Abstract

An experimental study of horizontal laser beam propagation over paths up to 145 km long was made in which beam diameter and shape, intensity fluctuations, and optical phase distortion were measured. It was found that (1) received beam diameter decreases (on-axis power density increases) with increasing transmitter aperture to a limit reached at an aperture of about 11 cm, (2) beam diameter varies as the 1.2 power of path length, (3) the amplitude of intensity fluctuations decreases with increasing receiver aperture and is nearly independent of path length for paths longer than 0.55 km, (4) the fluctuation spectrum shows a decrease in spectral power with increasing frequency, this negative slope becoming steeper with increasing receiver aperture and remaining constant with path length, and (5) rms fluctuation in phase path length was observed to be 0.25 μ over a 48.8-m path. In addition, it is shown that geometrical optics based on the effects of large scale atmospheric irregularities does not adequately account for signal intensity fluctuations. These results may be helpful in predicting the capability of specific communications systems and in understanding better the nature of atmospheric turbulence.

© 1967 Optical Society of America

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References

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  1. P. Beckmann, Radio Sci. J. Res. 69D, 629 (1965).
  2. H. Hodara, Proc. IEEE 54, 368 (1966).
    [CrossRef]
  3. A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldo di Francia, Radio Sci. J. Res. 1, 523 (1966).
  4. D. L. Fried, J. D. Cloud, “Atmospheric Turbulence and Its Effect on Laser Communication Systems,” Tech. Memo. Nos. 91, 118, 119, 120, North American Aviation, Inc.
  5. R. E. Hufnagel, N. R. Stanley, J. Opt. Soc. Am., 54, 52 (1964).
    [CrossRef]
  6. B. N. Edwards, R. R. Steen, Appl. Opt. 4, 311 (1965).
    [CrossRef]
  7. E. Ryznar, Appl. Opt. 4, 1416 (1965).
    [CrossRef]
  8. H. R. Carlon, Appl. Opt. 4, 1089 (1965).
    [CrossRef]
  9. M. Subramanian, J. A. Collinson, Bell System Tech. J. 44, 543 (1965).
  10. I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
    [CrossRef]
  11. J. R. Meyer-Arendt, C. B. Emmanuel, “Optical Scintillation; A Survey of the Literature”, Tech. Note No. 225, 5April, 1965.
  12. K. Tomiyasu, IEEE Trans. QE-2, No. 6 (1966).
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), p. 441.
  14. J. D. Cloud, D. L. Fried, P. G. Eltgroth, “Atmospheric Turbulence and Its Effect on Laser Communication Systems: Preliminary Report”, Electro-Optical Lab. Tech. Memo. No. 69, October, 1963. This paper gives a summary of various experimental determinations of inner and outer scales of turbulence.
  15. B. H. Briggs, I. A. Parkin, Atmospheric Terrest. Phys. 25, 339 (1963).
    [CrossRef]
  16. L. Elterman, “A Model of a Clear Standard Atmosphere for Attenuation in the Visible Region and Infrared Windows”, AFCRL Research Report 63–675, July, 1963.
  17. G. E. Mevers, D. L. Fried, M. P. Keister, “Experimental Measurements of the Character of Intensity Fluctuations of a Laser Beam Propagating in the Atmosphere,” presented at the meeting of the Optical Society of America, October, 1965.
  18. R. B. Blackman, J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958), pp. 21–23.
  19. W. R. Hinchman, A. L. Buck, Proc. IEEE 52, 305 (1964).
    [CrossRef]

1966 (3)

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldo di Francia, Radio Sci. J. Res. 1, 523 (1966).

K. Tomiyasu, IEEE Trans. QE-2, No. 6 (1966).

1965 (6)

B. N. Edwards, R. R. Steen, Appl. Opt. 4, 311 (1965).
[CrossRef]

E. Ryznar, Appl. Opt. 4, 1416 (1965).
[CrossRef]

H. R. Carlon, Appl. Opt. 4, 1089 (1965).
[CrossRef]

M. Subramanian, J. A. Collinson, Bell System Tech. J. 44, 543 (1965).

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

P. Beckmann, Radio Sci. J. Res. 69D, 629 (1965).

1964 (2)

W. R. Hinchman, A. L. Buck, Proc. IEEE 52, 305 (1964).
[CrossRef]

R. E. Hufnagel, N. R. Stanley, J. Opt. Soc. Am., 54, 52 (1964).
[CrossRef]

1963 (1)

B. H. Briggs, I. A. Parkin, Atmospheric Terrest. Phys. 25, 339 (1963).
[CrossRef]

Beckmann, P.

