Abstract

In this paper we compare the theoretical performances of two schemes of optical communication through the atmospheric turbulence: (1) heterodyne detection and (2) video detection. The signal-to-noise ratios (S/N) in the output current of a detector are expressed for both schemes in terms of the correlation function of the refractive index fluctuations of the turbulence. The results of a separate theoretical analysis of optical wave propagation through a random turbulence are used in order to obtain a numerical estimate of the performance criterion (S/N)(2)/(S/N)(1) in terms of the length of propagation through the atmosphere, the turbulence strength, the wavelength of the optical wave, and the diameter of the receiving aperture.

© 1969 Optical Society of America

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References

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  1. R. F. Lucy, K. Lang, C. J. Peters, K. Duval, Appl. Opt. 6, 1333 (1967).
    [CrossRef] [PubMed]
  2. J. R. Kerr, Proc. IEEE 55, 1686 (1967).
    [CrossRef]
  3. D. L. Fried, J. B. Seidman, Appl. Opt. 6, 245 (1967).
    [CrossRef] [PubMed]
  4. J. P. Laussade, A. Yariv, “A Theoretical Study of Optical Wave Propagation through Random Atmospheric Turbulence,” to be published.
  5. A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Inc., Princeton, 1962).
  6. M. E. Gracheva, Izv. VUZ Radiofiz. 8, 775 (1967).
  7. M. E. Gracheva, A. S. Gurvich, Izv. VUZ Radiofiz. 8, 717 (1965).
  8. G. R. Ochs, R. R. Bergman, J. R. Snyder, “Laser Beam Scintillations over Horizontal Paths from 5.5 to 145 Kilometers,” to be published.
  9. G. R. Ochs, R. S. Lawrence, “Saturation of Laser Beam Scintillation under Conditions of Strong Atmospheric Turbulence,” to be published.
  10. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961), p. 110.
  11. R. F. Lucy, K. Lang, Appl. Opt. 7, 1965 (1968).
    [CrossRef] [PubMed]

1968 (1)

1967 (4)

1965 (1)

M. E. Gracheva, A. S. Gurvich, Izv. VUZ Radiofiz. 8, 717 (1965).

Bergman, R. R.

G. R. Ochs, R. R. Bergman, J. R. Snyder, “Laser Beam Scintillations over Horizontal Paths from 5.5 to 145 Kilometers,” to be published.

Duval, K.

Fried, D. L.

Gracheva, M. E.

M. E. Gracheva, Izv. VUZ Radiofiz. 8, 775 (1967).

M. E. Gracheva, A. S. Gurvich, Izv. VUZ Radiofiz. 8, 717 (1965).

Gurvich, A. S.

M. E. Gracheva, A. S. Gurvich, Izv. VUZ Radiofiz. 8, 717 (1965).

Kerr, J. R.

J. R. Kerr, Proc. IEEE 55, 1686 (1967).
[CrossRef]

Lang, K.

Laussade, J. P.

J. P. Laussade, A. Yariv, “A Theoretical Study of Optical Wave Propagation through Random Atmospheric Turbulence,” to be published.

Lawrence, R. S.

G. R. Ochs, R. S. Lawrence, “Saturation of Laser Beam Scintillation under Conditions of Strong Atmospheric Turbulence,” to be published.

Lucy, R. F.

Ochs, G. R.

G. R. Ochs, R. R. Bergman, J. R. Snyder, “Laser Beam Scintillations over Horizontal Paths from 5.5 to 145 Kilometers,” to be published.

G. R. Ochs, R. S. Lawrence, “Saturation of Laser Beam Scintillation under Conditions of Strong Atmospheric Turbulence,” to be published.

Peters, C. J.

Seidman, J. B.

Snyder, J. R.

G. R. Ochs, R. R. Bergman, J. R. Snyder, “Laser Beam Scintillations over Horizontal Paths from 5.5 to 145 Kilometers,” to be published.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961), p. 110.

Yaglom, A. M.

A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Inc., Princeton, 1962).

Yariv, A.

J. P. Laussade, A. Yariv, “A Theoretical Study of Optical Wave Propagation through Random Atmospheric Turbulence,” to be published.

Appl. Opt. (3)

Izv. VUZ Radiofiz. (2)

M. E. Gracheva, Izv. VUZ Radiofiz. 8, 775 (1967).

M. E. Gracheva, A. S. Gurvich, Izv. VUZ Radiofiz. 8, 717 (1965).

Proc. IEEE (1)

J. R. Kerr, Proc. IEEE 55, 1686 (1967).
[CrossRef]

Other (5)

J. P. Laussade, A. Yariv, “A Theoretical Study of Optical Wave Propagation through Random Atmospheric Turbulence,” to be published.

A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Inc., Princeton, 1962).

G. R. Ochs, R. R. Bergman, J. R. Snyder, “Laser Beam Scintillations over Horizontal Paths from 5.5 to 145 Kilometers,” to be published.

G. R. Ochs, R. S. Lawrence, “Saturation of Laser Beam Scintillation under Conditions of Strong Atmospheric Turbulence,” to be published.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961), p. 110.

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Figures (6)

Fig. 1
Fig. 1

Configuration of the polarizations in the case of a video communication scheme. The direction X is the direction of the laser polarization and of the parallel polarizer.

Fig. 2
Fig. 2

R vs D for a weak turbulence Cn; = 10−8 m− ⅓ at λ = 1/μ.

