Abstract

The physical basis for various effects of atmospheric turbulence on laser systems is briefly discussed, and certain limitations of the theoretical results given by Tatarski are summarized. The most important conclusion is that Tatarski’s results for amplitude and phase fluctuations, while they are not applicable for a laser beam of arbitrary diameter, do provide an adequate approximation when the beam diameter is at least a factor of 2 greater than the lateral correlation length for amplitude fluctuations, which is true in many applications. The effects analyzed in some detail are beam steering, beam spreading, image dancing, image blurring, scintillation, and phase fluctuations, certain of which are intimately related. As to specific applications, the signal-to-noise ratio for an AM signal passing through the turbulent atmosphere is derived in terms of the power fluctuation, and communication links are considered in terms of this ratio; the effect of power fluctuations on the probability of detection for the laser radar is discussed in general, and a special example is given; finally, the spot size on the moon’s surface for a transmitter located on the earth’s surface is calculated for different turbulence conditions.

© 1966 Optical Society of America

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References

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  2. W. P. Brown, “On the Validity of the Rytov Approximation in Optical Propagation Calculations”, submitted for publication.
  3. J. L. Lumley, H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).
  4. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 132.
  5. J. D. Rigden, E. I. Gordon, Proc. Inst. Radio Engrs. 50, 2367 (1962).
  6. B. M. Oliver, Proc. IEEE 51, 220 (1963).
    [CrossRef]
  7. R. V. Langmuir, Appl. Phys. Letters 2, 2 (1963).
    [CrossRef]
  8. J. W. Goodman, “Statistical Properties of Laser Sparkle Patterns”, Stanford Electronics Labs., Tech. Rept. No. 2303-1, 1963.
  9. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 229.
  10. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 242.
  11. R. H. Genoud, “Intensity Scintillation of Terrestrial Radiation Sources,” 6th Natl. IRIS, 7–9 Nov. 1961.
  12. F. E. Goodwin, private communication.
  13. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 189.
  14. R. E. Hufnagel, N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
    [CrossRef]
  15. E. K. Webb, Appl. Opt. 3, 1329 (1964).
    [CrossRef]
  16. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 215.
  17. F. E. Goodwin, paper presented at the Conf. on Atmospheric Limitations to Optical Propagation, Boulder, Colo., 17–19, March 1965.

1964 (2)

1963 (2)

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[CrossRef]

R. V. Langmuir, Appl. Phys. Letters 2, 2 (1963).
[CrossRef]

1962 (1)

J. D. Rigden, E. I. Gordon, Proc. Inst. Radio Engrs. 50, 2367 (1962).

Brown, W. P.

W. P. Brown, “On the Validity of the Rytov Approximation in Optical Propagation Calculations”, submitted for publication.

Genoud, R. H.

R. H. Genoud, “Intensity Scintillation of Terrestrial Radiation Sources,” 6th Natl. IRIS, 7–9 Nov. 1961.

Goodman, J. W.

J. W. Goodman, “Statistical Properties of Laser Sparkle Patterns”, Stanford Electronics Labs., Tech. Rept. No. 2303-1, 1963.

Goodwin, F. E.

F. E. Goodwin, paper presented at the Conf. on Atmospheric Limitations to Optical Propagation, Boulder, Colo., 17–19, March 1965.

F. E. Goodwin, private communication.

Gordon, E. I.

J. D. Rigden, E. I. Gordon, Proc. Inst. Radio Engrs. 50, 2367 (1962).

Hufnagel, R. E.

Langmuir, R. V.

R. V. Langmuir, Appl. Phys. Letters 2, 2 (1963).
[CrossRef]

Lumley, J. L.

J. L. Lumley, H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).

Oliver, B. M.

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[CrossRef]

Panofsky, H. A.

J. L. Lumley, H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).

Rigden, J. D.

J. D. Rigden, E. I. Gordon, Proc. Inst. Radio Engrs. 50, 2367 (1962).

Stanley, N. R.

Tatarski, V. I.

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

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 132.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 189.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 215.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 229.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 242.

Webb, E. K.

Appl. Opt. (1)

Appl. Phys. Letters (1)

R. V. Langmuir, Appl. Phys. Letters 2, 2 (1963).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (1)

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[CrossRef]

Proc. Inst. Radio Engrs. (1)

J. D. Rigden, E. I. Gordon, Proc. Inst. Radio Engrs. 50, 2367 (1962).

Other (12)

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 215.

