Abstract

Atmospheric turbulence over long horizontal paths perturbs phase and can also cause severe intensity scintillation in the pupil of an optical communications receiver, which limits the data rate over which intensity-based modulation schemes can operate. The feasibility of using low-order adaptive optics by applying phase-only corrections over horizontal propagation paths is investigated. A Shack–Hartmann wave-front sensor was built and data were gathered on paths 1 m above ground and between a 1- and 2.5-km range. Both intensity fluctuations and optical path fluctuation statistics were gathered within a single frame, and the wave-front reconstructor was modified to allow for scintillated data. The temporal power spectral density for various Zernike polynomial modes was used to determine the effects of the expected corrections by adaptive optics. The slopes of the inertial subrange of turbulence were found to be less than predicted by Kolmogorov theory with an infinite outer scale, and the distribution of variance explained by increasing order was also found to be different. Statistical analysis of these data in the 1-km range indicates that at communications wavelengths of 1.3 μm, a significant improvement in transmitted beam quality could be expected most of the time, to a performance of 10% Strehl ratio or better.

© 1998 Optical Society of America

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References

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  1. P. R. Barbier, P. Polak-Dingels, D. W. Rush, D. M. Rosser, G. L. Burdge, R. W. Barnett, “A terrestrial laser communication link at 1.3 μm with quadrature amplitude modulation,” in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed., Proc. SPIE2699, 103–113 (1996).
    [CrossRef]
  2. D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  11. LINUX is a UNIX-line operating system for Intel-based personal computers. It is freely distributed under the terms of the GNU General Public License. More information can be found at the LINUX Documentation Project web site: http://confused.ume.maine.edu/mdw/ .
  12. P. Alexander, L. F. Gladden, “How to create an X-window interface to GNUplot and FORTRAN programs using the Tcl/Tk toolkit,” Comput. Phys. 9, 57–64 (1995).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1996 (1)

1995 (2)

P. Alexander, L. F. Gladden, “How to create an X-window interface to GNUplot and FORTRAN programs using the Tcl/Tk toolkit,” Comput. Phys. 9, 57–64 (1995).

C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrmann, “Atmospheric compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).
[CrossRef] [PubMed]

1993 (1)

1992 (2)

D. Dayton, B. Pierson, B. Spielbusch, J. Gonglewski, “Atmospheric structure function measurements with a Shack–Hartmann wave-front sensor,” Opt. Lett. 17, 1737–1739 (1992).
[CrossRef] [PubMed]

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

1991 (2)

D. M. Winker, “Effect of finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A 8, 1568–1573 (1991).
[CrossRef]

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

1980 (2)

1976 (2)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
[CrossRef]

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

1966 (1)

Alexander, P.

P. Alexander, L. F. Gladden, “How to create an X-window interface to GNUplot and FORTRAN programs using the Tcl/Tk toolkit,” Comput. Phys. 9, 57–64 (1995).

Anuskiewicz, J.

F. J. Roddier, J. Anuskiewicz, J. E. Graves, M. J. Northcott, C. A. Roddier, “Adaptive optics at the University of Hawaii I: current performance at the telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 2–9 (1994).
[CrossRef]

Barbier, P. R.

P. R. Barbier, P. Polak-Dingels, D. W. Rush, D. M. Rosser, G. L. Burdge, R. W. Barnett, “A terrestrial laser communication link at 1.3 μm with quadrature amplitude modulation,” in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed., Proc. SPIE2699, 103–113 (1996).
[CrossRef]

Barclay, H. T.

Barnett, R. W.

P. R. Barbier, P. Polak-Dingels, D. W. Rush, D. M. Rosser, G. L. Burdge, R. W. Barnett, “A terrestrial laser communication link at 1.3 μm with quadrature amplitude modulation,” in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed., Proc. SPIE2699, 103–113 (1996).
[CrossRef]

Beland, R. R.

R. R. Beland, “Propagation through atmospheric optical turbulence,” in Atmospheric Propagation of Radiation, F. G. Smith, ed., Vol. 2, of The Infrared and Electro-Optics Systems Handbook Series (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), Chap. 2, Subsec. 2.4.2.

Bester, M.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Burdge, G. L.

P. R. Barbier, P. Polak-Dingels, D. W. Rush, D. M. Rosser, G. L. Burdge, R. W. Barnett, “A terrestrial laser communication link at 1.3 μm with quadrature amplitude modulation,” in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed., Proc. SPIE2699, 103–113 (1996).
[CrossRef]

Butts, R. R.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

Cole, R.

D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
[CrossRef]

Danchi, W. C.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Dayton, D.

Degiacomi, C. G.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

DeMiranda, E. C.

D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
[CrossRef]

Earley, P. L.

D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
[CrossRef]

Fried, D. L.

Gladden, L. F.

P. Alexander, L. F. Gladden, “How to create an X-window interface to GNUplot and FORTRAN programs using the Tcl/Tk toolkit,” Comput. Phys. 9, 57–64 (1995).

