Abstract

In experimental measurements of the bit-error rate for a laser communication system, we show improved performance with the implementation of low-order (tip/tilt) adaptive optics in a free-space link. With simulated atmospheric tilt injected by a conventional piezoelectric tilt mirror, an adaptive optics system with a Xinetics tilt mirror was used in a closed loop. The laboratory experiment replicated a monostatic propagation with a cooperative wave front beacon at the receiver. Owing to constraints in the speed of the processing hardware, the data is scaled to represent an actual propagation of a few kilometers under moderate scintillation conditions. We compare the experimental data and indirect measurement of the bit-error rate before correction and after correction, with a theoretical prediction.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Scintillation model for a satellite communication link at large zenith angles,” Opt. Eng. 39, 3272–3280 (2000).
    [CrossRef]
  9. R. J. Hill, R. G. Frehlich, “Probability distribution of irradiance for the onset of strong scintillation,” J. Opt. Soc. Am. A 14, 1530–1540 (1997).
    [CrossRef]
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    [CrossRef]
  14. M. Nakagami, “The m distribution — a general formula of intensity distribution of rapid fading,” in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, ed. (Pergamon, New York, 1960), pp. 3–36.
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    [CrossRef]
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2002 (1)

2001 (1)

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[CrossRef]

2000 (1)

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Scintillation model for a satellite communication link at large zenith angles,” Opt. Eng. 39, 3272–3280 (2000).
[CrossRef]

1999 (1)

1997 (2)

1995 (2)

H. Ansari, L. H. Roberts, “Charge-coupled device imaging system for precision beam steering in laser communications,” Opt. Eng. 34, 3261–3264 (1995).
[CrossRef]

L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34, 7742–7751, (1995).
[CrossRef] [PubMed]

1994 (3)

1993 (1)

1987 (1)

J. H. Churnside, R. J. Hill, “Probability density of irradiance scintillations for strong path-integrated refractive turbulence, J. Opt. Soc. Am. A 4, 723–733 (1987).
[CrossRef]

1983 (1)

1981 (1)

1976 (1)

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[CrossRef]

Andrews, L. C.

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Scintillation model for a satellite communication link at large zenith angles,” Opt. Eng. 39, 3272–3280 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system: errata,” Appl. Opt. 36, 6068 (1997).
[CrossRef]

L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34, 7742–7751, (1995).
[CrossRef] [PubMed]

W. B. Miller, J. C. Ricklin, L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A 11, 2719–2726 (1994).
[CrossRef]

R. L. Phillips, L. C. Andrews, “Measured statistics of laser-light scattering in atmospheric turbulence,” J. Opt. Soc. Am. 71, 1440–1445 (1981).
[CrossRef]

L. C. Andrews, R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, Bellingham, Wash., 1998).

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, Bellingham, Wash., 2001).
[CrossRef]

Ansari, H.

H. Ansari, L. H. Roberts, “Charge-coupled device imaging system for precision beam steering in laser communications,” Opt. Eng. 34, 3261–3264 (1995).
[CrossRef]

Barakat, R.

Bracher, C.

Churnside, J. H.

J. H. Churnside, R. J. Hill, “Probability density of irradiance scintillations for strong path-integrated refractive turbulence, J. Opt. Soc. Am. A 4, 723–733 (1987).
[CrossRef]

Flatté, S. M.

Frehlich, R. G.

R. J. Hill, R. G. Frehlich, “Probability distribution of irradiance for the onset of strong scintillation,” J. Opt. Soc. Am. A 14, 1530–1540 (1997).
[CrossRef]

R. J. Hill, R. G. Frehlich, W. D. Otto, “The probability distribution of irradiance scintillation,” (National Oceanic and Atmospheric Administration Environmental Research Laboratories, Boulder, Colo., 1996).

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communications, 2nd ed. (Wiley, New York, 1995).

Hill, R. J.

R. J. Hill, R. G. Frehlich, “Probability distribution of irradiance for the onset of strong scintillation,” J. Opt. Soc. Am. A 14, 1530–1540 (1997).
[CrossRef]

J. H. Churnside, R. J. Hill, “Probability density of irradiance scintillations for strong path-integrated refractive turbulence, J. Opt. Soc. Am. A 4, 723–733 (1987).
[CrossRef]

R. J. Hill, R. G. Frehlich, W. D. Otto, “The probability distribution of irradiance scintillation,” (National Oceanic and Atmospheric Administration Environmental Research Laboratories, Boulder, Colo., 1996).

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Scintillation model for a satellite communication link at large zenith angles,” Opt. Eng. 39, 3272–3280 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, Bellingham, Wash., 2001).
[CrossRef]

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communications, 2nd ed. (Wiley, New York, 1995).

McKinley, W. G.

Miller, W. B.

Nakagami, M.

M. Nakagami, “The m distribution — a general formula of intensity distribution of rapid fading,” in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, ed. (Pergamon, New York, 1960), pp. 3–36.

Noll, R. J.

Otto, W. D.

R. J. Hill, R. G. Frehlich, W. D. Otto, “The probability distribution of irradiance scintillation,” (National Oceanic and Atmospheric Administration Environmental Research Laboratories, Boulder, Colo., 1996).