P. Beckmann, Radio Sci. J. Res. 69D, 629 (1965).

Blackman, R. B.

R. B. Blackman, J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958), pp. 21–23.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), p. 441.

Briggs, B. H.

B. H. Briggs, I. A. Parkin, Atmospheric Terrest. Phys. 25, 339 (1963).
[CrossRef]

Buck, A. L.

W. R. Hinchman, A. L. Buck, Proc. IEEE 52, 305 (1964).
[CrossRef]

Carlon, H. R.

Chabot, A.

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

Cloud, J. D.

J. D. Cloud, D. L. Fried, P. G. Eltgroth, “Atmospheric Turbulence and Its Effect on Laser Communication Systems: Preliminary Report”, Electro-Optical Lab. Tech. Memo. No. 69, October, 1963. This paper gives a summary of various experimental determinations of inner and outer scales of turbulence.

D. L. Fried, J. D. Cloud, “Atmospheric Turbulence and Its Effect on Laser Communication Systems,” Tech. Memo. Nos. 91, 118, 119, 120, North American Aviation, Inc.

Collinson, J. A.

M. Subramanian, J. A. Collinson, Bell System Tech. J. 44, 543 (1965).

Consortini, A.

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldo di Francia, Radio Sci. J. Res. 1, 523 (1966).

Edwards, B. N.

Elterman, L.

L. Elterman, “A Model of a Clear Standard Atmosphere for Attenuation in the Visible Region and Infrared Windows”, AFCRL Research Report 63–675, July, 1963.

Eltgroth, P. G.

J. D. Cloud, D. L. Fried, P. G. Eltgroth, “Atmospheric Turbulence and Its Effect on Laser Communication Systems: Preliminary Report”, Electro-Optical Lab. Tech. Memo. No. 69, October, 1963. This paper gives a summary of various experimental determinations of inner and outer scales of turbulence.

Emmanuel, C. B.

J. R. Meyer-Arendt, C. B. Emmanuel, “Optical Scintillation; A Survey of the Literature”, Tech. Note No. 225, 5April, 1965.

Fried, D. L.

J. D. Cloud, D. L. Fried, P. G. Eltgroth, “Atmospheric Turbulence and Its Effect on Laser Communication Systems: Preliminary Report”, Electro-Optical Lab. Tech. Memo. No. 69, October, 1963. This paper gives a summary of various experimental determinations of inner and outer scales of turbulence.

G. E. Mevers, D. L. Fried, M. P. Keister, “Experimental Measurements of the Character of Intensity Fluctuations of a Laser Beam Propagating in the Atmosphere,” presented at the meeting of the Optical Society of America, October, 1965.

D. L. Fried, J. D. Cloud, “Atmospheric Turbulence and Its Effect on Laser Communication Systems,” Tech. Memo. Nos. 91, 118, 119, 120, North American Aviation, Inc.

Goldstein, I.

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

Hinchman, W. R.

W. R. Hinchman, A. L. Buck, Proc. IEEE 52, 305 (1964).
[CrossRef]

Hodara, H.

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

Hufnagel, R. E.

Keister, M. P.

G. E. Mevers, D. L. Fried, M. P. Keister, “Experimental Measurements of the Character of Intensity Fluctuations of a Laser Beam Propagating in the Atmosphere,” presented at the meeting of the Optical Society of America, October, 1965.

Mevers, G. E.

G. E. Mevers, D. L. Fried, M. P. Keister, “Experimental Measurements of the Character of Intensity Fluctuations of a Laser Beam Propagating in the Atmosphere,” presented at the meeting of the Optical Society of America, October, 1965.

Meyer-Arendt, J. R.

J. R. Meyer-Arendt, C. B. Emmanuel, “Optical Scintillation; A Survey of the Literature”, Tech. Note No. 225, 5April, 1965.

Miles, P. A.

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

Parkin, I. A.

B. H. Briggs, I. A. Parkin, Atmospheric Terrest. Phys. 25, 339 (1963).
[CrossRef]

Ronchi, L.

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldo di Francia, Radio Sci. J. Res. 1, 523 (1966).

Ryznar, E.

Scheggi, A. M.

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldo di Francia, Radio Sci. J. Res. 1, 523 (1966).

Stanley, N. R.

Steen, R. R.

Subramanian, M.

M. Subramanian, J. A. Collinson, Bell System Tech. J. 44, 543 (1965).

Tomiyasu, K.

K. Tomiyasu, IEEE Trans. QE-2, No. 6 (1966).

Toraldo di Francia, G.

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldo di Francia, Radio Sci. J. Res. 1, 523 (1966).

