Abstract

It is well known that photoelectric measurements yield information about the statistical behavior of fluctuating light beams. The probability of <i>n</i> photoelectrons being ejected, in a fixed time interval, from the photosensitive surface of the photoelectric detector, upon which the light beam is normally incident, is a linear (Poisson) transform of the probability density for the intensity of the beam. With the help of some plausible assumptions, the present analysis provides solutions to the problem of inverting the Poisson transform, thus determining the probability density for the intensity from experimentally obtained photo-counting distributions. The effectiveness of the method is demonstrated by an actual inversion of a typical experimental counting distribution. The technique is of particular interest in connection with efforts to understand the statistical behavior of optical fields, especially of laser fields.

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  1. L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958); 74, 233 (1959); 81, 1104 (1963).
  2. L. Mandel, in Progress in Optics, Vol. II, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1963), p. 181.
  3. F. A. Johnson, T. P. McLean, and E. R. Pike, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 706.
  4. C. Freed and H. A. Haus, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 715.
  5. F. T. Arecchi, Phys. Rev. Letters 15, 912 (1965).
  6. C. Freed and H. A. Haus, Phys. Rev. Letters 15, 943 (1965).
  7. C. Freed and H. A. Haus, IEEE J. Quantum Electronics QE-2, 190 (1966).
  8. A. W. Smith and J. A. Armstrong, Phys. Letters 19, 650 (1966); see also Phys. Rev. Letters 16, 1169 (1966).
  9. F. T. Arecchi, A. Berné, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).
  10. F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. Letters 16, 589 (1966).
  11. W. Martienssen and E. Spiller, Phys. Rev. Letters 16, 531 (1966).
  12. P. J. Magill and R. P. Soni, Phys. Rev. Letters 16, 911 (1966).
  13. S. Fray, F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. 153, 357 (1967); see also F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Opt. Acta 14, 35 (1967).
  14. E. Wolf and C. L. Mehta, Phys. Rev. Letters 13, 705 (1964).
  15. L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
  16. G. Bédard, Proc. Phys. Soc. (London) 90, 131 (1967).
  17. See, for example, P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Co., New York, 1963), p. 947.
  18. See, for example, I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press Inc., New York, 1965), p. 1038.
  19. G. Lachs, Phys. Rev. 138, B1012 (1965).
  20. R. J. Glauber, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 788.
  21. See, for example, M. G. Kendall and A. Stuart, The Advanced Theory of Statistics (Hafner Publ. Co., New York, 1958), Vol. 1, p. 148.
  22. W. P. Elderton, Frequency Curves and Correlation (Cambridge Univ. Press, London, 1938).

Arecchi, F. T.

F. T. Arecchi, Phys. Rev. Letters 15, 912 (1965).

F. T. Arecchi, A. Berné, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).

Armstrong, J. A.

A. W. Smith and J. A. Armstrong, Phys. Letters 19, 650 (1966); see also Phys. Rev. Letters 16, 1169 (1966).

Bédard, G.

G. Bédard, Proc. Phys. Soc. (London) 90, 131 (1967).

Berné, A.

F. T. Arecchi, A. Berné, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).

Bulamacchi, P.

F. T. Arecchi, A. Berné, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).

Elderton, W. P.

W. P. Elderton, Frequency Curves and Correlation (Cambridge Univ. Press, London, 1938).

Feshbach, H.

See, for example, P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Co., New York, 1963), p. 947.

Fray, S.

S. Fray, F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. 153, 357 (1967); see also F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Opt. Acta 14, 35 (1967).

Freed, C.

C. Freed and H. A. Haus, Phys. Rev. Letters 15, 943 (1965).

C. Freed and H. A. Haus, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 715.

C. Freed and H. A. Haus, IEEE J. Quantum Electronics QE-2, 190 (1966).

Glauber, R. J.

R. J. Glauber, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 788.

Gradshteyn, I. S.

See, for example, I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press Inc., New York, 1965), p. 1038.

Haus, H. A.

C. Freed and H. A. Haus, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 715.

C. Freed and H. A. Haus, IEEE J. Quantum Electronics QE-2, 190 (1966).

C. Freed and H. A. Haus, Phys. Rev. Letters 15, 943 (1965).

Johnson, F. A.

S. Fray, F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. 153, 357 (1967); see also F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Opt. Acta 14, 35 (1967).

F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. Letters 16, 589 (1966).

