presented here, in which the field cannot fall to zero. The square of this field represents the relative probability for detection of a photon, and, although this probability similarly does not fall to zero, it is clearly possible to obtain a count of zero over a selected short time scale with a sufficiently weak signal.
  22. H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
    [CrossRef]
  23. P. G. Cummins, E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E 14, 1171–1177 (1981).
    [CrossRef]
  24. S. Sasaki, M. Mandel, “Equipment for photon-correlation spectroscopy measurements in the heterodyne mode,” J. Phys. E 17, 738–740 (1984).
    [CrossRef]
  25. P. J. Nash, T. A. King, “A heterodyne photon-correlation spectrometer of advanced design,” J. Phys. E 18, 319–327 (1985).
    [CrossRef]
  26. R. G. W. Brown, “Dynamic light scattering using monomode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
    [CrossRef] [PubMed]
  27. J. Ricka, “Dynamic light scattering with single-mode and multimode receivers,” Appl. Opt. 32, 2860–2875 (1993).
    [CrossRef] [PubMed]
  28. M. Harris, R. Loudon, T. J. Shepherd, J. M. Vaughan, “Optical amplification and spontaneous emission in an Ar+ discharge,” J. Mod. Opt. 39, 1195–1203 (1992).
    [CrossRef]
  29. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594 (1966).
    [CrossRef] [PubMed]
  30. B. J. Rye, R. G. Frehlich, “Optical truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. 31, 2891–2899 (1992).
    [CrossRef] [PubMed]
  31. G. N. Pearson, M. Harris, E. Jakeman, D. Letalick, “Spectral filtering of light possessing non-Gaussian statistics,” J. Mod. Opt. (to be published).

1993 (1)

1992 (2)

B. J. Rye, R. G. Frehlich, “Optical truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

M. Harris, R. Loudon, T. J. Shepherd, J. M. Vaughan, “Optical amplification and spontaneous emission in an Ar+ discharge,” J. Mod. Opt. 39, 1195–1203 (1992).
[CrossRef]

1991 (1)

J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
[CrossRef]

1989 (1)

R. G. Frehlich, J. J. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
[CrossRef]

1987 (2)

1986 (1)

1985 (2)

J. H. Shapiro, “Correlation scales of laser speckle in heterodyne detection,” Appl. Opt. 24, 1883–1888 (1985).
[CrossRef] [PubMed]

P. J. Nash, T. A. King, “A heterodyne photon-correlation spectrometer of advanced design,” J. Phys. E 18, 319–327 (1985).
[CrossRef]

1984 (2)

P. H. Flamant, R. T. Menzies, M. J. Kavaya, “Evidence for speckle effects on pulsed CO2 lidar signal returns from remote targets,” Appl. Opt. 23, 1412–1417 (1984).
[CrossRef] [PubMed]

S. Sasaki, M. Mandel, “Equipment for photon-correlation spectroscopy measurements in the heterodyne mode,” J. Phys. E 17, 738–740 (1984).
[CrossRef]

1983 (2)

D. K. Killinger, N. Menyuk, W. E. DeFeo, “Experimental comparison of heterodyne and direct detection for pulsed differential absorption CO2 lidar,” Appl. Opt. 22, 682–689 (1983).
[CrossRef] [PubMed]

D. L. Jordan, R. C. Hollins, “Measurements of Gaussian speckle statistics using both direct and heterodyne detection of CO2 laser radiation,” Opt. Acta 30, 417–423 (1983).
[CrossRef]

1981 (2)

P. G. Cummins, E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E 14, 1171–1177 (1981).
[CrossRef]

R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, “Characteristics of coherent lidar returns from calibration targets and aerosols,” Appl. Opt. 20, 3763–3769 (1981).
[CrossRef] [PubMed]

1979 (1)

1976 (1)

1975 (1)

P. N. Pusey, E. Jakeman, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. II. Application to dynamic scattering in a liquid,” J. Phys. A 8, 392–410 (1975).
[CrossRef]

1972 (1)

1968 (2)

E. Jakeman, C. J. Oliver, E. R. Pike, “Measurements of the factorization properties of higher-order optical correlation functions,” J. Phys. A 1, 497–499 (1968).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “A measurement of optical linewidth by photon-counting statistics,” J. Phys. A 1, 406–408 (1968).
[CrossRef]

1966 (1)

1964 (1)

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Ancellet, G. M.

