Abstract

The construction process and characteristics of a deformable mirror eigenmode are introduced. The eigenmode of a 37-element micromachined membrane deformable mirror (MMDM) from OKO, Ltd. is analyzed. The Gaussian–Seidel low-order aberrations are fitted with eigenmodes as basic functions. An experimental adaptive optics (AO) system is constructed with the MMDM as the wavefront corrector, a deformable mirror eigenmode as the wavefront control algorithm, and a Shack–Hartmann wavefront sensor as the wavefront detector. The experimental results demonstrate that the deformable mirror eigenmode can act as the wavefront control algorithm for the AO system based on the MMDM.

© 2006 Optical Society of America

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References

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  1. W. Jiang, "Adaptive optics techniques investigations in the Institute of Optics and Electronics, Chinese Academy of Sciences," Opt-Electron. Eng. (Chinese) 22(1), 1-13 (1995).
  2. W. Jiang, "Adaptive optical image compensation experiments on stellar objects," Opt. Eng. 34, 7-14 (1995).
    [CrossRef]
  3. W. Jiang, "A 37-element adaptive optics system with H.-S. wavefront sensor," in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, E.S.O. Conf. and Workshop Proc. 48, 127-134 (1993).
  4. W. Jiang, "61-element adaptive optical system," Chin. J. Quantum Electron. (Chinese) 15, 193-199 (1998).
  5. Y. Zhang, N. Ling, Z. Yang, H. Duan, S. Jiao, and W. Jiang, "Adaptive optical system for ICF application," in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, and M. C. Roggemann, eds., Proc. SPIE 4494, 96-103 (2001).
  6. G. Vdovin, "Model of an adaptive optical system controlled by a neural network," Opt. Eng. 34, 3249-3253 (1995).
    [CrossRef]
  7. P. K. C. Wang and F. Y. Hadaegh, "Computation of static shapes and voltages for micromachined deformable mirrors with nonlinear electrostatic actuators," J. Microelectromechanical Syst. 5, 205-220 (1996).
    [CrossRef]
  8. L. Zhu, "Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation," Appl. Opt. 38, 168-176 (1999).
    [CrossRef]
  9. W. Lubeigt, P. Van Grol, G. J. Valentine, and D. Burns, "Use of intra-cavity adaptive optics in solid-state lasers operating at 1 μm," in Adaptive Optics for Industry and Medicine, Proceedings of the Fourth International Workshop (Springer, 2003), pp. 217-227.

1999

1998

W. Jiang, "61-element adaptive optical system," Chin. J. Quantum Electron. (Chinese) 15, 193-199 (1998).

1996

P. K. C. Wang and F. Y. Hadaegh, "Computation of static shapes and voltages for micromachined deformable mirrors with nonlinear electrostatic actuators," J. Microelectromechanical Syst. 5, 205-220 (1996).
[CrossRef]

1995

G. Vdovin, "Model of an adaptive optical system controlled by a neural network," Opt. Eng. 34, 3249-3253 (1995).
[CrossRef]

W. Jiang, "Adaptive optics techniques investigations in the Institute of Optics and Electronics, Chinese Academy of Sciences," Opt-Electron. Eng. (Chinese) 22(1), 1-13 (1995).

W. Jiang, "Adaptive optical image compensation experiments on stellar objects," Opt. Eng. 34, 7-14 (1995).
[CrossRef]

1993

W. Jiang, "A 37-element adaptive optics system with H.-S. wavefront sensor," in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, E.S.O. Conf. and Workshop Proc. 48, 127-134 (1993).

Burns, D.

W. Lubeigt, P. Van Grol, G. J. Valentine, and D. Burns, "Use of intra-cavity adaptive optics in solid-state lasers operating at 1 μm," in Adaptive Optics for Industry and Medicine, Proceedings of the Fourth International Workshop (Springer, 2003), pp. 217-227.

Duan, H.

Y. Zhang, N. Ling, Z. Yang, H. Duan, S. Jiao, and W. Jiang, "Adaptive optical system for ICF application," in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, and M. C. Roggemann, eds., Proc. SPIE 4494, 96-103 (2001).

Hadaegh, F. Y.

P. K. C. Wang and F. Y. Hadaegh, "Computation of static shapes and voltages for micromachined deformable mirrors with nonlinear electrostatic actuators," J. Microelectromechanical Syst. 5, 205-220 (1996).
[CrossRef]

Jiang, W.

W. Jiang, "61-element adaptive optical system," Chin. J. Quantum Electron. (Chinese) 15, 193-199 (1998).

W. Jiang, "Adaptive optics techniques investigations in the Institute of Optics and Electronics, Chinese Academy of Sciences," Opt-Electron. Eng. (Chinese) 22(1), 1-13 (1995).

