Abstract

An application of far-field optimization to dynamic compensation of atmospheric turbulence is reported. The new method eliminates the need for a wave-front sensor, which is required in conventional adaptive-optical systems, and utilizes simple measures of the point-spread function as figures of merit. Far-field optimization employs the simplex algorithm to configure a segmented or continuous (rubber) deformable mirror iteratively to a state that is conjugate to the local atmospheric turbulence. We achieve significant adaptive-optics correction with far-field optimization in the presence of both static and dynamic Kolmogorov turbulence. Computer simulations are used to predict the far-field performance in terms of the wavelength-dependent turbulence strength, the spatial resolution of adaptive mirrors, and the speed of drifting turbulence with respect to the temporal bandwidth of adaptive optics. Far-field optimization yields better performance with a coarser segmented mirror in the presence of dynamic atmospheric turbulence because of the reduced burden in the optimization process with fewer actuators. There may be a trade-off in terms of efficiency and robustness between segmented adaptive optics and a high-quality deformable mirror.

© 1994 Optical Society of America

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References

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  1. J. H. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
    [CrossRef]
  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]
  3. N. C. Mehta, C. W. Allen, “Remote alignment of segmented mirrors with far-field optimization,” Appl. Opt. 31, 6510–6518 (1992).
    [CrossRef] [PubMed]
  4. N. C. Mehta, C. W. Allen, “Segmented mirror alignment with far-field optimization in the presence of atmospheric turbulence,” Appl. Opt. 32, 2664–2673 (1993).
    [CrossRef] [PubMed]
  5. N. C. Mehta, “Remote alignment of adaptive otpical systems with far-field optimization,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere II, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1408, 96–111 (1991).
    [CrossRef]
  6. J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
    [CrossRef]
  7. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.
  8. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 386.
  9. B. J. Herman, L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1221, 183–192 (1990).
    [CrossRef]
  10. D. L. Fried, “Statistics of a geometric representation of wave front distortion,”J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]
  11. R. W. Sinnott, “The Keck Telescope’s giant eye,” Sky Telescope 80(1), 15–22 (1990).
  12. D. S. Acton, R. C. Smithson, “Solar imaging with a segmented adaptive mirror,” Appl. Opt. 31, 3161–3169 (1992).
    [CrossRef] [PubMed]
  13. N. C. Mehta, “GRAND: a 4-D wave optics code for atmospheric laser propagation,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, 398–409 (1991).
    [CrossRef]

1993 (1)

1992 (2)

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]

R. W. Sinnott, “The Keck Telescope’s giant eye,” Sky Telescope 80(1), 15–22 (1990).

1978 (1)

J. H. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

1965 (2)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

D. L. Fried, “Statistics of a geometric representation of wave front distortion,”J. Opt. Soc. Am. 55, 1427–1435 (1965).
[CrossRef]

Acton, D. S.

Allen, C. W.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

Fried, D. L.

Gardner, C. S.

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]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 386.

Hardy, J. H.

J. H. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

Herman, B. J.

B. J. Herman, L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1221, 183–192 (1990).
[CrossRef]

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Mehta, N. C.

N. C. Mehta, C. W. Allen, “Segmented mirror alignment with far-field optimization in the presence of atmospheric turbulence,” Appl. Opt. 32, 2664–2673 (1993).
[CrossRef] [PubMed]

N. C. Mehta, C. W. Allen, “Remote alignment of segmented mirrors with far-field optimization,” Appl. Opt. 31, 6510–6518 (1992).
[CrossRef] [PubMed]

N. C. Mehta, “Remote alignment of adaptive otpical systems with far-field optimization,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere II, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1408, 96–111 (1991).
[CrossRef]

N. C. Mehta, “GRAND: a 4-D wave optics code for atmospheric laser propagation,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, 398–409 (1991).
[CrossRef]

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

Sinnott, R. W.

