Abstract

By using the basic particle-scattering theory, the high-order moments of non-Gaussian light, including number fluctuations that are due to independent particles, have been deduced for a sampling interval that is much smaller than the characteristic time of the number fluctuations but comparable with that of the interference fluctuations. The results have been compared with experiment by measuring the second- and third-factorial moments.

© 1982 Optical Society of America

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  1. R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766–2788 (1963).
  2. L. Mandel and E. Wolf, "Coherence properties of optical fields," Rev. Mod. Phys. 37, 231–287 (1965).
  3. G. Bedard, "Photon counting statistics of Gaussian light," Phys. Rev. 151, 1038–1039 (1966).
  4. E. Jakeman and E. R. Pike, "The intensity-fluctuation distribution of Gaussian light," J. Phys. A 1, 128–138 (1968).
  5. C. L. Mehta, "Theory of photoelectron counting," in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. 8, pp. 373–440.
  6. C. D. Cantrell and J. R. Fields, "Effect of spatial coherence on the photoelectric counting statistics of Gaussian light," Phys. Rev. A 7, 2063–2069 (1973).
  7. R. Pecora, "Doppler shifts in light scattering from pure liquids and polymer solutions," J. Chem. Phys. 40, 1604–1614 (1964).
  8. G. J. Gabriel, "Microscopic theory of Rayleigh scattering," Phys. Rev. A 8, 963–990 (1973).
  9. B. Chu, Laser Light Scattering (Academic, New York, 1974),
  10. B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  11. D. W. Schaefer and B. J. Berne, "Light scattering from non-Gaussian concentration fluctuation," Phys. Rev. Lett. 28, 475–478 (1972).
  12. D. W. Schaefer, "Dynamics of number fluctuations: motile macroorganisms," Science 180, 1293–1295 (1973).
  13. S. H. Chen, P. Tartaglia, and P. N. Pusey, "Light scattering from independent particles—non-Gaussian correlation to the clipped intensity cortelation function," J. Phys. A 6, 490–495 (1975).
  14. R. F. Voss and J. Clark, "Number fluctuation spectra from light scattered by particles in Brownian motion," J. Phys. A 9, 561–571 (1976).
  15. P. N. Pusey, "Number fluctuations of interacting particles," J. Phys. A 12, 1805–1818 (1979).
  16. D. W. Schaefer and P. N. Pusey, "Statistics of non-Gaussian scattered light," Phys. Rev. Lett. 29, 843–845 (1972).
  17. D. W. Schaefer and P. N. Pusey, "Statistics of light scattered by non-Gaussian fluctuations," in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1973), pp. 839–85Q.
  18. P. N. Pusey, D. W. Schaefer, and D. E. Koppel, "Single interval statistics of light scattered by identical independent scatterers," J. Phys. A.7, 530–540 (1974).
  19. E. Jakeman, "Photon correlation," in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1974), pp. 75–149.
  20. R. Barakat and J. Blake, "Onefold photoelectron counting statistics for non-Gaussian light: scattering from polydispersive suspensions," Phys. Rev. A 13, 1122–1130 (1976).
  21. P. N. Pusey, "Statistical properties of scattered radiation," in Photon Correlation Spectroscopy and Velocimetry, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1977), pp. 45–141.
  22. H. Sato and N. Suzuki, "Factorial moment of the photon counting distribution of Gaussian—Lorentzian light under various spatial coherence," Opt. Commun. 33, 173–178 (1980).

1980

H. Sato and N. Suzuki, "Factorial moment of the photon counting distribution of Gaussian—Lorentzian light under various spatial coherence," Opt. Commun. 33, 173–178 (1980).

1979

P. N. Pusey, "Number fluctuations of interacting particles," J. Phys. A 12, 1805–1818 (1979).

1976

R. Barakat and J. Blake, "Onefold photoelectron counting statistics for non-Gaussian light: scattering from polydispersive suspensions," Phys. Rev. A 13, 1122–1130 (1976).

R. F. Voss and J. Clark, "Number fluctuation spectra from light scattered by particles in Brownian motion," J. Phys. A 9, 561–571 (1976).

1974

P. N. Pusey, D. W. Schaefer, and D. E. Koppel, "Single interval statistics of light scattered by identical independent scatterers," J. Phys. A.7, 530–540 (1974).

1973

D. W. Schaefer, "Dynamics of number fluctuations: motile macroorganisms," Science 180, 1293–1295 (1973).

S. H. Chen, P. Tartaglia, and P. N. Pusey, "Light scattering from independent particles—non-Gaussian correlation to the clipped intensity cortelation function," J. Phys. A 6, 490–495 (1975).

C. D. Cantrell and J. R. Fields, "Effect of spatial coherence on the photoelectric counting statistics of Gaussian light," Phys. Rev. A 7, 2063–2069 (1973).