F. E. Goodwin, paper presented at the Conf. on Atmospheric Limitations to Optical Propagation, Boulder, Colo., 17–19, March 1965.

J. W. Goodman, “Statistical Properties of Laser Sparkle Patterns”, Stanford Electronics Labs., Tech. Rept. No. 2303-1, 1963.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 229.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 242.

R. H. Genoud, “Intensity Scintillation of Terrestrial Radiation Sources,” 6th Natl. IRIS, 7–9 Nov. 1961.

F. E. Goodwin, private communication.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 189.

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

W. P. Brown, “On the Validity of the Rytov Approximation in Optical Propagation Calculations”, submitted for publication.

J. L. Lumley, H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), p. 132.

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Figures (8)

Fig. 1
Fig. 1

Range, R, vs lateral phase coherence length, ρ0, for intermediate turbulence.

Fig. 2
Fig. 2

Range, R, vs standard deviation in logarithmic level of amplitude, X A , for intermediate turbulence.

Fig. 3
Fig. 3

Diameter of wavefront, ρ, vs standard deviation in angle of arrival, σ θ , for intermediate turbulence.

Fig. 4
Fig. 4

Range, R, vs standard deviation in angle of arrival, σ θ , of a phase coherent portion with dimension ρ0 of a distorted wavefront in intermediate turbulence.

Fig. 5
Fig. 5

Beam spreading in intermediate turbulence.

Fig. 6
Fig. 6

Range, R, vs beam spreading factor, 2 θ , for intermediate turbulence.

Fig. 7
Fig. 7

Probability of fractional deviation, |δP/P0| = |(PP0)/P0|, in received power, P, from that received in absence of turbulence, P0, vs rms deivation, σ P .

Fig. 8
Fig. 8

Range, R, vs rms deviation in normalized differential power received, σ P , for intermediate turbulence.

Tables (1)

Tables Icon

Table I Aperture Average Factor, G[d/(λR)½] a

Equations (19)

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X A 2 = ( log A A 0 ) 2 = 0.56 K 7 / 6 0 R C n 2 ( r ) Z 5 / 6 d Z ,
X A 2 = 0.31 C n 2 K 7 / 6 R 11 / 6 .
X p 2 = X 1 2 G [ D / ( λ R ) 1 / 2 ] G [ d / ( λ R ) 1 / 2 ] .
σ ϕ 2 ( ρ ) = { 1.46 K 2 ρ 5 / 3 0 R C n 2 ( r ) d Z , l 0 ρ ( λ R ) ½ ; 2.91 K 2 ρ 5 / 3 0 R C n 2 ( r ) d Z , L 0 ρ ( λ R ) ½ .
Weak turbulence : C n = 8 × 10 - 9 m - 1 / 3 . Intermediate turbulence : C n = 4 × 10 - 8 m - 1 / 3 . Strong turbulence : C n = 5 × 10 - 7 m - 1 / 3 .
I ( x , y ) = I 0 P ( x - x , y - y ) d x d y ,
P ( x , y ) = 1 π ( R σ θ ) 2 exp [ - ( x 2 + y 2 ) ( R σ θ ) 2 ] .
η = 1 t k = 0 P ( k + 1 , t ) P ( k + 1 , s ) ,
P ( k + 1 , t ) = n = k + 1 t n n ! e - t
η = 1 - e - s = [ 1 - e - [ d / ( 2 R σ θ ) ] 2 ] , t < 0.01.
η = s t ( 1 - e - t ) = ( d D ) 2 [ 1 - e - [ D / ( 2 R σ θ ) ] 2 ] , s < 0.01.
σ 2 p = ( P - P P ) 2 = exp ( X p 2 ) - 1.
prob . { δ P P 0 < n σ p } = { Ψ [ 1og ( 1 + n σ p ) X p ] - Ψ [ log ( 1 - n σ p ) X p ] } ,
Ψ ( x ) = [ 1 / ( 2 π ) ½ ] 0 x exp ( - t 2 / 2 ) d t .
E ( t ) = A 0 [ 1 + m cos ω t + a ( t ) ] cos ω 0 t ,
S / N = 2 m 2 / σ 2 p .
D d = [ 1.65 C n 2 λ 7 / 6 R 25 / 6 / σ p 2 ] 3 / 7 .
X p 2 = 2.48 C n 2 K 7 / 6 R 11 / 6 G [ D / ( λ R ) ½ ] G [ d / ( λ R ) ½ ] ,
0 C n 2 ( Z ) d Z = 1.3 × 10 - 11 m 1 / 3 ,

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