Tukey, J. W.

R. B. Blackman, J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958), pp. 21–23.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), p. 441.

Appl. Opt. (3)

Atmospheric Terrest. Phys. (1)

B. H. Briggs, I. A. Parkin, Atmospheric Terrest. Phys. 25, 339 (1963).
[CrossRef]

Bell System Tech. J. (1)

M. Subramanian, J. A. Collinson, Bell System Tech. J. 44, 543 (1965).

IEEE Trans (1)

K. Tomiyasu, IEEE Trans. QE-2, No. 6 (1966).

J. Opt. Soc. Am. (1)

Proc. IEEE (3)

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

W. R. Hinchman, A. L. Buck, Proc. IEEE 52, 305 (1964).
[CrossRef]

Radio Sci. J. Res. (2)

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldo di Francia, Radio Sci. J. Res. 1, 523 (1966).

P. Beckmann, Radio Sci. J. Res. 69D, 629 (1965).

Other (7)

D. L. Fried, J. D. Cloud, “Atmospheric Turbulence and Its Effect on Laser Communication Systems,” Tech. Memo. Nos. 91, 118, 119, 120, North American Aviation, Inc.

J. R. Meyer-Arendt, C. B. Emmanuel, “Optical Scintillation; A Survey of the Literature”, Tech. Note No. 225, 5April, 1965.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), p. 441.

J. D. Cloud, D. L. Fried, P. G. Eltgroth, “Atmospheric Turbulence and Its Effect on Laser Communication Systems: Preliminary Report”, Electro-Optical Lab. Tech. Memo. No. 69, October, 1963. This paper gives a summary of various experimental determinations of inner and outer scales of turbulence.

L. Elterman, “A Model of a Clear Standard Atmosphere for Attenuation in the Visible Region and Infrared Windows”, AFCRL Research Report 63–675, July, 1963.

G. E. Mevers, D. L. Fried, M. P. Keister, “Experimental Measurements of the Character of Intensity Fluctuations of a Laser Beam Propagating in the Atmosphere,” presented at the meeting of the Optical Society of America, October, 1965.

R. B. Blackman, J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1958), pp. 21–23.

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Figures (10)

Fig. 1
Fig. 1

Laser beam configuration at 4 km. Exposure time: 1/200 sec. Transmitting aperture: 15 cm.

Fig. 2
Fig. 2

Cross section intensity of laser beam under excellent seeing conditions, for two transmitting apertures. Path length: 2 km. Exposure time: 30 sec.

Fig. 3
Fig. 3

Diameter of received beam vs transmitting aperture. Beam diameter is taken as distance between points of half power. Path length: 2 km. Exposure time: 30 sec.

Fig. 4
Fig. 4

Beam diameter vs path length for 10-cm transmitting aperture. Each point represents the mean of measurements made on a single evening. Exposure time: 30 sec.

Fig. 5
Fig. 5

Typical received signal fluctuations for a small detector. Path length: 145 km. Receiver aperture: 7 cm.

Fig. 6
Fig. 6

Fluctuation index σ n and mean μ of received signal vs receiver aperture. Path length: 4 km. Transmitting aperture: 15 cm.

Fig. 7
Fig. 7

Typical power spectra of receiving signal fluctuations. Transmitting aperture: 15 cm. Receiver aperture: 1 mm.

Fig. 8
Fig. 8

Spectral slope of signal fluctuations vs receiver aperture. Path length: 4 km. Transmitting aperture: 15 cm.

Fig. 9
Fig. 9

Experimental setup used for absolute phase measurements.

Fig. 10
Fig. 10

Phase fluctuations vs time for 48.8-m path.

Equations (12)

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I = A ( L ) [ ( 1 + cos θ ) J 1 ( β a sin θ ) β a sin θ ] 2 ,
I = 4 A ( L ) [ J 1 ( β a θ ) / β a θ ] 2 .
D = 1.029 λ L / 2 a ,
D = α L β ,
L < < l 2 / λ .
σ n = σ / μ .
ϕ ( t ) = 2 π λ 0 L n ( x , t ) d x ,
E = A exp [ j ( ω t + ϕ ¯ + ϕ ) ] ,
i = η 0 a 0 2 π ( E + E 0 ) * ( E + E 0 ) r d r d θ ,
i 1 = η π a 2 [ A 2 + A 0 2 + 2 A A 0 cos ( Δ ϕ ¯ + ϕ ) ] ,
i 2 = η π a 2 [ A 2 + A 0 2 + 2 A A 0 cos ( Δ ϕ ¯ + ϕ + π / 2 ) ] .
σ = a L ½ .

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