Abstract

Tilt compensation performance is generally suboptimal when phase measurements from natural or laser guide stars are used as the conjugate phase in an adaptive optics system. Optimal compensation is obtained when the conjugate-phase coefficients are estimated from beacon measurements, given knowledge of the correlation between the on-axis object phase and the beacon measurements. We apply optimal compensation theory to tilt correction for the case of an off-axis beacon. Because off-axis higher-order modes are correlated with the on-axis tilt components, a performance gain can be realized when the tilt estimator includes higher-order modal measurements. For natural guide star compensation, it is shown that equivalent tilt compensation can be achieved at beacon offsets that are three times larger when higher-order modes through Zernike 15 are used in the tilt estimator. For a laser guide star, although tilt information cannot be measured directly because of beam reciprocity, off-axis higher-order modal measurements can be used to estimate tilt components, leading to a maximum Strehl ratio of approximately 0.3 for the relative aperture diameter D/ r0 = 4 and the relative turbulence outer scale L0/D = 10.

© 1998 Optical Society of America

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  2. L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
    [CrossRef]
  3. C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
    [CrossRef]
  4. 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]
  5. C. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
    [CrossRef]
  6. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  7. P. H. Hu, J. Stone, T. Stanley, “Application of Zernike polynomials to atmospheric propagation problems,” J. Opt. Soc. Am. A 6, 1595–1608 (1989).
    [CrossRef]
  8. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  17. G. A. Tyler, “Wave-front compensation for imaging with off-axis guide stars,” J. Opt. Soc. Am. A 11, 339–346 (1994).
    [CrossRef]
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    [CrossRef]
  19. J. Stone, P. H. Hu, S. P. Mills, S. Ma, “Anisoplanatic effects in finite-aperture optical systems,” J. Opt. Soc. Am. A 11, 347–357 (1994).
    [CrossRef]
  20. G. Molodij, G. Rousset, “Angular correlation of Zernike polynomials for a laser guide star in adaptive optics,” J. Opt. Soc. Am. A 14, 1949–1966 (1997).
    [CrossRef]
  21. M. R. Whiteley, B. M. Welsh, M. C. Roggemann, “Optimal modal wave-front compensation for anisoplanatism in adaptive optics,” J. Opt. Soc. Am. A 15, 2097–2106 (1998).
    [CrossRef]
  22. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Upper Saddle River, N.J., 1993).
  23. M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).
  24. M. R. Whiteley, M. C. Roggemann, B. M. Welsh, “Temporal properties of the Zernike expansion coefficients of turbulence-induced phase aberrations for aperture and source motion,” J. Opt. Soc. Am. A 15, 993–1005 (1998).
    [CrossRef]
  25. J. D. H. Pilkington, “Artificial guide stars for adaptive imaging,” Nature (London) 330, 116 (1987).
    [CrossRef]
  26. R. Q. Fugate, “Laser beacon adaptive optics,” Opt. Photon. News 9, 14–19 (1993).
    [CrossRef]
  27. M. S. Belen’kii, “Fundamental limitation in adaptive optics: how to eliminate it? A full aperture tilt measurement technique with a laser guide star,” in Adaptive Optics in Astromony, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 321–323 (1994).
  28. M. S. Belen’kii, “Full aperture tilt measurement technique with a laser guide star,” in Atmospheric Propagations and Remote Sensing IV, J. C. Dainty, ed., Proc. SPIE2471, 289–300 (1995).
  29. M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 206–217 (1996).
  30. M. S. Belen’kii, “Multiple aperture averaging technique for measuring full aperture tilt with a laser guide star,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 101–112 (1997).
  31. R. Ragazzoni, S. Esposito, E. Marchetti, “Auxilary telescopes for the absolute tip-tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).
  32. R. Ragazzoni, “Absolute tip-tilt determination with laser beacons,” Astron. Astrophys. 305, L13–L16 (1996).
  33. D. G. Sandler, S. Stahl, J. R. P. Angel, M. Lloyd-Hart, D. McCarthy, “Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes,” J. Opt. Soc. Am. A 11, 925–945 (1994).
    [CrossRef]
  34. G. C. Valley, S. M. Wandzura, “Spatial correlation of phase-expansion coefficients for propagation through atmospheric turbulence,” J. Opt. Soc. Am. 69, 712–717 (1979).
    [CrossRef]
  35. R. V. Hogg, A. T. Craig, Introduction to Mathematical Statistics, 5th ed. (Macmillan, New York, 1995).
  36. N. Takato, I. Yamaguchi, “Spatial correlation of Zernike phase-expansion coefficients for atmospheric turbulence with finite outer scale,” J. Opt. Soc. Am. A 12, 958–963 (1995).
    [CrossRef]
  37. W. H. Press, Numerical Recipes in C: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992).
  38. R. Avila, A. Ziad, J. Borgnino, F. Martin, A. Agabi, “Theoretical spatiotemporal analysis of angle of arrival induced by atmospheric turbulence as observed with a grating scale monitor experiment,” J. Opt. Soc. Am. A 14, 3070–3082 (1997).
    [CrossRef]

