Abstract

We present the results of research aimed at optimizing adaptive-optics closed-loop bandwidth settings to maximize imaging-system performance. The optimum closed-loop bandwidth settings are determined as a function of target-object light levels and atmospheric seeing conditions. Our work shows that, for bright objects, the optimum closed-loop bandwidth is near the Greenwood frequency. However, for dim objects without the use of a laser beacon the preferred closed-loop bandwidth settings are a small fraction of the Greenwood frequency. In addition, under low light levels selection of the proper closed-loop bandwidth is more critical for achieving maximum performance than it is under high light levels. We also present a strategy for selecting the closed-loop bandwidth to provide robust system performance for different target-object light levels.

© 1998 Optical Society of America

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    [CrossRef]
  9. M. C. Roggemann, B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).
  10. C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
    [CrossRef]
  11. M. Lloyd-Hart, R. Angel, B. Jacobsen, D. Wittman, D. McCarthy, “Preliminary closed-loop results from an adaptive optics system using a sodium resonance guide star,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 364–372 (1994).
    [CrossRef]

1994

1987

1977

Angel, R.

M. Lloyd-Hart, R. Angel, B. Jacobsen, D. Wittman, D. McCarthy, “Preliminary closed-loop results from an adaptive optics system using a sodium resonance guide star,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 364–372 (1994).
[CrossRef]

Avicola, K.

C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
[CrossRef]

Boyer, C.

Brase, J. M.

C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
[CrossRef]

Ellerbroek, B. L.

Friedman, H. W.

C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
[CrossRef]

Gaffard, J. P.

Gavel, D. T.

D. T. Gavel, J. R. Morris, R. G. Vernon, “Systematic design and analysis of laser-guide-star adaptive-optics systems for large telescopes,” J. Opt. Soc. Am. A 11, 914–924 (1994).
[CrossRef]

C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Greenwood, D. P.

Harrington, P. M.

P. M. Harrington, B. M. Welsh, “Frequency-domain analysis of an adaptive optical system’s temporal response,” Opt. Eng. 33, 2336–2342 (1994).
[CrossRef]

Jacobsen, B.

M. Lloyd-Hart, R. Angel, B. Jacobsen, D. Wittman, D. McCarthy, “Preliminary closed-loop results from an adaptive optics system using a sodium resonance guide star,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 364–372 (1994).
[CrossRef]

Lloyd-Hart, M.

M. Lloyd-Hart, R. Angel, B. Jacobsen, D. Wittman, D. McCarthy, “Preliminary closed-loop results from an adaptive optics system using a sodium resonance guide star,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 364–372 (1994).
[CrossRef]

Max, C. E.

C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
[CrossRef]

McCarthy, D.

M. Lloyd-Hart, R. Angel, B. Jacobsen, D. Wittman, D. McCarthy, “Preliminary closed-loop results from an adaptive optics system using a sodium resonance guide star,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 364–372 (1994).
[CrossRef]

Morris, J. R.

Olivier, S. S.

C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

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

Salmon, J. T.

C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
[CrossRef]

Stoudt, C. A.

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

Vernon, R. G.

Welsh, B.

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

Welsh, B. M.

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

P. M. Harrington, B. M. Welsh, “Frequency-domain analysis of an adaptive optical system’s temporal response,” Opt. Eng. 33, 2336–2342 (1994).
[CrossRef]

Wittman, D.

M. Lloyd-Hart, R. Angel, B. Jacobsen, D. Wittman, D. McCarthy, “Preliminary closed-loop results from an adaptive optics system using a sodium resonance guide star,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 364–372 (1994).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

P. M. Harrington, B. M. Welsh, “Frequency-domain analysis of an adaptive optical system’s temporal response,” Opt. Eng. 33, 2336–2342 (1994).
[CrossRef]

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

Other

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

C. E. Max, D. T. Gavel, S. S. Olivier, J. M. Brase, H. W. Friedman, K. Avicola, J. T. Salmon, “Issues in the design and optimization of adaptive optics and laser guide stars for the Keck telescopes,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 189–200 (1994).
[CrossRef]

M. Lloyd-Hart, R. Angel, B. Jacobsen, D. Wittman, D. McCarthy, “Preliminary closed-loop results from an adaptive optics system using a sodium resonance guide star,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 364–372 (1994).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (11)

Fig. 1
Fig. 1

Summary of parameters used to model the AMOS 1.6-m AOS and variables used in this study.

Fig. 2
Fig. 2

Simulated satellite for extended-object imaging.

Fig. 3
Fig. 3

Effect of increasing the close-loop bandwidth on AOS performance: The closed-loop bandwidth is given in hertz. The ISR for the case in which the AOS is turned off is also shown. In all cases the sampling rate was 1000 Hz. Seeing conditions: r 0 = 0.05, f g = 106.5, mv = 0.

Fig. 4
Fig. 4

Mean ISR versus the closed-loop bandwidth for different object visual magnitudes for case 1. Seeing conditions: r 0 = 0.05, f g = 106.5.

Fig. 5
Fig. 5

Mean ISR versus the closed-loop bandwidth for different object visual magnitudes for case 2. Seeing conditions: r 0 = 0.40, f g = 13.3.

Fig. 6
Fig. 6

Mean ISR versus the closed-loop bandwidth for different object visual magnitudes for case 3. Seeing conditions: r 0 = 0.05, f g = 213.0.

Fig. 7
Fig. 7

Optimal closed-loop bandwidth versus the object visual magnitudes for case 1: The open circles indicate optimal bandwidths that provide the maximum mean ISR value, and the vertical bars indicate ranges of f c settings that yield 95% of these maxima. Shown is 95% of the optimum closed-loop bandwidth intervals, with f g = 106.5.

Fig. 8
Fig. 8

Optimal closed-loop bandwidth versus the object visual magnitudes for case 2: The open circles indicate optimal bandwidths that provide the maximum mean ISR values, and the vertical bars indicate the ranges of f c settings that yield 95% of these maxima. Shown is 95% of the optimum closed-loop bandwidth intervals, with f g = 13.3.

Fig. 9
Fig. 9

Optimal closed-loop bandwidth versus the object visual magnitudes for case 3: The open circles indicate optimal bandwidths that provide the maximum mean ISR value, and the vertical bars indicate ranges of f c settings that yield 95% of these maxima. Shown is 95% of the optimum closed-loop bandwidth intervals, with f g = 213.0.

Fig. 10
Fig. 10

Optimal closed-loop bandwidth versus the object visual magnitudes for cases 1–3: The legend indicates the optimal bandwidth settings that provide the maximum mean ISR value for the different Greenwood frequencies examined. The vertical bars indicate intervals of f c settings that yield 95% of these maxima. Shown is 95% of the optimum closed-loop bandwidth intervals.

Fig. 11
Fig. 11

Sample extended-object output images for object visual magnitudes of 0 and 9 and indicated closed-loop bandwidths: Seeing conditions were r 0 = 0.05 and f g = 106.5 Hz.

Tables (1)

Tables Icon

Table 1 Summary of Parameters for the Different Cases Studied

Equations (7)

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ISR =   MTF ist f d f   MTF dl f d f ,
f g = 0.426   | v | r 0 .
C j = C j - 1 + k g e j ,     0 k g 1 ,
e j = MS j - C j - 1 ,
C j = C j - 1 ( 1 - k g ) + k g MS j .
ρ n = k g ( 1 - k g ) n ,
f c = k g 2 π × sample   rate .

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