Abstract

Two kinds of algorithm for an adaptive optics (AO) system that uses two deformable mirrors (DMs), one with large stroke and the other with high spatial frequency, to correct different aberrations are described. The algorithms are based on modal method and direction-gradient method, respectively. Numerical simulations for the algorithms have been made. The simulation results indicate that the two DMs in the AO system can correct different aberrations with different characteristics, and the closed-loop performance of a double-DM AO system will be almost the same as that of an AO system that uses a single DM with an ideal stroke.

© 2006 Optical Society of America

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  1. Y. -K. Li, D. K. Ghen, and X.-W. Du, " Simulation of full field correction with two-deformable-mirror adaptive optics," J. High Power Lasers Particle Beams 6, 665- 669 ( 2000), in Chinese.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. A. van den Bos, " Aberration and the Strehl ratio," J. Opt. Soc. Am. A 17, 356- 358 ( 2000).
    [CrossRef]

2002

J. D. Barchers, " Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations," J. Opt. Soc. Am. A 19, 926- 945 ( 2002).
[CrossRef]

B. Qi, H. -B. Chen, and N. L. Dong, " Wavefront fitting of interferograms with Zernike polynomials," Opt. Eng. A 7, 1565- 1569 ( 2002).
[CrossRef]

2000

Y. -K. Li, D. K. Ghen, and X.-W. Du, " Simulation of full field correction with two-deformable-mirror adaptive optics," J. High Power Lasers Particle Beams 6, 665- 669 ( 2000), in Chinese.

A. van den Bos, " Aberration and the Strehl ratio," J. Opt. Soc. Am. A 17, 356- 358 ( 2000).
[CrossRef]

1998

M. C. Roggemann and D. J. Lee, " Two-deformable-mirror concept for correcting scintillation efforts in laser beam projection through the turbulent atmosphere," J. Appl. Opt. 37, 4577- 4585 ( 1998).
[CrossRef]

1996

1991

W. -H. Jiang, N. Ling, X. -J. Rao, and F. Shi, " Fitting capability of deformable mirror," in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE 1542, 130- 139 ( 1991).
[CrossRef]

F. Y. Kanev and V. P. Lukin, " Amplitude-phase beam control in a two-mirror adaptive system," J. Atmos. Opt. 4, 1273- 1279 ( 1991).

1990

W. -H. Jiang and H. -G. Li, " Hartman-Shack wavefront sensing and wavefront control algorithm," Adaptive Optics and Optical Structures, J. J. Schulte-in-den-Baeumen and R. J. Tyson, eds., Proc. SPIE 1271, 103- 108 ( 1990).

T. J. Karr, " Instabilities of atmospheric laser propagation," in Propagation of High-Energy Laser Beams through the Earth's Atmosphere, P. B. Ulrich and L. Wilson, eds., Proc. SPIE 1221, 26- 55 ( 1990).
[CrossRef]

1979

Barchers, J. D.

Chen, H. -B.

B. Qi, H. -B. Chen, and N. L. Dong, " Wavefront fitting of interferograms with Zernike polynomials," Opt. Eng. A 7, 1565- 1569 ( 2002).
[CrossRef]

Cubalchini, R.

Dai, G. -M.

Dong, N. L.

B. Qi, H. -B. Chen, and N. L. Dong, " Wavefront fitting of interferograms with Zernike polynomials," Opt. Eng. A 7, 1565- 1569 ( 2002).
[CrossRef]

Du, X. -W.

Y. -K. Li, D. K. Ghen, and X.-W. Du, " Simulation of full field correction with two-deformable-mirror adaptive optics," J. High Power Lasers Particle Beams 6, 665- 669 ( 2000), in Chinese.

Ghen, D. K.

Y. -K. Li, D. K. Ghen, and X.-W. Du, " Simulation of full field correction with two-deformable-mirror adaptive optics," J. High Power Lasers Particle Beams 6, 665- 669 ( 2000), in Chinese.

Jiang, W. -H.

W. -H. Jiang, N. Ling, X. -J. Rao, and F. Shi, " Fitting capability of deformable mirror," in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE 1542, 130- 139 ( 1991).
[CrossRef]

W. -H. Jiang and H. -G. Li, " Hartman-Shack wavefront sensing and wavefront control algorithm," Adaptive Optics and Optical Structures, J. J. Schulte-in-den-Baeumen and R. J. Tyson, eds., Proc. SPIE 1271, 103- 108 ( 1990).

Kanev, F. Y.

F. Y. Kanev and V. P. Lukin, " Amplitude-phase beam control in a two-mirror adaptive system," J. Atmos. Opt. 4, 1273- 1279 ( 1991).

Karr, T. J.

T. J. Karr, " Instabilities of atmospheric laser propagation," in Propagation of High-Energy Laser Beams through the Earth's Atmosphere, P. B. Ulrich and L. Wilson, eds., Proc. SPIE 1221, 26- 55 ( 1990).
[CrossRef]

Lee, D. J.

M. C. Roggemann and D. J. Lee, " Two-deformable-mirror concept for correcting scintillation efforts in laser beam projection through the turbulent atmosphere," J. Appl. Opt. 37, 4577- 4585 ( 1998).
[CrossRef]

Li, H. -G.

W. -H. Jiang and H. -G. Li, " Hartman-Shack wavefront sensing and wavefront control algorithm," Adaptive Optics and Optical Structures, J. J. Schulte-in-den-Baeumen and R. J. Tyson, eds., Proc. SPIE 1271, 103- 108 ( 1990).

Li, Y. -K.