1998 (2)

1997 (2)

1996 (1)

R. Ragazzoni, “Absolute tip-tilt determination with laser beacons,” Astron. Astrophys. 305, L13–L16 (1996).

1995 (3)

1994 (3)

1993 (1)

R. Q. Fugate, “Laser beacon adaptive optics,” Opt. Photon. News 9, 14–19 (1993).
[CrossRef]

1991 (3)

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion 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]

B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
[CrossRef]

1990 (2)

C. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[CrossRef]

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

1989 (1)

1987 (2)

J. D. H. Pilkington, “Artificial guide stars for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
[CrossRef]

1985 (1)

R. Foy, A. Labeyrie, “Feasibility of adaptive telescopes with laser probe,” Astron. Astophys. 152, 129–131 (1985).

1982 (1)

1979 (1)

1978 (1)

1976 (1)

1975 (1)

1966 (1)

Agabi, A.

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]

Angel, J. R. P.

Avila, R.

Barclay, H. T.

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

Belen’kii, M. S.

M. S. Belen’kii, “Full aperture tilt measurement technique with a laser guide star,” in Atmospheric Propagations and Remote Sensing IV, J. C. Dainty, ed., Proc. SPIE2471, 289–300 (1995).

M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 206–217 (1996).

M. S. Belen’kii, “Fundamental limitation in adaptive optics: how to eliminate it? A full aperture tilt measurement technique with a laser guide star,” in Adaptive Optics in Astromony, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 321–323 (1994).

M. S. Belen’kii, “Multiple aperture averaging technique for measuring full aperture tilt with a laser guide star,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 101–112 (1997).

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]

Borgnino, J.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

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]

Craig, A. T.

R. V. Hogg, A. T. Craig, Introduction to Mathematical Statistics, 5th ed. (Macmillan, New York, 1995).

Dai, G.

Dryden, G.

Esposito, S.

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxilary telescopes for the absolute tip-tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

Foy, R.

R. Foy, A. Labeyrie, “Feasibility of adaptive telescopes with laser probe,” Astron. Astophys. 152, 129–131 (1985).

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, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
[CrossRef]

D. L. Fried, “Varieties of isoplanatism,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. SPIE75, 20–29 (1976).

Fugate, R. Q.

R. Q. Fugate, “Laser beacon adaptive optics,” Opt. Photon. News 9, 14–19 (1993).
[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]

Gardner, C. S.

B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
[CrossRef]

C. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[CrossRef]

L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
[CrossRef]

Hogg, R. V.

R. V. Hogg, A. T. Craig, Introduction to Mathematical Statistics, 5th ed. (Macmillan, New York, 1995).

Hu, P. H.

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Upper Saddle River, N.J., 1993).

Korff, D.

Labeyrie, A.

R. Foy, A. Labeyrie, “Feasibility of adaptive telescopes with laser probe,” Astron. Astophys. 152, 129–131 (1985).

Leavitt, R. P.

Lloyd-Hart, M.

Ma, S.

Marchetti, E.

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxilary telescopes for the absolute tip-tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

Markey, J. K.

Martin, F.

McCarthy, D.

Mills, S. P.

Molodij, G.

Murphy, D. V.

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

Pilkington, J. D. H.

J. D. H. Pilkington, “Artificial guide stars for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

Press, W. H.

W. H. Press, Numerical Recipes in C: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992).

Primmerman, C. A.

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

Ragazzoni, R.

R. Ragazzoni, “Absolute tip-tilt determination with laser beacons,” Astron. Astrophys. 305, L13–L16 (1996).

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxilary telescopes for the absolute tip-tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

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]

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Roggemann, M. C.

Rousset, G.

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]

Sandler, D. G.

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, Berlin, 1994).

Stahl, S.

Stanley, T.

Stone, J.

Takato, N.

Thompson, L. A.

C. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[CrossRef]

L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
[CrossRef]

Tyler, G. A.