Bluemel, V.

Brown, D.

J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
[CrossRef]

Brown, R. G. W.

Callan, R. D.

J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
[CrossRef]

Churnside, J. J.

R. G. Frehlich, J. J. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Cummins, P. G.

P. G. Cummins, E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E 14, 1171–1177 (1981).
[CrossRef]

Davies, P. H.

J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
[CrossRef]

DeFeo, W. E.

Flamant, P. H.

Foord, R.

J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
[CrossRef]

Frehlich, R. G.

B. J. Rye, R. G. Frehlich, “Optical truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

R. G. Frehlich, J. J. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
[CrossRef]

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976), Chap. 6.

Goodman, J. W.

Hardesty, R. M.

Harris, M.

M. Harris, R. Loudon, T. J. Shepherd, J. M. Vaughan, “Optical amplification and spontaneous emission in an Ar+ discharge,” J. Mod. Opt. 39, 1195–1203 (1992).
[CrossRef]

G. N. Pearson, M. Harris, E. Jakeman, D. Letalick, “Spectral filtering of light possessing non-Gaussian statistics,” J. Mod. Opt. (to be published).

Hollins, R. C.

D. L. Jordan, R. C. Hollins, “Measurements of Gaussian speckle statistics using both direct and heterodyne detection of CO2 laser radiation,” Opt. Acta 30, 417–423 (1983).
[CrossRef]

Hoversten, E. V.

E. V. Hoversten, “Optical communication theory,” in Laser Handbook, F. T. Arecchi, E. O. Schulz-DuBois, eds. (North-Holland, Amsterdam, 1972), pp. 1805–1862.

Jakeman, E.

P. N. Pusey, E. Jakeman, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. II. Application to dynamic scattering in a liquid,” J. Phys. A 8, 392–410 (1975).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “Measurements of the factorization properties of higher-order optical correlation functions,” J. Phys. A 1, 497–499 (1968).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “A measurement of optical linewidth by photon-counting statistics,” J. Phys. A 1, 406–408 (1968).
[CrossRef]

G. N. Pearson, M. Harris, E. Jakeman, D. Letalick, “Spectral filtering of light possessing non-Gaussian statistics,” J. Mod. Opt. (to be published).

Jelalian, A. V.

A. V. Jelalian, Laser Radar Systems (Artech, Boston, Mass., 1992).

Jordan, D. L.

D. L. Jordan, R. C. Hollins, “Measurements of Gaussian speckle statistics using both direct and heterodyne detection of CO2 laser radiation,” Opt. Acta 30, 417–423 (1983).
[CrossRef]

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976), Chap. 6.

Kavaya, M. J.

Keeler, R. J.

Killinger, D. K.

King, T. A.

P. J. Nash, T. A. King, “A heterodyne photon-correlation spectrometer of advanced design,” J. Phys. E 18, 319–327 (1985).
[CrossRef]

Knable, N.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Letalick, D.

D. Letalick, I. Renhorn, O. Steinvall, “Measured signal amplitude distributions for a coherent FM-cw CO2 laser radar,” Appl. Opt. 25, 3927–3938 (1986).
[CrossRef] [PubMed]

G. N. Pearson, M. Harris, E. Jakeman, D. Letalick, “Spectral filtering of light possessing non-Gaussian statistics,” J. Mod. Opt. (to be published).

Loudon, R.

M. Harris, R. Loudon, T. J. Shepherd, J. M. Vaughan, “Optical amplification and spontaneous emission in an Ar+ discharge,” J. Mod. Opt. 39, 1195–1203 (1992).
[CrossRef]

Mandel, M.

S. Sasaki, M. Mandel, “Equipment for photon-correlation spectroscopy measurements in the heterodyne mode,” J. Phys. E 17, 738–740 (1984).
[CrossRef]

Menyuk, N.

Menzies, R. T.

Narducci, L. M.

Nash, P. J.

P. J. Nash, T. A. King, “A heterodyne photon-correlation spectrometer of advanced design,” J. Phys. E 18, 319–327 (1985).
[CrossRef]

Oliver, C. J.

E. Jakeman, C. J. Oliver, E. R. Pike, “A measurement of optical linewidth by photon-counting statistics,” J. Phys. A 1, 406–408 (1968).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “Measurements of the factorization properties of higher-order optical correlation functions,” J. Phys. A 1, 497–499 (1968).
[CrossRef]

Parry, G.