Fig. 3
Fig. 3

R vs D for an intermediate turbulence Cn = 3 × 10−8 m−⅓ at λ = 10 μ.

Fig. 4
Fig. 4

R vs D for a strong turbulence Cn = 10−7 m−⅓ at λ =10 μ.

Fig. 5
Fig. 5

R vs D for an intermediate turbulence Cn = 3 × 10−8 m−⅓ at λ = 10 μ.

Fig. 6
Fig. 6

R vs D for a strong turbulence Cn = 10−7 m−⅓ at λ =10 μ.

Equations (23)

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E S ( L , r ) = A S ( L , r ) exp { i [ ω 0 t + ϕ m ( t ) + ϕ s ( L , r ) ] } ,
E R ( L , r ) = A R ( L , r ) exp { i [ ( ω 0 + Δ ω ) t + ϕ + ϕ R ( L , r ) ] } ,
E T ( L , r ) = E S ( L , r ) + E R ( L , r ) ,
i ( t ) = η q 2 h ν Σ d r E T ( L , r ) E T * ( L , r ) ,
i DC = η q 2 h ν Σ d r [ A S 2 ( L , r ) + A R 2 ( L , r ) ] ,
i S ( t ) = η q h ν 2 J 1 ( δ ) sin ω m t Σ d r A R ( L , r ) A S ( L , r ) × cos [ Δ ω t + Δ ϕ ( L , r ) ] ,
Δ ϕ ( L , r ) = ϕ S ( L , r ) ϕ R ( L , r ) .
i S ( t ) = η q h ν 2 J 1 ( δ ) A R sin ω m t Σ d r A ( 1 ) ( L , r ) × cos [ Δ ω t + ϕ ( 1 ) ( L , r ) ] ;
i S ( t ) = η q h ν 2 J 1 ( δ ) A R Σ d r A ( 1 ) ( L , r ) sin [ ( Δ ω + ω m ) × t + ϕ ( 1 ) ( L , r ) ] .
S ( 1 ) ( t ) = ( η q h ν ) 2 4 J 1 2 ( δ ) A R 2 Σ d r 1 Σ d r 2 A ( 1 ) ( L , r 1 ) A ( 1 ) ( L , r 2 ) × sin [ ( Δ ω t + ω m ) t + ϕ ( 1 ) ( L , r 1 ) ] sin [ ( Δ ω t + ω m ) t + ϕ ( 1 ) ( L , r 2 ) ] .
S ( 1 ) = ( η q h ν ) 2 2 J 1 2 ( δ ) A R Σ d r 1 Σ d r 2 A ( 1 ) ( L , r 1 ) A ( 1 ) ( L , r 2 ) × cos [ ϕ ( 1 ) ( L , r 1 ) ϕ ( 1 ) ( L , r 2 ) ] ,
S ( 1 ) = ( η q h ν ) 2 2 J 1 2 ( δ ) A R 2 Σ Σ d r 1 d r 2 u ( 1 ) ( L , r 1 ) u * ( 1 ) ( L , r 2 ) ,
N ( 1 ) = 2 q B i DC = ( η q 2 / h ν ) B A R 2 ( π D 2 / 4 ) ,
( S / N ) ( 1 ) = S ( 1 ) / N ( 1 ) = η h ν B 2 J 1 2 ( δ ) 1 ( π D 2 / 4 ) Σ d r 1 Σ d r 2 × u ( 1 ) ( L , r 1 ) u * ( 1 ) ( L , r 2 ) .
ϕ R ( L , r ) = ϕ S ( L , r ) or Δ ϕ ( L , r ) = 0 .
S ( 2 ) = ( η q h ν ) 2 2 J 1 2 ( δ ) Σ Σ d r 1 d r 2 I ( 2 ) ( L , r 1 ) I ( 2 ) ( L , r 2 ) ,
N ( 2 ) = 2 B η q 2 h ν Σ d r I ( 2 ) ( L , r ) ,
S / N ( 2 ) = η h ν B J 1 2 ( δ ) Σ Σ d r 1 d r 2 I ( 2 ) ( L , r 1 ) I ( 2 ) ( L , r 2 ) Σ d r I ( 2 ) ( L , r ) .
R = 1 2 ( π D 2 / 4 ) Σ d r B u ( 2 ) ( L , r , r ) Σ Σ d r 1 d r 2 B I ( 2 ) ( L , r 1 , r 2 ) Σ Σ d r 1 d r 2 B u ( 1 ) ( L , r 1 , r 2 )
B u ( 1 ) ( L , r 1 , r 2 ) = B u ( 1 ) ( L , ρ ) = A ( 1 ) 2 [ 2 k 2 L × ( 0 L 0 B n ( α ) d α 0 ( L 0 2 ρ 2 ) 1 2 B n ( α 2 + ρ 2 ) 1 2 ) d α ] ;
B I ( 2 ) ( L , r 1 , r 2 ) = B I ( 2 ) ( L , ρ ) = A ( 2 ) 4 [ 2 1 1 + σ 1 2 ( L , ρ ) ] ,
σ 1 2 ( L , ρ ) = 8 π 2 k 2 L 0 J 0 ( K ρ ) × ( 1 k K 2 L sin K 2 L k ) ϕ n ( K ) K dK ;
ϕ n ( K ) = { 0.033 C n 2 K 11 3 for K < K m = 5.48 / l 0 0 for K > K m

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