Y. -K. Li, D. K. Ghen, and X.-W. Du, " Simulation of full field correction with two-deformable-mirror adaptive optics," J. High Power Lasers Particle Beams 6, 665- 669 ( 2000), in Chinese.

Ling, N.

W. -H. Jiang, N. Ling, X. -J. Rao, and F. Shi, " Fitting capability of deformable mirror," in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE 1542, 130- 139 ( 1991).
[CrossRef]

Lukin, V. P.

F. Y. Kanev and V. P. Lukin, " Amplitude-phase beam control in a two-mirror adaptive system," J. Atmos. Opt. 4, 1273- 1279 ( 1991).

Qi, B.

B. Qi, H. -B. Chen, and N. L. Dong, " Wavefront fitting of interferograms with Zernike polynomials," Opt. Eng. A 7, 1565- 1569 ( 2002).
[CrossRef]

Rao, X. -J.

W. -H. Jiang, N. Ling, X. -J. Rao, and F. Shi, " Fitting capability of deformable mirror," in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE 1542, 130- 139 ( 1991).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann and D. J. Lee, " Two-deformable-mirror concept for correcting scintillation efforts in laser beam projection through the turbulent atmosphere," J. Appl. Opt. 37, 4577- 4585 ( 1998).
[CrossRef]

Shi, F.

W. -H. Jiang, N. Ling, X. -J. Rao, and F. Shi, " Fitting capability of deformable mirror," in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE 1542, 130- 139 ( 1991).
[CrossRef]

van den Bos, A.

J. Appl. Opt.

M. C. Roggemann and D. J. Lee, " Two-deformable-mirror concept for correcting scintillation efforts in laser beam projection through the turbulent atmosphere," J. Appl. Opt. 37, 4577- 4585 ( 1998).
[CrossRef]

J. Atmos. Opt.

F. Y. Kanev and V. P. Lukin, " Amplitude-phase beam control in a two-mirror adaptive system," J. Atmos. Opt. 4, 1273- 1279 ( 1991).

J. High Power Lasers Particle Beams

Y. -K. Li, D. K. Ghen, and X.-W. Du, " Simulation of full field correction with two-deformable-mirror adaptive optics," J. High Power Lasers Particle Beams 6, 665- 669 ( 2000), in Chinese.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng. A

B. Qi, H. -B. Chen, and N. L. Dong, " Wavefront fitting of interferograms with Zernike polynomials," Opt. Eng. A 7, 1565- 1569 ( 2002).
[CrossRef]

Proc. SPIE

W. -H. Jiang and H. -G. Li, " Hartman-Shack wavefront sensing and wavefront control algorithm," Adaptive Optics and Optical Structures, J. J. Schulte-in-den-Baeumen and R. J. Tyson, eds., Proc. SPIE 1271, 103- 108 ( 1990).

W. -H. Jiang, N. Ling, X. -J. Rao, and F. Shi, " Fitting capability of deformable mirror," in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE 1542, 130- 139 ( 1991).
[CrossRef]

T. J. Karr, " Instabilities of atmospheric laser propagation," in Propagation of High-Energy Laser Beams through the Earth's Atmosphere, P. B. Ulrich and L. Wilson, eds., Proc. SPIE 1221, 26- 55 ( 1990).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Two-DM. WFS, wavefront sensor; BS, beam splitter.

Fig. 2
Fig. 2

Configurations of subaperture (squares) and deformable mirror actuators (filled circles) of (a) a 19 element and (b) a 61-element AO system.

Fig. 3
Fig. 3

(a) Original wavefront with power and (b) original wavefront without power. (c) Open-loop far field. PV, peak to valley.

Fig. 4
Fig. 4

(a) Wavefront corrected by the 61-element DM with an ideal stroke and (b) residual wavefront. (c) Far field after the closed loop.

Fig. 5
Fig. 5

Limited stroke 61 element DM corrected wavefront, residual wavefront, and far field after the closed loop.

Fig. 6
Fig. 6

Wavefront corrected by (a) a 61 element DM, (b) a 19 element DM, and (c) two DMs together. (d) Residual wavefront after correction by two DMs. (e) Closed-loop far field of a double-DM AO system with 19 and 61 element DMs after a separating model coefficient correction algorithm was used.

Fig. 7
Fig. 7

(a) Wavefront corrected by (a) a 61 element DM, (b) a 19 element DM, and (c) two DMs together. (d) Residual wavefront after correction by two DMs. (e) Closed-loop far field of a double-DM AO system with 19 and 61 element DMs after a confinement correction algorithm was used.

Equations (21)

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

Φ 1 = a k Z k ,
Φ 2 = n = 1 l a n Z n ( n k ) ,
G = D A ,
A = D + G ,
A = A 1 + A 2 ,
G = R V ,
D A = R V ,
V = R + D A .
V 1 = R 1     + D 1 A 1 , V 2 = R 2     + D 2 A 2 .
Φ 2 = i = 1 m 2 R 2 i ( x , y ) V i .
Φ 2 = n = 1 l a n Z n = i = 1 m 2 R 2 i ( x , y ) V i ( n k ) .
Φ 1 Φ 2 d x d y = a k Z k n = 1 l a n Z n d x d y
= a k Z k i = 1 m 2 R 2 i ( x , y ) V i d x d y
= 0 ( n k ) .
i = 1 m 2 V i Z k R 2 i ( x , y ) d x d y = 0.
i = 1 m 2 R m i V i = 0.
R 2 = [ R 2 R m ] .
V 2 = R 2     + [ G 0 ] ,
G 2 = R 2 V 2 .
G 1 = G G 2 .
V 1 = R 1     + G 1 .

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