Pearson, G. N.

G. N. Pearson, M. Harris, E. Jakeman, D. Letalick, “Spectral filtering of light possessing non-Gaussian statistics,” J. Mod. Opt. (to be published).

Pike, E. R.

E. Jakeman, C. J. Oliver, E. R. Pike, “Measurements of the factorization properties of higher-order optical correlation functions,” J. Phys. A 1, 497–499 (1968).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “A measurement of optical linewidth by photon-counting statistics,” J. Phys. A 1, 406–408 (1968).
[CrossRef]

Pomeroy, W. R. M.

J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
[CrossRef]

Post, M. J.

Pusey, P. N.

G. Parry, P. N. Pusey, “K distributions in atmospheric propagation of light,” J. Opt. Soc. Am. 69, 796–798 (1979).
[CrossRef]

P. N. Pusey, E. Jakeman, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. II. Application to dynamic scattering in a liquid,” J. Phys. A 8, 392–410 (1975).
[CrossRef]

P. N. Pusey, J. M. Vaughan, “Light scattering and intensity fluctuation spectroscopy,” in Dielectric and Related Molecular Processes, M. Davies, ed. (Chemical Society, London, 1976), Vol. 2, pp. 48–105.
[CrossRef]

Renhorn, I.

Richter, R. A.

Ricka, J.

Rye, B. J.

Sasaki, S.

S. Sasaki, M. Mandel, “Equipment for photon-correlation spectroscopy measurements in the heterodyne mode,” J. Phys. E 17, 738–740 (1984).
[CrossRef]

Shapiro, J. H.

Shepherd, T. J.

M. Harris, R. Loudon, T. J. Shepherd, J. M. Vaughan, “Optical amplification and spontaneous emission in an Ar+ discharge,” J. Mod. Opt. 39, 1195–1203 (1992).
[CrossRef]

Siegman, A. E.

Staples, E. J.

P. G. Cummins, E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E 14, 1171–1177 (1981).
[CrossRef]

Steinvall, O.

Tuft, R. A.

Vaughan, J. M.

M. Harris, R. Loudon, T. J. Shepherd, J. M. Vaughan, “Optical amplification and spontaneous emission in an Ar+ discharge,” J. Mod. Opt. 39, 1195–1203 (1992).
[CrossRef]

J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
[CrossRef]

P. N. Pusey, J. M. Vaughan, “Light scattering and intensity fluctuation spectroscopy,” in Dielectric and Related Molecular Processes, M. Davies, ed. (Chemical Society, London, 1976), Vol. 2, pp. 48–105.
[CrossRef]

Yeh, Y.

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Appl. Opt. (9)

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594 (1966).
[CrossRef] [PubMed]

R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, “Characteristics of coherent lidar returns from calibration targets and aerosols,” Appl. Opt. 20, 3763–3769 (1981).
[CrossRef] [PubMed]

D. K. Killinger, N. Menyuk, W. E. DeFeo, “Experimental comparison of heterodyne and direct detection for pulsed differential absorption CO2 lidar,” Appl. Opt. 22, 682–689 (1983).
[CrossRef] [PubMed]

P. H. Flamant, R. T. Menzies, M. J. Kavaya, “Evidence for speckle effects on pulsed CO2 lidar signal returns from remote targets,” Appl. Opt. 23, 1412–1417 (1984).
[CrossRef] [PubMed]

J. H. Shapiro, “Correlation scales of laser speckle in heterodyne detection,” Appl. Opt. 24, 1883–1888 (1985).
[CrossRef] [PubMed]

D. Letalick, I. Renhorn, O. Steinvall, “Measured signal amplitude distributions for a coherent FM-cw CO2 laser radar,” Appl. Opt. 25, 3927–3938 (1986).
[CrossRef] [PubMed]

R. G. W. Brown, “Dynamic light scattering using monomode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
[CrossRef] [PubMed]

B. J. Rye, R. G. Frehlich, “Optical truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

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

J. Mod. Opt. (3)

J. M. Vaughan, D. Brown, R. D. Callan, P. H. Davies, R. Foord, W. R. M. Pomeroy, “Correlation analysis of fluctuations in coherent lidar signals at 10.6 μm,” J. Mod. Opt. 38, 623–648 (1991).
[CrossRef]