G. J. Gabriel, "Microscopic theory of Rayleigh scattering," Phys. Rev. A 8, 963–990 (1973).

1972

D. W. Schaefer and B. J. Berne, "Light scattering from non-Gaussian concentration fluctuation," Phys. Rev. Lett. 28, 475–478 (1972).

D. W. Schaefer and P. N. Pusey, "Statistics of non-Gaussian scattered light," Phys. Rev. Lett. 29, 843–845 (1972).

1970

C. L. Mehta, "Theory of photoelectron counting," in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. 8, pp. 373–440.

1968

E. Jakeman and E. R. Pike, "The intensity-fluctuation distribution of Gaussian light," J. Phys. A 1, 128–138 (1968).

1966

G. Bedard, "Photon counting statistics of Gaussian light," Phys. Rev. 151, 1038–1039 (1966).

1965

L. Mandel and E. Wolf, "Coherence properties of optical fields," Rev. Mod. Phys. 37, 231–287 (1965).

1964

R. Pecora, "Doppler shifts in light scattering from pure liquids and polymer solutions," J. Chem. Phys. 40, 1604–1614 (1964).

1963

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766–2788 (1963).

Barakat, R.

R. Barakat and J. Blake, "Onefold photoelectron counting statistics for non-Gaussian light: scattering from polydispersive suspensions," Phys. Rev. A 13, 1122–1130 (1976).

Bedard, G.

G. Bedard, "Photon counting statistics of Gaussian light," Phys. Rev. 151, 1038–1039 (1966).

Berne, B. J.

D. W. Schaefer and B. J. Berne, "Light scattering from non-Gaussian concentration fluctuation," Phys. Rev. Lett. 28, 475–478 (1972).

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

Blake, J.

R. Barakat and J. Blake, "Onefold photoelectron counting statistics for non-Gaussian light: scattering from polydispersive suspensions," Phys. Rev. A 13, 1122–1130 (1976).

Cantrell, C. D.

C. D. Cantrell and J. R. Fields, "Effect of spatial coherence on the photoelectric counting statistics of Gaussian light," Phys. Rev. A 7, 2063–2069 (1973).

Chen, S. H.

S. H. Chen, P. Tartaglia, and P. N. Pusey, "Light scattering from independent particles—non-Gaussian correlation to the clipped intensity cortelation function," J. Phys. A 6, 490–495 (1975).

Chu, B.

B. Chu, Laser Light Scattering (Academic, New York, 1974),

Clark, J.

R. F. Voss and J. Clark, "Number fluctuation spectra from light scattered by particles in Brownian motion," J. Phys. A 9, 561–571 (1976).

Fields, J. R.

C. D. Cantrell and J. R. Fields, "Effect of spatial coherence on the photoelectric counting statistics of Gaussian light," Phys. Rev. A 7, 2063–2069 (1973).

Gabriel, G. J.

G. J. Gabriel, "Microscopic theory of Rayleigh scattering," Phys. Rev. A 8, 963–990 (1973).

Glauber, R. J.

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766–2788 (1963).

Jakeman, E.

E. Jakeman and E. R. Pike, "The intensity-fluctuation distribution of Gaussian light," J. Phys. A 1, 128–138 (1968).

E. Jakeman, "Photon correlation," in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1974), pp. 75–149.

Koppel, D. E.

P. N. Pusey, D. W. Schaefer, and D. E. Koppel, "Single interval statistics of light scattered by identical independent scatterers," J. Phys. A.7, 530–540 (1974).

Mandel, L.

L. Mandel and E. Wolf, "Coherence properties of optical fields," Rev. Mod. Phys. 37, 231–287 (1965).

Mehta, C. L.

C. L. Mehta, "Theory of photoelectron counting," in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. 8, pp. 373–440.

Pecora, R.

R. Pecora, "Doppler shifts in light scattering from pure liquids and polymer solutions," J. Chem. Phys. 40, 1604–1614 (1964).

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

Pike, E. R.

E. Jakeman and E. R. Pike, "The intensity-fluctuation distribution of Gaussian light," J. Phys. A 1, 128–138 (1968).

Pusey, P. N.

P. N. Pusey, "Number fluctuations of interacting particles," J. Phys. A 12, 1805–1818 (1979).

P. N. Pusey, D. W. Schaefer, and D. E. Koppel, "Single interval statistics of light scattered by identical independent scatterers," J. Phys. A.7, 530–540 (1974).

S. H. Chen, P. Tartaglia, and P. N. Pusey, "Light scattering from independent particles—non-Gaussian correlation to the clipped intensity cortelation function," J. Phys. A 6, 490–495 (1975).

D. W. Schaefer and P. N. Pusey, "Statistics of non-Gaussian scattered light," Phys. Rev. Lett. 29, 843–845 (1972).

D. W. Schaefer and P. N. Pusey, "Statistics of light scattered by non-Gaussian fluctuations," in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1973), pp. 839–85Q.

