Abstract

The relationships between laser communication system parameters and adaptive optics system parameters are addressed. Improvement in optical signal propagation between space-based receivers and ground-based transmitters is possible with adaptive optics systems that compensate for a few degrees of freedom. Beginning with the relationship between optical signal fade and surge and the atmospheric log-amplitude variance and coupling to expressions that combine adaptive optics systems performance with the reduction in log-amplitude variance, system level examinations of the effects of adaptive optics can be done. Examples are given that show the advantageous reduction in signal fade and surge when adaptive optics are built into the optical system.

© 1996 Optical Society of America

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References

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  1. R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991), Chap. 1, p. 1.
  2. H. T. Yura, W. G. McKinley, “Optical scintillation statistics for IR ground-to-space laser communication systems,” Appl. Opt. 22, 3353–3358 (1983).
    [Crossref] [PubMed]
  3. D. L. Fried, “Aperture averaging of scintillation,” J. Opt. Soc. Am. 57, 169–175 (1967).
    [Crossref]
  4. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7, p. 153.
  5. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1970), Chap. 7, p. 295.
  6. R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
    [Crossref]
  7. J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
    [Crossref] [PubMed]
  8. L. C. Andrews, “Aperture-averaging factor for optical scintillations of plane and spherical waves in the atmosphere,” J. Opt. Soc. Am. A 9, 597–600 (1992).
    [Crossref]
  9. H. T. Yura, W. G. McKinley, “Aperture averaging of scintillation for space-to-ground optical communication applications,” Appl. Opt. 22, 1608–1609 (1983).
    [Crossref] [PubMed]
  10. J. W. Hardy, “Instrumental limitations in adaptive optics for astronomy,” in Active Telescope Systems, F. J. Roddier, ed., Proc. SPIE1114, 2–13 (1989).
  11. D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
    [Crossref]
  12. R. J. Sasiela, “A unified approach to electromagnetic wave propagation in turbulence and the evaluation of multiparameter integrals,” MIT Lincoln Laboratory Report 807 (MIT Lincoln Laboratory, Lexington, Mass., 1988).
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 9, p. 464.
  14. B. M. Levine, K. Kiasaleh, “Intensity fluctuations in the Compensated Earth-Moon-Earth Retroreflector Laser Link (CEMERLL) experiment,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 409–422 (1994).
    [Crossref]
  15. D. P. Greenwood, “Bandwidth specification for adaptive optics systems,” J. Opt. Soc. Am. 67, 390–393 (1977).
    [Crossref]
  16. G. A. Tyler, “Bandwidth considerations for tracking through turbulence,” J. Opt. Soc. Am. A 11, 358–367 (1994).
    [Crossref]
  17. R. R. Beland, “Propagation through atmospheric optical turbulence,” Chap. 2 in Atmospheric Propagation of Radiation, Vol. 2, F. G. Smith, ed., in The Infrared & Electro-Optical Systems Handbook Series (Infrared Information Analysis Center, Ann Arbor, Mich., 1993).
  18. J. L. Bufton, “An investigation of atmospheric turbulence by stellar observations,” NASA Tech. Rep. R-369 (NASA, Washington, D.C., 1971).
  19. R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
    [Crossref]

1994 (1)

1992 (1)

1991 (2)

J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
[Crossref] [PubMed]

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

1983 (2)

1982 (1)

1980 (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[Crossref]

1977 (1)

1967 (1)

Ameer, G. A.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Andrews, L. C.

Beland, R. R.

R. R. Beland, “Propagation through atmospheric optical turbulence,” Chap. 2 in Atmospheric Propagation of Radiation, Vol. 2, F. G. Smith, ed., in The Infrared & Electro-Optical Systems Handbook Series (Infrared Information Analysis Center, Ann Arbor, Mich., 1993).

Boeke, B. R.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 9, p. 464.

Browne, S. L.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Bufton, J. L.

J. L. Bufton, “An investigation of atmospheric turbulence by stellar observations,” NASA Tech. Rep. R-369 (NASA, Washington, D.C., 1971).

Churnside, J. H.

