Abstract

Most atmospheric-turbulence-compensation experiments have been performed under weak-scintillation conditions; conventional phase-conjugate adaptive-optics systems usually provide good correction for these conditions. We have performed an experiment over a 5.5-km horizontal propagation path to explore the efficacy of conventional adaptive optics in strong-scintillation conditions. The experimental results showed a significant degradation in correction as the scintillation increased. The presence of branch points in the phase appears to be the primary reason for the degradation in correction as the scintillation increases.

© 1995 Optical Society of America

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References

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    [CrossRef]
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1992 (2)

H. T. Barclay, P. H. Malyak, W. H. McGonagle, R. K. Reich, G. S. Rowe, J. C. Twichell, “The SWAT wavefront sensor,” Lincoln Laboratory J. 5, 115–130 (1992).

D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
[CrossRef] [PubMed]

1991 (2)

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortions using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[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]

1988 (1)

1985 (1)

M. S. Scivier, M. A. Fiddy, “Phase ambiguities and the zeros of multidimensional band-limited functions,” J. Opt. Soc. Am. A 5, 693–697 (1985).
[CrossRef]

1980 (1)

1979 (1)

1977 (1)

1976 (1)

1974 (1)

1970 (1)

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 58, 1523–1546 (1970).
[CrossRef]

1968 (1)

J. W. Strohbehn, “Line-of-sight propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

1966 (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]

Barclay, H. T.

H. T. Barclay, P. H. Malyak, W. H. McGonagle, R. K. Reich, G. S. Rowe, J. C. Twichell, “The SWAT wavefront sensor,” Lincoln Laboratory J. 5, 115–130 (1992).

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortions using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

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]

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]

Fiddy, M. A.

M. S. Scivier, M. A. Fiddy, “Phase ambiguities and the zeros of multidimensional band-limited functions,” J. Opt. Soc. Am. A 5, 693–697 (1985).
[CrossRef]

Fried, D. L.

D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
[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]

D. L. Fried, “Limiting resolution looking down through the atmosphere,” J. Opt. Soc. Am. 56, 1380–1384 (1966).
[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]

Gilmartin, T. J.

Greenwood, D. P.

Hardy, J. W.

J. W. Hardy, “Adaptive optics—a progress review,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 2–17 (1991).

Herrmann, J.

Holz, J. Z.

Hufnagel, R. E.

R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook, W. I. Wolfe, G. J. Zissis, eds. (U.S. Office of Naval Research, Washington, D.C., 1978).

Lawrence, R. S.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 58, 1523–1546 (1970).
[CrossRef]

Malyak, P. H.

H. T. Barclay, P. H. Malyak, W. H. McGonagle, R. K. Reich, G. S. Rowe, J. C. Twichell, “The SWAT wavefront sensor,” Lincoln Laboratory J. 5, 115–130 (1992).

McGonagle, W. H.

H. T. Barclay, P. H. Malyak, W. H. McGonagle, R. K. Reich, G. S. Rowe, J. C. Twichell, “The SWAT wavefront sensor,” Lincoln Laboratory J. 5, 115–130 (1992).

Mooney, J. G.

R. J. Sasiela, J. G. Mooney, “An optical phase reconstructor based on using a multiplier-accumulator approach,” in Adaptive Optics, J. E. Ludman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.551, 170–176 (1985).

Murphy, D. V.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortions using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Noll, R. J.

Page, D. A.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortions using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Primmerman, C. A.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortions using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Reich, R. K.

H. T. Barclay, P. H. Malyak, W. H. McGonagle, R. K. Reich, G. S. Rowe, J. C. Twichell, “The SWAT wavefront sensor,” Lincoln Laboratory J. 5, 115–130 (1992).

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]

Rowe, G. S.

H. T. Barclay, P. H. Malyak, W. H. McGonagle, R. K. Reich, G. S. Rowe, J. C. Twichell, “The SWAT wavefront sensor,” Lincoln Laboratory J. 5, 115–130 (1992).

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, J. G. Mooney, “An optical phase reconstructor based on using a multiplier-accumulator approach,” in Adaptive Optics, J. E. Ludman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.551, 170–176 (1985).

Scivier, M. S.

M. S. Scivier, M. A. Fiddy, “Phase ambiguities and the zeros of multidimensional band-limited functions,” J. Opt. Soc. Am. A 5, 693–697 (1985).
[CrossRef]

Strohbehn, J. W.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 58, 1523–1546 (1970).
[CrossRef]

J. W. Strohbehn, “Line-of-sight propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

Takahashi, T.

Takajo, H.

Twichell, J. C.