R. G. Frehlich, J. J. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
[CrossRef]

M. Harris, R. Loudon, T. J. Shepherd, J. M. Vaughan, “Optical amplification and spontaneous emission in an Ar+ discharge,” J. Mod. Opt. 39, 1195–1203 (1992).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

J. Phys. A (3)

P. N. Pusey, E. Jakeman, “Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. II. Application to dynamic scattering in a liquid,” J. Phys. A 8, 392–410 (1975).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “Measurements of the factorization properties of higher-order optical correlation functions,” J. Phys. A 1, 497–499 (1968).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, “A measurement of optical linewidth by photon-counting statistics,” J. Phys. A 1, 406–408 (1968).
[CrossRef]

J. Phys. E (3)

P. G. Cummins, E. J. Staples, “Particle size measurements on turbid latex systems using heterodyne intensity autocorrelation spectroscopy,” J. Phys. E 14, 1171–1177 (1981).
[CrossRef]

S. Sasaki, M. Mandel, “Equipment for photon-correlation spectroscopy measurements in the heterodyne mode,” J. Phys. E 17, 738–740 (1984).
[CrossRef]

P. J. Nash, T. A. King, “A heterodyne photon-correlation spectrometer of advanced design,” J. Phys. E 18, 319–327 (1985).
[CrossRef]

Opt. Acta (1)

D. L. Jordan, R. C. Hollins, “Measurements of Gaussian speckle statistics using both direct and heterodyne detection of CO2 laser radiation,” Opt. Acta 30, 417–423 (1983).
[CrossRef]

Phys. Rev. Lett. (1)

H. Z. Cummins, N. Knable, Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12, 150–153 (1964).
[CrossRef]

Other (7)

G. N. Pearson, M. Harris, E. Jakeman, D. Letalick, “Spectral filtering of light possessing non-Gaussian statistics,” J. Mod. Opt. (to be published).

Strictly, this is true only for the simple classical picture presented here, in which the field cannot fall to zero. The square of this field represents the relative probability for detection of a photon, and, although this probability similarly does not fall to zero, it is clearly possible to obtain a count of zero over a selected short time scale with a sufficiently weak signal.

H. Z. Cummins, E. R. Pike, eds., Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1974); Photon Correlation and Velocimetry (Plenum, New York, 1977).

P. N. Pusey, J. M. Vaughan, “Light scattering and intensity fluctuation spectroscopy,” in Dielectric and Related Molecular Processes, M. Davies, ed. (Chemical Society, London, 1976), Vol. 2, pp. 48–105.
[CrossRef]

A. V. Jelalian, Laser Radar Systems (Artech, Boston, Mass., 1992).

E. V. Hoversten, “Optical communication theory,” in Laser Handbook, F. T. Arecchi, E. O. Schulz-DuBois, eds. (North-Holland, Amsterdam, 1972), pp. 1805–1862.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976), Chap. 6.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the experimental layout showing the two alternative arrangements for the examination of forward scatter and backscatter. Beam splitters BS1 and BS2 and mirrors M1 and M2 form an interferometer, and the beams are shaped by lenses L1–L4. Lenses L3 and L4 form a mode-matching telescope. In backscatter measurements, M2 is replaced by a third beam splitter. AOM, acousto-optic modulator; L.O., local oscillator; target, ground-glass screen.

Fig. 2
Fig. 2

Intensity versus time for (a) Gaussian and (b) non-Gaussian scattering conditions. Note that the signal level repeatedly takes values very close to zero; note also for (b) the occasional very prominent glintlike spikes. In each case, the intensity is expressed in units of its mean value.

Fig. 3
Fig. 3

Probability distributions of intensity (in units of the mean) for (a) Gaussian and (b) non-Gaussian scattering statistics. For (a), note the characteristic negative-exponential distribution.

Fig. 4
Fig. 4

Histograms from 40 experiments for the second (a) and third (b) normalized moments of the intensity distributions. The theoretical values for Gaussian scattering are 2.0 ± 0.12 and 6.0 ± 0.64 for the second and third moments, respectively, under the conditions of our observations.

Tables (1)

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Table 1 Theoretically Calculated and Experimentally Determined Values for the Normalized Moments of the Intensity Distributionsa

Equations (2)

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M ( n ) = I n I n .
M ( n ) = n ! .

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