Gonglewski, J.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985, Sec. 3.3.

Graves, J. E.

F. Roddier, M. J. Northcott, J. E. Graves, D. L. McKenna, D. Roddier, “One-dimensional spectra of turbulence-induced Zernike aberrations: time-delay and isoplanicity error in partial adaptive compensation,” J. Opt. Soc. Am. A 10, 957–965 (1993).
[CrossRef]

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

F. J. Roddier, J. Anuskiewicz, J. E. Graves, M. J. Northcott, C. A. Roddier, “Adaptive optics at the University of Hawaii I: current performance at the telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 2–9 (1994).
[CrossRef]

Greenhill, L. J.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Herrmann, J.

Hogge, C. B.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

Humphreys, R. A.

Luthra, D.

D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
[CrossRef]

McCullagh, M. J.

D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
[CrossRef]

McKenna, D. L.

Noll, R. J.

Northcott, M.

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Northcott, M. J.

F. Roddier, M. J. Northcott, J. E. Graves, D. L. McKenna, D. Roddier, “One-dimensional spectra of turbulence-induced Zernike aberrations: time-delay and isoplanicity error in partial adaptive compensation,” J. Opt. Soc. Am. A 10, 957–965 (1993).
[CrossRef]

F. J. Roddier, J. Anuskiewicz, J. E. Graves, M. J. Northcott, C. A. Roddier, “Adaptive optics at the University of Hawaii I: current performance at the telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 2–9 (1994).
[CrossRef]

Pierson, B.

Polak-Dingels, P.

P. R. Barbier, P. Polak-Dingels, D. W. Rush, D. M. Rosser, G. L. Burdge, R. W. Barnett, “A terrestrial laser communication link at 1.3 μm with quadrature amplitude modulation,” in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed., Proc. SPIE2699, 103–113 (1996).
[CrossRef]

Price, T. R.

Primmerman, C. A.

Roddier, C. A.

F. J. Roddier, J. Anuskiewicz, J. E. Graves, M. J. Northcott, C. A. Roddier, “Adaptive optics at the University of Hawaii I: current performance at the telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 2–9 (1994).
[CrossRef]

Roddier, D.

Roddier, F.

F. Roddier, M. J. Northcott, J. E. Graves, D. L. McKenna, D. Roddier, “One-dimensional spectra of turbulence-induced Zernike aberrations: time-delay and isoplanicity error in partial adaptive compensation,” J. Opt. Soc. Am. A 10, 957–965 (1993).
[CrossRef]

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Chap. 5, p. 353.

Roddier, F. J.

F. J. Roddier, J. Anuskiewicz, J. E. Graves, M. J. Northcott, C. A. Roddier, “Adaptive optics at the University of Hawaii I: current performance at the telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 2–9 (1994).
[CrossRef]

Roggemmann, M.

Rosser, D. M.

P. R. Barbier, P. Polak-Dingels, D. W. Rush, D. M. Rosser, G. L. Burdge, R. W. Barnett, “A terrestrial laser communication link at 1.3 μm with quadrature amplitude modulation,” in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed., Proc. SPIE2699, 103–113 (1996).
[CrossRef]

Rush, D. W.

P. R. Barbier, P. Polak-Dingels, D. W. Rush, D. M. Rosser, G. L. Burdge, R. W. Barnett, “A terrestrial laser communication link at 1.3 μm with quadrature amplitude modulation,” in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed., Proc. SPIE2699, 103–113 (1996).
[CrossRef]

Silbaugh, E. E.

Southwell, W.

Spielbusch, B.

Symth, P. P.

D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
[CrossRef]

Townes, C. H.

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991), p. 33.

Welsh, B. B.

B. B. Welsh, Practical Programming in Tcl and Tk, (Prentice-Hall, Upper Saddle River, N.J., 1995).

Welsh, B. M.

Wesseling, P.

P. Wesseling, “Linear multigrid methods,” in Multigrid Methods, S. F. McCormick, ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1987), Chap. 1.
[CrossRef]

Winker, D. M.

Wisely, D. R.

D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
[CrossRef]

Zollars, B. G.

Appl. Opt. (1)

Astrophys. J. (1)

M. Bester, W. C. Danchi, C. G. Degiacomi, L. J. Greenhill, C. H. Townes, “Atmospheric fluctuations: empirical structure functions and projected performance of future instruments,” Astrophys. J. 392, 357–374 (1992).
[CrossRef]

Comput. Phys. (1)

P. Alexander, L. F. Gladden, “How to create an X-window interface to GNUplot and FORTRAN programs using the Tcl/Tk toolkit,” Comput. Phys. 9, 57–64 (1995).