F. A. Johnson, T. P. McLean, and E. R. Pike, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 706.

Jones, R.

F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. Letters 16, 589 (1966).

S. Fray, F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. 153, 357 (1967); see also F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Opt. Acta 14, 35 (1967).

Kendall, M. G.

See, for example, M. G. Kendall and A. Stuart, The Advanced Theory of Statistics (Hafner Publ. Co., New York, 1958), Vol. 1, p. 148.

Lachs, G.

G. Lachs, Phys. Rev. 138, B1012 (1965).

Magill, P. J.

P. J. Magill and R. P. Soni, Phys. Rev. Letters 16, 911 (1966).

Mandel, L.

L. Mandel, in Progress in Optics, Vol. II, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1963), p. 181.

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958); 74, 233 (1959); 81, 1104 (1963).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Martienssen, W.

W. Martienssen and E. Spiller, Phys. Rev. Letters 16, 531 (1966).

McLean, T. P.

F. A. Johnson, T. P. McLean, and E. R. Pike, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 706.

S. Fray, F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. 153, 357 (1967); see also F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Opt. Acta 14, 35 (1967).

F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. Letters 16, 589 (1966).

Mehta, C. L.

E. Wolf and C. L. Mehta, Phys. Rev. Letters 13, 705 (1964).

Morse, P. M.

See, for example, P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Co., New York, 1963), p. 947.

Pike, E. R.

S. Fray, F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. 153, 357 (1967); see also F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Opt. Acta 14, 35 (1967).

F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. Letters 16, 589 (1966).

F. A. Johnson, T. P. McLean, and E. R. Pike, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 706.

Ryzhik, I. M.

See, for example, I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press Inc., New York, 1965), p. 1038.

Smith, A. W.

A. W. Smith and J. A. Armstrong, Phys. Letters 19, 650 (1966); see also Phys. Rev. Letters 16, 1169 (1966).

Soni, R. P.

P. J. Magill and R. P. Soni, Phys. Rev. Letters 16, 911 (1966).

Spiller, E.

W. Martienssen and E. Spiller, Phys. Rev. Letters 16, 531 (1966).

Stuart, A.

See, for example, M. G. Kendall and A. Stuart, The Advanced Theory of Statistics (Hafner Publ. Co., New York, 1958), Vol. 1, p. 148.

Wolf, E.

E. Wolf and C. L. Mehta, Phys. Rev. Letters 13, 705 (1964).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Other (22)

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958); 74, 233 (1959); 81, 1104 (1963).

L. Mandel, in Progress in Optics, Vol. II, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1963), p. 181.

F. A. Johnson, T. P. McLean, and E. R. Pike, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 706.

C. Freed and H. A. Haus, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 715.

F. T. Arecchi, Phys. Rev. Letters 15, 912 (1965).

C. Freed and H. A. Haus, Phys. Rev. Letters 15, 943 (1965).

C. Freed and H. A. Haus, IEEE J. Quantum Electronics QE-2, 190 (1966).

A. W. Smith and J. A. Armstrong, Phys. Letters 19, 650 (1966); see also Phys. Rev. Letters 16, 1169 (1966).

F. T. Arecchi, A. Berné, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).

F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. Letters 16, 589 (1966).

W. Martienssen and E. Spiller, Phys. Rev. Letters 16, 531 (1966).

P. J. Magill and R. P. Soni, Phys. Rev. Letters 16, 911 (1966).

S. Fray, F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Phys. Rev. 153, 357 (1967); see also F. A. Johnson, R. Jones, T. P. McLean, and E. R. Pike, Opt. Acta 14, 35 (1967).

E. Wolf and C. L. Mehta, Phys. Rev. Letters 13, 705 (1964).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

G. Bédard, Proc. Phys. Soc. (London) 90, 131 (1967).

See, for example, P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Co., New York, 1963), p. 947.

See, for example, I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press Inc., New York, 1965), p. 1038.

G. Lachs, Phys. Rev. 138, B1012 (1965).

R. J. Glauber, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, Eds. (McGraw-Hill Book Co., New York, 1965), p. 788.

See, for example, M. G. Kendall and A. Stuart, The Advanced Theory of Statistics (Hafner Publ. Co., New York, 1958), Vol. 1, p. 148.

W. P. Elderton, Frequency Curves and Correlation (Cambridge Univ. Press, London, 1938).

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