H. T. Barclay, P. H. Malyak, W. H. McGonagle, R. K. Reich, G. S. Rowe, J. C. Twichell, “The SWAT wavefront sensor,” Lincoln Laboratory J. 5, 115–130 (1992).

Tyler, 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]

Vaughn, J. L.

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]

Zollars, B. G.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortions using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (5)

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

Lincoln Laboratory J. (1)

H. T. Barclay, P. H. Malyak, W. H. McGonagle, R. K. Reich, G. S. Rowe, J. C. Twichell, “The SWAT wavefront sensor,” Lincoln Laboratory J. 5, 115–130 (1992).

Nature (London) (2)

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortions using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[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]

Proc. IEEE (2)

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 58, 1523–1546 (1970).
[CrossRef]

J. W. Strohbehn, “Line-of-sight propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

Other (3)

R. J. Sasiela, J. G. Mooney, “An optical phase reconstructor based on using a multiplier-accumulator approach,” in Adaptive Optics, J. E. Ludman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.551, 170–176 (1985).

R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook, W. I. Wolfe, G. J. Zissis, eds. (U.S. Office of Naval Research, Washington, D.C., 1978).

J. W. Hardy, “Adaptive optics—a progress review,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 2–17 (1991).

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Figures (12)

Fig. 1
Fig. 1

Saturation of σχ2 as the Rytov variance σχ R 2 moves into the strong-scintillation range, which was the area of primary interest in the experiments (adapted from Fig. 6-7 of Ref. 6). Note that the level of scintillation is quite low (<0.1) for typical ground-to-space propagation situations in the visible region.

Fig. 2
Fig. 2

Propagation-code results that show the (a) intensity and (b) phase of a laser beam (1 = 514 nm) propagated over a 5.5-km path through fairly weak, uniform turbulence (C n 2 = 5.6 × 10−15 m−2/3). The beam becomes strongly scintillated, and there are branch cuts (indicated by vertical lines) in the phase, starting from points where the intensity is zero.

Fig. 3
Fig. 3

Experimental configuration.

Fig. 4
Fig. 4

Topography of the Firepond propagation path.

Fig. 5
Fig. 5

Illustration of scoring-laser compensation for typical conditions with moderate scintillation (D/r0 = 6, σχ R 2 = 0.4).

Fig. 6
Fig. 6

Example showing good scoring-laser compensation for weak turbulence near the time of transition (D/r0 = 1.9, σχ R 2 = 0.1).

Fig. 7
Fig. 7

Simulated Hartmann spots on CCD focal plane. Note that, as a result of strong scintillation, the spots vary greatly in size, shape, and intensity.

Fig. 8
Fig. 8

Simulated deformable-mirror figure obtained by reconstruction of the Hartmann measurements in Fig. 7.

Fig. 9
Fig. 9

Simulation of Firepond results with wave-optics propagation code. The Strehl ratio is plotted against turbulence strength for perfect phase compensation and for compensation with a realistic adaptive-optics hardware model.

Fig. 10
Fig. 10

Number of branch points as a function of σχ R 2 for the same turbulence realizations as in Fig. 9. Note that for σχ R 2 ≅ 0.85, one of the turbulence realizations gave no branch point pairs. For this case, Fig. 9 shows excellent correction with the adaptive-optics model, thus indicating that it is primarily the presence of branch points that degrades the correction.

Fig. 11
Fig. 11

Firepond measurements compared with propagation-code predictions. The experimental results are 128-frame averages; the code results are single turbulence realizations.

Fig. 12
Fig. 12

Standard deviation of the curl (an indicator of branch points) as measured by the wave-front sensor compared with the measured beacon area. The curves show good correlation (correlation coefficient = 0.66).

Tables (1)

Tables Icon

Table 1 Representative Atmospheric Turbulence Conditions at Firepond (λ = 514 nm)

Equations (8)

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E ( r , t ) I 0 exp [ i k · r i ω t + χ ( r , t ) + i ϕ ( r , t ) ] ,
I ( r , t ) I 0 exp [ 2 χ ( r , t ) ] .
σ χ 2 = In [ ( σ I 2 / I 0 2 ) + 1 ] 4 .
σ χ R 2 = 0 . 56 k 7 / 6 0 L C n 2 ( z ) ( z / L ) 5 / 6 ( L z ) 5 / 6 d z ,
σ χ R 2 = 0 . 124 k 7 / 6 C n 2 L 11 / 6 .
σ ϕ 2 = 0 . 0567 k 2 D 5 / 3 0 L C n 2 ( z ) ( z / L ) 5 / 3 d z ,
σ ϕ 2 = 0 . 0213 k 2 D 5 / 3 C n 2 L .
σ χ R 2 = 5 . 82 ( L / k D 2 ) 5 / 6 σ ϕ 2 .

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