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[Crossref]

Fried, D. L.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
[Crossref]

D. L. Fried, “Aperture averaging of scintillation,” J. Opt. Soc. Am. 57, 169–175 (1967).
[Crossref]

Fugate, R. Q.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Greenwood, D. P.

Hardy, J. W.

J. W. Hardy, “Instrumental limitations in adaptive optics for astronomy,” in Active Telescope Systems, F. J. Roddier, ed., Proc. SPIE1114, 2–13 (1989).

Kiasaleh, K.

B. M. Levine, K. Kiasaleh, “Intensity fluctuations in the Compensated Earth-Moon-Earth Retroreflector Laser Link (CEMERLL) experiment,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 409–422 (1994).
[Crossref]

Levine, B. M.

B. M. Levine, K. Kiasaleh, “Intensity fluctuations in the Compensated Earth-Moon-Earth Retroreflector Laser Link (CEMERLL) experiment,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 409–422 (1994).
[Crossref]

McKinley, W. G.

Roberts, P. H.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Ruane, R. E.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Sasiela, R. J.

R. J. Sasiela, “A unified approach to electromagnetic wave propagation in turbulence and the evaluation of multiparameter integrals,” MIT Lincoln Laboratory Report 807 (MIT Lincoln Laboratory, Lexington, Mass., 1988).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7, p. 153.

Tyler, G. A.

G. A. Tyler, “Bandwidth considerations for tracking through turbulence,” J. Opt. Soc. Am. A 11, 358–367 (1994).
[Crossref]

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991), Chap. 1, p. 1.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 9, p. 464.

Wopat, L. M.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Yura, H. T.

Appl. Opt. (3)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

Nature (London) (1)

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[Crossref]

Proc. IEEE (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[Crossref]

Other (9)

R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991), Chap. 1, p. 1.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7, p. 153.

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1970), Chap. 7, p. 295.

R. R. Beland, “Propagation through atmospheric optical turbulence,” Chap. 2 in Atmospheric Propagation of Radiation, Vol. 2, F. G. Smith, ed., in The Infrared & Electro-Optical Systems Handbook Series (Infrared Information Analysis Center, Ann Arbor, Mich., 1993).

J. L. Bufton, “An investigation of atmospheric turbulence by stellar observations,” NASA Tech. Rep. R-369 (NASA, Washington, D.C., 1971).

R. J. Sasiela, “A unified approach to electromagnetic wave propagation in turbulence and the evaluation of multiparameter integrals,” MIT Lincoln Laboratory Report 807 (MIT Lincoln Laboratory, Lexington, Mass., 1988).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 9, p. 464.

B. M. Levine, K. Kiasaleh, “Intensity fluctuations in the Compensated Earth-Moon-Earth Retroreflector Laser Link (CEMERLL) experiment,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 409–422 (1994).
[Crossref]

J. W. Hardy, “Instrumental limitations in adaptive optics for astronomy,” in Active Telescope Systems, F. J. Roddier, ed., Proc. SPIE1114, 2–13 (1989).

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Figures (3)

Fig. 1
Fig. 1

Effect of adaptive optics for reducing scintillation of a laser communication downlink from a low Earth-orbiting satellite.

Fig. 2
Fig. 2

Effect of adaptive optics for reducing signal fade and surge of a laser communication uplink to a GEO satellite with no isoplanatic error compensation.

Fig. 3
Fig. 3

Effect of adaptive optics for reducing signal fade and surge of a laser communication uplink to a GEO satellite using a point-ahead beacon isoplanatic error compensation.

Equations (33)