IEEE Trans. Antennas Propag. (1)

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (3)

Opt. Lett. (1)

Publ. Astron. Soc. Pac. (1)

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Other (12)

F. J. Roddier, J. Anuskiewicz, J. E. Graves, M. J. Northcott, C. A. Roddier, “Adaptive optics at the University of Hawaii I: current performance at the telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 2–9 (1994).
[CrossRef]

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Chap. 5, p. 353.

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991), p. 33.

R. R. Beland, “Propagation through atmospheric optical turbulence,” in Atmospheric Propagation of Radiation, F. G. Smith, ed., Vol. 2, of The Infrared and Electro-Optics Systems Handbook Series (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), Chap. 2, Subsec. 2.4.2.

LINUX is a UNIX-line operating system for Intel-based personal computers. It is freely distributed under the terms of the GNU General Public License. More information can be found at the LINUX Documentation Project web site: http://confused.ume.maine.edu/mdw/ .

Ref. 10, Chap. 2, Subsec. 2.3.4.

P. Wesseling, “Linear multigrid methods,” in Multigrid Methods, S. F. McCormick, ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1987), Chap. 1.
[CrossRef]

B. B. Welsh, Practical Programming in Tcl and Tk, (Prentice-Hall, Upper Saddle River, N.J., 1995).

P. R. Barbier, P. Polak-Dingels, D. W. Rush, D. M. Rosser, G. L. Burdge, R. W. Barnett, “A terrestrial laser communication link at 1.3 μm with quadrature amplitude modulation,” in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed., Proc. SPIE2699, 103–113 (1996).
[CrossRef]

D. R. Wisely, M. J. McCullagh, P. L. Earley, P. P. Symth, D. Luthra, E. C. DeMiranda, R. Cole, “4-km terrestrial line-of-sight optical free-space link operating at 155 Mbit/s,” in Free-Space Laser Communication Technologies VI, G. S. Mecherle, ed., Proc. SPIE2123, 108–119 (1994).
[CrossRef]

Ref. 21, Subsec. 8.4.2.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985, Sec. 3.3.

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Figures (10)

Fig. 1
Fig. 1

Schematic of the wave-front sensor used to gather horizontal-path turbulence data. WFOV, wide field of view; MLM, monolithic lenslet module.

Fig. 2
Fig. 2

Hartmann spot array with subaperture boundaries. The intensity statistics were computed by summation of all pixel values within each subaperture.

Fig. 3
Fig. 3

Intensity histogram showing variations in the shape of distribution-normalized intensity.

Fig. 4
Fig. 4

Left, Hartmann spot image from a single frame of data; right, wave-front reconstruction with low-intensity subapertures thresholded.

Fig. 5
Fig. 5

Histogram of opd measurements of all subapertures in a data run.

Fig. 6
Fig. 6

PSD’s of horizontal-path turbulence for 1-km (upper) and 2.5-km (lower) paths. Left, taken approximately 1 h before sunset; right, taken 1 h after sunset.

Fig. 7
Fig. 7

Summary of all slope values for inertial scale frequencies of the PSD. The mean is -1.71, and the standard deviation is 0.15.

Fig. 8
Fig. 8

Proportion of opd variance contained by the Zernike polynomial expansion. Left, proportion of variance explained by the first 11 Zernike terms; right, proportion of variance explained by 22 Zernike terms.

Fig. 9
Fig. 9

Development of Strehl ratio calculation for horizontal-beam propagation. (a), total PSD, PSD(f), and some of its modal components; (b), temporal variance, as the integral of the PSD, plotted as a function of the various modal sums.

Fig. 10
Fig. 10

Temporal Strehl ratio as a function of the residual temporal variance and the total variance in the wave front.

Tables (2)

Tables Icon

Table 1 Summary of Hartmann Spot Data Sets Acquired during the Two Field Trials 12–15 August 1996 and 28–31 October 1996

Tables Icon

Table 2 Frequency of Obtaining the Indicated Strehl Ratio for a 1-km Horizontal Propagation Path with Correction by 22 Zernike Modes

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

N D / r 0 2 ,
r 0 = 0.423 k 2 sec β 0 L   C n 2 h h L 5 / 3 d h - 3 / 5 = 3.02 C n 2 Lk 2 - 3 / 5 ,
σ I 2 = exp 4 σ χ 2 - 1 .
OPD x ,   y ,   t = n   a n t Z n x ,   y .
PSD x ,   y ,   f = | OPD x ,   y ,   f | 2 = n   a f f Z n x ,   y 2 ,
PSD f = 1 A     PSD x ,   y ,   f d x d y = 1 A     n n   a n f a n * f × Z n x ,   y Z n x ,   y d x d y = n   | a n f | 2 .
σ 2 =   PSD f d f .
Δ σ k 2 f = σ OPD 2 - 0 f n = 1 k   | a n f | 2 d f ,
σ OPD 2 f = 0 f PSD u d u .
σ ϕ 2 = 2 π λ 2 σ OPD 2 .
Strehl f = exp Δ σ ϕ 2 f = exp σ ϕ 2 - σ ϕ 2 f .

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