R. W. Sinnott, “The Keck Telescope’s giant eye,” Sky Telescope 80(1), 15–22 (1990).

Smithson, R. C.

Strugala, L. A.

B. J. Herman, L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1221, 183–192 (1990).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

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]

Vettering, W.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

Welsh, B. M.

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]

Appl. Opt. (3)

Comput. J. (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (2)

J. H. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[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]

Sky Telescope (1)

R. W. Sinnott, “The Keck Telescope’s giant eye,” Sky Telescope 80(1), 15–22 (1990).

Other (5)

N. C. Mehta, “GRAND: a 4-D wave optics code for atmospheric laser propagation,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, 398–409 (1991).
[CrossRef]

N. C. Mehta, “Remote alignment of adaptive otpical systems with far-field optimization,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere II, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1408, 96–111 (1991).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 386.

B. J. Herman, L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1221, 183–192 (1990).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Optical layout of a generic adaptive-optical system. A figure of merit based on far-field intensity provides feedback control for the adaptive mirror. When the adaptive mirror is in a state that is conjugate to the turbulence phase, the corrected wave front is flat and gives diffraction-limited far-field performance.

Fig. 2
Fig. 2

Block diagram of far-field optimization. Starting with N + 1 initial conditions, the simplex algorithm uses a figure of merit based on far-field intensity to specify a new adaptive-mirror configuration on each iteration.

Fig. 3
Fig. 3

Gray-level contour plot of deformable-mirror surface with all 19 actuators positioned in uniform piston. Significant variations on the mirror surface can be seen.

Fig. 4
Fig. 4

Gray-level contour plots: (a) the static-turbulence phase screen and (b) the corrected near-field phase, plotted on the same vertical scale. Within the 19-segment mirror boundary, the residual phase is nearly zero, leading to a near-diffraction-limited far-field performance.

Fig. 5
Fig. 5

Performance of far-field optimization with static turbulence. (a) The convergence behavior of the simplex algorithm, with the arrows representing ten nudges of the simplex. (b) The Strehl ratio and (c) the residual phase error versus the number of iterations for the turbulence-limited, segmented mirror and the corrected cases.

Fig. 6
Fig. 6

Far-field performance for stronger static turbulence: (a) the corrected Strehl ratio and (b) the residual phase error versus the number of iterations.

Fig. 7
Fig. 7

Corrected near-field phase: (a) a single segment and (b) two areas with flat phase displaced in piston, i.e., ambiguity (see text).

Fig. 8
Fig. 8

(a) Corrected Strehl ratio and (b) the rms phase error versus normalized time (represented as the fractional transport of the turbulence phase screen) for drifting turbulence. The turbulence-limited performance is shown for comparison. (c) The improvement factor versus normalized time (see text).

Fig. 9
Fig. 9

Effect of turbulence speed on dynamic performance for M = 10 and M = 100: (a) the Strehl ratio [the vertical lines A, B, and C are the three patches of local turbulence that are discussed in (c)] and (b) the improvement factor versus normalized time. (c) The Strehl-ratio improvement versus the turbulence speed for turbulence strengths at A, B, C.

Fig. 10
Fig. 10

Corrected Strehl ratio as a function of segmented-mirror resolution (number of segments). With far-field optimization a coarser mirror provides better dynamic-turbulence correction.

Fig. 11
Fig. 11

Far-field performance for the 19- and the 37-actuator deformable mirrors for static turbulence [see Fig. 4(a)]. There is better performance with the higher-resolution deformable mirror.

Fig. 12
Fig. 12

Effect of turbulence speed on dynamic performance of deformable mirror. There is no significant performance improvement with slower turbulence or with a higher bandwidth.

Fig. 13
Fig. 13

Somewhat better Strehl ratio is obtained with a deformable mirror with more actuators, especially in the presence of strong turbulence.

Tables (1)

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Table 1 Dependence of Far-Field Performance on Wavelength (or r0) and Mirror Resolution (d)

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