Abstract

Photoelectron-counting distributions are obtained for stochastic light that is caused to scintillate by passage through a random medium. The result is applied specifically to transmission of amplitude-stabilized radiation, with and without independent additive background, and of chaotic radiation, through the turbulent atmosphere. The counting distribution is found to broaden markedly and its peak occurs at decreasing count numbers for increasing turbulence. The cases studied here are of particular interest for low-level direct optical communications and radar using single-mode lasers, multimode lasers, thermal sources, and scattering targets. The results are obtained by extending the usual formulation of photoelectron counting; a product of two random variables, the source intensity and the effect of the turbulent medium, rather than the usual single stochastic irradiance, is considered. Plots of the counting distributions for various degrees of turbulence and for several signal-to-noise ratios are presented. A possible explanation is given for the observed decrease of the log-amplitude variance to values below the saturation value in long path length and high turbulence experiments.

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  1. l. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  2. D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
  3. D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).
  4. D. L. Fried and R. A. Schmeltzer, Appl. Opt. 6, 1729 (1967).
  5. G. R. Ochs and R. S. Lawrence, J. Opt. Soc. Am. 59, 226 (1969).
  6. G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).
  7. P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 59, 527 (1969).
  8. G. E. Mevers, M. P. Keister, Jr., and D. L. Fried, J. Opt. Soc. Am. 59, 491A (1969).
  9. D. A. deWolf, J. Opt. Soc. Am. 59, 1455 (1969).
  10. J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
  11. W. K. Pratt, Laser Commnunications Systems (Wiley, New York, 1969), p. 145.
  12. L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958).
  13. J. A. Armstrong and A. W. Smith, in Progress in Optics VI, edited by E. Wolf (North-Holland, Amsterdam, 1967), p. 213
  14. M. C. Teich and P. Diament, J. Appl. Phys. 40, 625 (1969); Phys. Letters 30A, 93 (1969); J. Appl. Phys. 41, 415 (1970).
  15. R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
  16. E. Jakeman and E. R. Pike, J. Phys. A2, Ser. 2, 115 (1969)
  17. J. Peřina and R. Horáik, J. Phys. A2, Ser. 2, 702 (1969).
  18. P. Diament and M. C. Teich, J. Opt. Soc. Am. 60, 682 (1970).
  19. M. C. Teich, in Semiconductors and Semimetals, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1970), Vol. 5 (Infrared Detectors), p. 361. See also Proc. IEEE 57, 786 (1969) and Appl. Phys. Letters 14, 201 (1969).
  20. G. Bédard, J. C. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

Alley, C. O.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).

Armstrong, J. A.

J. A. Armstrong and A. W. Smith, in Progress in Optics VI, edited by E. Wolf (North-Holland, Amsterdam, 1967), p. 213

Bédard, G.

G. Bédard, J. C. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

Bergman, R. R.

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

Chang, J. C.

G. Bédard, J. C. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

Chang, R. F.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).

Deitz, P. H.

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 59, 527 (1969).

Detenbeck, R. W.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).

deWolf, D. A.

D. A. deWolf, J. Opt. Soc. Am. 59, 1455 (1969).

Diament, P.

P. Diament and M. C. Teich, J. Opt. Soc. Am. 60, 682 (1970).

M. C. Teich and P. Diament, J. Appl. Phys. 40, 625 (1969); Phys. Letters 30A, 93 (1969); J. Appl. Phys. 41, 415 (1970).

Fried, D. L.

G. E. Mevers, M. P. Keister, Jr., and D. L. Fried, J. Opt. Soc. Am. 59, 491A (1969).

D. L. Fried and R. A. Schmeltzer, Appl. Opt. 6, 1729 (1967).

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).

D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).

Horáik, R.

J. Peřina and R. Horáik, J. Phys. A2, Ser. 2, 702 (1969).

Jakeman, E.

E. Jakeman and E. R. Pike, J. Phys. A2, Ser. 2, 115 (1969)

Keister, Jr., M. P.

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).

G. E. Mevers, M. P. Keister, Jr., and D. L. Fried, J. Opt. Soc. Am. 59, 491A (1969).

Korenman, V.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).

Lawrence, R. S.

G. R. Ochs and R. S. Lawrence, J. Opt. Soc. Am. 59, 226 (1969).

Mandel, L.

G. Bédard, J. C. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958).

Mevers, G. E.

G. E. Mevers, M. P. Keister, Jr., and D. L. Fried, J. Opt. Soc. Am. 59, 491A (1969).

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).

Ochs, G. R.

G. R. Ochs and R. S. Lawrence, J. Opt. Soc. Am. 59, 226 (1969).

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

Perina, J.

J. Peřina and R. Horáik, J. Phys. A2, Ser. 2, 702 (1969).

Pike, E. R.

E. Jakeman and E. R. Pike, J. Phys. A2, Ser. 2, 115 (1969)

Pratt, W. K.

W. K. Pratt, Laser Commnunications Systems (Wiley, New York, 1969), p. 145.

Schmeltzer, R. A.

D. L. Fried and R. A. Schmeltzer, Appl. Opt. 6, 1729 (1967).

Smith, A. W.

J. A. Armstrong and A. W. Smith, in Progress in Optics VI, edited by E. Wolf (North-Holland, Amsterdam, 1967), p. 213

Snyder, J. R.

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

Strohbehn, J. W.

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).

Tatarski, V. I.

l. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

Teich, M. C.

P. Diament and M. C. Teich, J. Opt. Soc. Am. 60, 682 (1970).

M. C. Teich, in Semiconductors and Semimetals, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1970), Vol. 5 (Infrared Detectors), p. 361. See also Proc. IEEE 57, 786 (1969) and Appl. Phys. Letters 14, 201 (1969).

M. C. Teich and P. Diament, J. Appl. Phys. 40, 625 (1969); Phys. Letters 30A, 93 (1969); J. Appl. Phys. 41, 415 (1970).

Wright, N. J.

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 59, 527 (1969).

Other (20)

l. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).

D. L. Fried and R. A. Schmeltzer, Appl. Opt. 6, 1729 (1967).

G. R. Ochs and R. S. Lawrence, J. Opt. Soc. Am. 59, 226 (1969).

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 59, 527 (1969).

G. E. Mevers, M. P. Keister, Jr., and D. L. Fried, J. Opt. Soc. Am. 59, 491A (1969).

D. A. deWolf, J. Opt. Soc. Am. 59, 1455 (1969).

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).

W. K. Pratt, Laser Commnunications Systems (Wiley, New York, 1969), p. 145.

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958).

J. A. Armstrong and A. W. Smith, in Progress in Optics VI, edited by E. Wolf (North-Holland, Amsterdam, 1967), p. 213

M. C. Teich and P. Diament, J. Appl. Phys. 40, 625 (1969); Phys. Letters 30A, 93 (1969); J. Appl. Phys. 41, 415 (1970).

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).

E. Jakeman and E. R. Pike, J. Phys. A2, Ser. 2, 115 (1969)

J. Peřina and R. Horáik, J. Phys. A2, Ser. 2, 702 (1969).

P. Diament and M. C. Teich, J. Opt. Soc. Am. 60, 682 (1970).

M. C. Teich, in Semiconductors and Semimetals, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1970), Vol. 5 (Infrared Detectors), p. 361. See also Proc. IEEE 57, 786 (1969) and Appl. Phys. Letters 14, 201 (1969).

G. Bédard, J. C. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

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