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

Sato, H.

H. Sato and N. Suzuki, "Factorial moment of the photon counting distribution of Gaussian—Lorentzian light under various spatial coherence," Opt. Commun. 33, 173–178 (1980).

Schaefer, D. W.

P. N. Pusey, D. W. Schaefer, and D. E. Koppel, "Single interval statistics of light scattered by identical independent scatterers," J. Phys. A.7, 530–540 (1974).

D. W. Schaefer, "Dynamics of number fluctuations: motile macroorganisms," Science 180, 1293–1295 (1973).

D. W. Schaefer and P. N. Pusey, "Statistics of non-Gaussian scattered light," Phys. Rev. Lett. 29, 843–845 (1972).

D. W. Schaefer and B. J. Berne, "Light scattering from non-Gaussian concentration fluctuation," Phys. Rev. Lett. 28, 475–478 (1972).

D. W. Schaefer and P. N. Pusey, "Statistics of light scattered by non-Gaussian fluctuations," in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1973), pp. 839–85Q.

Suzuki, N.

H. Sato and N. Suzuki, "Factorial moment of the photon counting distribution of Gaussian—Lorentzian light under various spatial coherence," Opt. Commun. 33, 173–178 (1980).

Tartaglia, P.

S. H. Chen, P. Tartaglia, and P. N. Pusey, "Light scattering from independent particles—non-Gaussian correlation to the clipped intensity cortelation function," J. Phys. A 6, 490–495 (1975).

Voss, R. F.

R. F. Voss and J. Clark, "Number fluctuation spectra from light scattered by particles in Brownian motion," J. Phys. A 9, 561–571 (1976).

Wolf, E.

L. Mandel and E. Wolf, "Coherence properties of optical fields," Rev. Mod. Phys. 37, 231–287 (1965).

J. Chem. Phys.

R. Pecora, "Doppler shifts in light scattering from pure liquids and polymer solutions," J. Chem. Phys. 40, 1604–1614 (1964).

J. Phys. A

E. Jakeman and E. R. Pike, "The intensity-fluctuation distribution of Gaussian light," J. Phys. A 1, 128–138 (1968).

S. H. Chen, P. Tartaglia, and P. N. Pusey, "Light scattering from independent particles—non-Gaussian correlation to the clipped intensity cortelation function," J. Phys. A 6, 490–495 (1975).

R. F. Voss and J. Clark, "Number fluctuation spectra from light scattered by particles in Brownian motion," J. Phys. A 9, 561–571 (1976).

P. N. Pusey, "Number fluctuations of interacting particles," J. Phys. A 12, 1805–1818 (1979).

J. Phys. A.

P. N. Pusey, D. W. Schaefer, and D. E. Koppel, "Single interval statistics of light scattered by identical independent scatterers," J. Phys. A.7, 530–540 (1974).

Opt. Commun.

H. Sato and N. Suzuki, "Factorial moment of the photon counting distribution of Gaussian—Lorentzian light under various spatial coherence," Opt. Commun. 33, 173–178 (1980).

Phys. Rev.

G. Bedard, "Photon counting statistics of Gaussian light," Phys. Rev. 151, 1038–1039 (1966).

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766–2788 (1963).

Phys. Rev. A

G. J. Gabriel, "Microscopic theory of Rayleigh scattering," Phys. Rev. A 8, 963–990 (1973).

C. D. Cantrell and J. R. Fields, "Effect of spatial coherence on the photoelectric counting statistics of Gaussian light," Phys. Rev. A 7, 2063–2069 (1973).

R. Barakat and J. Blake, "Onefold photoelectron counting statistics for non-Gaussian light: scattering from polydispersive suspensions," Phys. Rev. A 13, 1122–1130 (1976).

Phys. Rev. Lett.

D. W. Schaefer and B. J. Berne, "Light scattering from non-Gaussian concentration fluctuation," Phys. Rev. Lett. 28, 475–478 (1972).

D. W. Schaefer and P. N. Pusey, "Statistics of non-Gaussian scattered light," Phys. Rev. Lett. 29, 843–845 (1972).

Rev. Mod. Phys.

L. Mandel and E. Wolf, "Coherence properties of optical fields," Rev. Mod. Phys. 37, 231–287 (1965).

Science

D. W. Schaefer, "Dynamics of number fluctuations: motile macroorganisms," Science 180, 1293–1295 (1973).

Other

D. W. Schaefer and P. N. Pusey, "Statistics of light scattered by non-Gaussian fluctuations," in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1973), pp. 839–85Q.

C. L. Mehta, "Theory of photoelectron counting," in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. 8, pp. 373–440.

B. Chu, Laser Light Scattering (Academic, New York, 1974),

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

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

E. Jakeman, "Photon correlation," in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1974), pp. 75–149.

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