G. A. Tyler, “Wave-front compensation for imaging with off-axis guide stars,” J. Opt. Soc. Am. A 11, 339–346 (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]

Valley, G. C.

Wandzura, S. M.

Wang, J. Y.

Welsh, B.

M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Welsh, B. M.

Whiteley, M. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

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]

Yamaguchi, I.

Ziad, A.

Zollars, B. G.

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

Astron. Astophys. (1)

R. Foy, A. Labeyrie, “Feasibility of adaptive telescopes with laser probe,” Astron. Astophys. 152, 129–131 (1985).

Astron. Astrophys. (1)

R. Ragazzoni, “Absolute tip-tilt determination with laser beacons,” Astron. Astrophys. 305, L13–L16 (1996).

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (11)

G. Dai, “Modal compensation of atmospheric turbulence with the use of Zernike polynomials and Karhunen-Loeve functions,” J. Opt. Soc. Am. A 12, 2182–2193 (1995).
[CrossRef]

G. A. Tyler, “Wave-front compensation for imaging with off-axis guide stars,” J. Opt. Soc. Am. A 11, 339–346 (1994).
[CrossRef]

J. Stone, P. H. Hu, S. P. Mills, S. Ma, “Anisoplanatic effects in finite-aperture optical systems,” J. Opt. Soc. Am. A 11, 347–357 (1994).
[CrossRef]

D. G. Sandler, S. Stahl, J. R. P. Angel, M. Lloyd-Hart, D. McCarthy, “Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes,” J. Opt. Soc. Am. A 11, 925–945 (1994).
[CrossRef]

M. R. Whiteley, M. C. Roggemann, B. M. Welsh, “Temporal properties of the Zernike expansion coefficients of turbulence-induced phase aberrations for aperture and source motion,” J. Opt. Soc. Am. A 15, 993–1005 (1998).
[CrossRef]

M. R. Whiteley, B. M. Welsh, M. C. Roggemann, “Optimal modal wave-front compensation for anisoplanatism in adaptive optics,” J. Opt. Soc. Am. A 15, 2097–2106 (1998).
[CrossRef]

G. Molodij, G. Rousset, “Angular correlation of Zernike polynomials for a laser guide star in adaptive optics,” J. Opt. Soc. Am. A 14, 1949–1966 (1997).
[CrossRef]

R. Avila, A. Ziad, J. Borgnino, F. Martin, A. Agabi, “Theoretical spatiotemporal analysis of angle of arrival induced by atmospheric turbulence as observed with a grating scale monitor experiment,” J. Opt. Soc. Am. A 14, 3070–3082 (1997).
[CrossRef]

P. H. Hu, J. Stone, T. Stanley, “Application of Zernike polynomials to atmospheric propagation problems,” J. Opt. Soc. Am. A 6, 1595–1608 (1989).
[CrossRef]

B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
[CrossRef]

N. Takato, I. Yamaguchi, “Spatial correlation of Zernike phase-expansion coefficients for atmospheric turbulence with finite outer scale,” J. Opt. Soc. Am. A 12, 958–963 (1995).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxilary telescopes for the absolute tip-tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

Nature (London) (4)

J. D. H. Pilkington, “Artificial guide stars for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
[CrossRef]

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion 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]

Opt. Eng. (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Opt. Photon. News (1)

R. Q. Fugate, “Laser beacon adaptive optics,” Opt. Photon. News 9, 14–19 (1993).
[CrossRef]

Proc. IEEE (1)

C. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[CrossRef]

Other (11)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, Berlin, 1994).

D. L. Fried, “Varieties of isoplanatism,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. SPIE75, 20–29 (1976).

M. S. Belen’kii, “Fundamental limitation in adaptive optics: how to eliminate it? A full aperture tilt measurement technique with a laser guide star,” in Adaptive Optics in Astromony, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 321–323 (1994).

M. S. Belen’kii, “Full aperture tilt measurement technique with a laser guide star,” in Atmospheric Propagations and Remote Sensing IV, J. C. Dainty, ed., Proc. SPIE2471, 289–300 (1995).

M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 206–217 (1996).

M. S. Belen’kii, “Multiple aperture averaging technique for measuring full aperture tilt with a laser guide star,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 101–112 (1997).

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Upper Saddle River, N.J., 1993).

M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

R. V. Hogg, A. T. Craig, Introduction to Mathematical Statistics, 5th ed. (Macmillan, New York, 1995).

W. H. Press, Numerical Recipes in C: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1992).

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