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Scintillation model for a satellite communication link at large zenith angles,” Opt. Eng. 39, 3272–3280 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system: errata,” Appl. Opt. 36, 6068 (1997).
[CrossRef]

L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34, 7742–7751, (1995).
[CrossRef] [PubMed]

R. L. Phillips, L. C. Andrews, “Measured statistics of laser-light scattering in atmospheric turbulence,” J. Opt. Soc. Am. 71, 1440–1445 (1981).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, Bellingham, Wash., 2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, Bellingham, Wash., 1998).

Ricklin, J. C.

Roberts, L. H.

H. Ansari, L. H. Roberts, “Charge-coupled device imaging system for precision beam steering in laser communications,” Opt. Eng. 34, 3261–3264 (1995).
[CrossRef]

Sasiela, R. J.

Shelton, J. D.

R. J. Sasiela, J. D. Shelton, “Transverse spectral filtering and Mellin transform techniques applied to the effect of outer scale on tilt and tilt anisoplanatism,” J. Opt. Soc. Am. A 10, 646–659 (1993).
[CrossRef]

R. J. Sasiela, J. D. Shelton, “Guide star system considerations,” in Adaptive Optics Engineering Handbook, R. K. Tyson, ed., (Marcel Dekker, New York, 2000), Chap. 3.

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), translated by R. A. Silverman.

Tyson, R. K.

Wang, G. -Yu

Yu, P. T.

Yura, H. T.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (8)

Opt. Eng. (3)

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[CrossRef]

H. Ansari, L. H. Roberts, “Charge-coupled device imaging system for precision beam steering in laser communications,” Opt. Eng. 34, 3261–3264 (1995).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Scintillation model for a satellite communication link at large zenith angles,” Opt. Eng. 39, 3272–3280 (2000).
[CrossRef]

Other (8)

L. C. Andrews, R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, Bellingham, Wash., 1998).

R. M. Gagliardi, S. Karp, Optical Communications, 2nd ed. (Wiley, New York, 1995).

R. J. Hill, R. G. Frehlich, W. D. Otto, “The probability distribution of irradiance scintillation,” (National Oceanic and Atmospheric Administration Environmental Research Laboratories, Boulder, Colo., 1996).

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, Bellingham, Wash., 2001).
[CrossRef]

M. Nakagami, “The m distribution — a general formula of intensity distribution of rapid fading,” in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, ed. (Pergamon, New York, 1960), pp. 3–36.

R. J. Sasiela, J. D. Shelton, “Guide star system considerations,” in Adaptive Optics Engineering Handbook, R. K. Tyson, ed., (Marcel Dekker, New York, 2000), Chap. 3.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), translated by R. A. Silverman.

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, Boston, Mass., 1998).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the adaptive optics lasercom experiment. The long propagation path is simulated by a diverging lens and a semitransparent screen to provide the proper size scintillation speckles across the receiver aperture. The screen is physically close to the aberration generator with the propagation path of the “speckled” tilting beam approximately 1.6 m to the receiver. The 4-F pupil relay eliminates beam walk (translation) over the tilt mirrors.

Fig. 2
Fig. 2

Intensity at the receiver versus time. (a), with the adaptive optics off; (b), is with the tip/tilt system on. These are not simultaneous measurements; there is no correlation between the time scales. The intensities were normalized to their mean over a data collection period of a few minutes (approximately 100,000 counts). A drift of the signal of up to 10% was noticed over many data collection sets as evident in (b). This drift affects the central portion of the PDF and does not noticeably affect the overlapping area of the PDF under the receiver electronic noise curves on Figs. 3 and 4.

Fig. 3
Fig. 3

PDF for the measured data with the adaptive optics system off. The input data is shown in Fig. 2(a). The electronic noise curve, from Eq. (1) is magnified 1000× for clarity. The solid curve is a lognormal distribution with the same variance as the data. The dashed curve is the Γ-Γ distribution. The result is a BER of 5.2 × 10-6.

Fig. 4
Fig. 4

PDF for the measured data with the adaptive optics system on. The input data is shown in Fig. 2(b). The electronic noise curve, from Eq. (1), is magnified 1000× for clarity. The curve is a Γ-Γ distribution with the same variance as the data. The result is a BER of 1.7 × 10-8.

Equations (11)

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Ps, SNR=12erfcis22σN,
BEROOK=120pIserfcSNRs22isds.
pIs=2αβα+β/2ΓαΓβissisα+β2-1 Kα-β2αβsis.
α=1/σx2; σx2=expσln x2-1; σln x2=0.20σ121+0.19σ112/57/6,
β=1/σy2; σy2=expσln y2-1; σln y2=0.20σ121+0.23σ112/55/6,
σ12=2.6062π k2Cn202π0L-kκ2sinLκ2k×κ-8/31-i=1N Fiκ, D, ϕdκ dϕ,
Feven m,nκ, D, ϕ=2n+1×2Jn+1κD/2κD/22 cos2mϕ
Fodd m,nκ, D, ϕ=2n+1×2Jn+1κD/2κD/22 sin2mϕ,
Fm=0,nκ, D, ϕ=n+12Jn+1κD/2κD/22.
1-222J2κD/2κD/22 cos2ϕ,
1-222J2κD/2κD/22.

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