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σ int 2 = exp ( σ l 2 ) 1 .
σ int 2 = exp ( 4 σ χ 2 ) 1 ,
F = 10 log ( I / I m ) ,
S = 10 log ( I / I m ) ,
P F ( F 0 ) = 1 2 [ 1 + erf ( 0.23 F 0 + 2 σ χ 2 2 2 σ χ ) ] ,
P S ( S 0 ) = 1 2 [ 1 + erf ( + 0.23 S 0 + 2 σ χ 2 2 2 σ χ ) ] .
P ( f ) = 8.27 sec 7 / 3 Ψ k 2 / 3 0 L C n 2 ( z ) z 4 / 3 V ( z ) d z × 0 [ x 2 + f 2 f 0 2 ( z ) ] 11 / 6 sin ( x 2 + f 2 f 0 2 ( z ) ) d x ,
0 [ x 2 + f 2 f 0 2 ( z ) ] 11 / 6 sin ( x 2 + f 2 f 0 2 ( z ) ) d x exp [ 1.8 ( f / f 0 0.5 ) 1.9 ] , f / f 0 0.5 , 0 [ x 2 + f 2 f 0 2 ( z ) ] 11 / 6 sin ( x 2 + f 2 f 0 2 ( z ) ) d x 1 , f / f 0 < 0.5 .
ν ( F 0 ) = ν 0 exp [ ( 0.23 F 0 + 2 σ χ 2 ) 2 8 σ χ 2 ] ,
ν ( S 0 ) = ν 0 exp [ ( + 0.23 S 0 + 2 σ χ 2 ) 2 8 σ χ 2 ] ,
ν 0 = [ 0 f 2 P ( f ) d f 0 P ( f ) d f ] 1 / 2 .
D F = P F ( F 0 ) / ν ( F 0 ) ,
D S = P S ( S 0 ) / ν ( S 0 ) .
σ χ 2 = 4.78 sec 11 / 6 Ψ λ 7 / 6 0 L C n 2 ( z ) ( z ) 5 / 6 d z ,
σ int 2 = A [ exp ( 4 σ χ 2 ) 1 ] ,
A = [ 1 + 1.07 ( D 2 λ h 0 sec Ψ ) 7 / 6 ] 1 .
h 0 = 0 L C n 2 ( z ) z 2 d z 0 L C n 2 ( z ) z 5 / 6 d z .
σ χ 2 = 0.2073 k 2 0 L d z C n 2 ( z ) d κ κ 11 / 3 × sin 2 [ κ 2 ( z L ) 2 k ] i = 0 N F i ( κ , z ) ,
F even m , n ( κ ) = 2 ( n + 1 ) [ 2 J n + 1 + ( κ D / 2 ) κ D / 2 ] 2 cos 2 ( m ϕ ) , F odd m , n ( κ ) = 2 ( n + 1 ) [ 2 J n + 1 ( κ D / 2 ) κ D / 2 ] 2 sin 2 ( m ϕ ) , F m = 0 , n ( κ ) = ( n + 1 ) [ 2 J n + 1 ( κ D / 2 ) κ D / 2 ] 2 .
i = 0 N F ( κ , z ) 1 n , m N F n , m ( κ ) .
σ int , compensated 2 σ int , uncompensated 2 N ,
σ χ 2 ( compensated ) σ χ 2 ( uncompensated ) N ,
N eff = S iso S servo N ,
S servo = exp [ ( f G / f BW ) 5 / 3 ] ,
f G ( A O ) = 2.13 λ 6 / 5 sec 3 / 5 Ψ [ 0 L C n 2 ( z ) V ( z ) 5 / 3 d z ] 3 / 5 .
S servo = [ 1 + π 2 2 ( f T / f T , BW ) 2 ] 1
f T ( tilt ) = 0.331 D 1 / 6 λ 1 sec 1 / 2 Ψ [ 0 L C n 2 ( z ) V ( z ) 2 d z ] 1 / 2 .
S iso = exp [ ( θ / θ 0 ) 5 / 3 ] ,
θ 0 = 0.0582 λ 6 / 5 sec 8 / 5 Ψ [ 0 L C n 2 ( z ) z 5 / 3 d z ] 3 / 5 .
P ( f ) eff = P ( f ) ( 1 1 1 + f 2 / f BW 2 ) ,
C n 2 ( z ) = 5.94 × 10 23 z 10 exp ( z ) ( W 27 ) 2 + 2.7 × 10 16 exp ( 2 z / 3 ) + A exp ( 10 z ) .
W = 27 ( 75 θ 0 5 / 3 λ 2 0.14 ) 1 / 2 , A = 1.29 × 10 12 r 0 5 / 3 λ 2 1.61 × 10 13 θ 0 5 / 3 λ 2 3.89 × 10 15 .
V ( z ) = 5 + 30 exp { [ ( z 9.4 ) / 4.8 ] 2 } ,

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