W. Jiang, "Adaptive optical image compensation experiments on stellar objects," Opt. Eng. 34, 7-14 (1995).
[CrossRef]

W. Jiang, "A 37-element adaptive optics system with H.-S. wavefront sensor," in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, E.S.O. Conf. and Workshop Proc. 48, 127-134 (1993).

Y. Zhang, N. Ling, Z. Yang, H. Duan, S. Jiao, and W. Jiang, "Adaptive optical system for ICF application," in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, and M. C. Roggemann, eds., Proc. SPIE 4494, 96-103 (2001).

Jiao, S.

Y. Zhang, N. Ling, Z. Yang, H. Duan, S. Jiao, and W. Jiang, "Adaptive optical system for ICF application," in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, and M. C. Roggemann, eds., Proc. SPIE 4494, 96-103 (2001).

Ling, N.

Y. Zhang, N. Ling, Z. Yang, H. Duan, S. Jiao, and W. Jiang, "Adaptive optical system for ICF application," in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, and M. C. Roggemann, eds., Proc. SPIE 4494, 96-103 (2001).

Lubeigt, W.

W. Lubeigt, P. Van Grol, G. J. Valentine, and D. Burns, "Use of intra-cavity adaptive optics in solid-state lasers operating at 1 μm," in Adaptive Optics for Industry and Medicine, Proceedings of the Fourth International Workshop (Springer, 2003), pp. 217-227.

Valentine, G. J.

W. Lubeigt, P. Van Grol, G. J. Valentine, and D. Burns, "Use of intra-cavity adaptive optics in solid-state lasers operating at 1 μm," in Adaptive Optics for Industry and Medicine, Proceedings of the Fourth International Workshop (Springer, 2003), pp. 217-227.

Van Grol, P.

W. Lubeigt, P. Van Grol, G. J. Valentine, and D. Burns, "Use of intra-cavity adaptive optics in solid-state lasers operating at 1 μm," in Adaptive Optics for Industry and Medicine, Proceedings of the Fourth International Workshop (Springer, 2003), pp. 217-227.

Vdovin, G.

G. Vdovin, "Model of an adaptive optical system controlled by a neural network," Opt. Eng. 34, 3249-3253 (1995).
[CrossRef]

Wang, P. K. C.

P. K. C. Wang and F. Y. Hadaegh, "Computation of static shapes and voltages for micromachined deformable mirrors with nonlinear electrostatic actuators," J. Microelectromechanical Syst. 5, 205-220 (1996).
[CrossRef]

Yang, Z.

Y. Zhang, N. Ling, Z. Yang, H. Duan, S. Jiao, and W. Jiang, "Adaptive optical system for ICF application," in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, and M. C. Roggemann, eds., Proc. SPIE 4494, 96-103 (2001).

Zhang, Y.

Y. Zhang, N. Ling, Z. Yang, H. Duan, S. Jiao, and W. Jiang, "Adaptive optical system for ICF application," in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, and M. C. Roggemann, eds., Proc. SPIE 4494, 96-103 (2001).

Zhu, L.

Appl. Opt.

Chin. J. Quantum Electron.

W. Jiang, "61-element adaptive optical system," Chin. J. Quantum Electron. (Chinese) 15, 193-199 (1998).

J. Microelectromechanical Syst.

P. K. C. Wang and F. Y. Hadaegh, "Computation of static shapes and voltages for micromachined deformable mirrors with nonlinear electrostatic actuators," J. Microelectromechanical Syst. 5, 205-220 (1996).
[CrossRef]

Opt-Electron. Eng.

W. Jiang, "Adaptive optics techniques investigations in the Institute of Optics and Electronics, Chinese Academy of Sciences," Opt-Electron. Eng. (Chinese) 22(1), 1-13 (1995).

Opt. Eng.

W. Jiang, "Adaptive optical image compensation experiments on stellar objects," Opt. Eng. 34, 7-14 (1995).
[CrossRef]

G. Vdovin, "Model of an adaptive optical system controlled by a neural network," Opt. Eng. 34, 3249-3253 (1995).
[CrossRef]

Other

W. Lubeigt, P. Van Grol, G. J. Valentine, and D. Burns, "Use of intra-cavity adaptive optics in solid-state lasers operating at 1 μm," in Adaptive Optics for Industry and Medicine, Proceedings of the Fourth International Workshop (Springer, 2003), pp. 217-227.

W. Jiang, "A 37-element adaptive optics system with H.-S. wavefront sensor," in Proceedings of the ICO-16 Satellite Conference on Active and Adaptive Optics, E.S.O. Conf. and Workshop Proc. 48, 127-134 (1993).

Y. Zhang, N. Ling, Z. Yang, H. Duan, S. Jiao, and W. Jiang, "Adaptive optical system for ICF application," in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, and M. C. Roggemann, eds., Proc. SPIE 4494, 96-103 (2001).

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Figures (7)

Fig. 1
Fig. 1

(a) Initial surface of the MMDM. (b) Influence function of actuator number 1.

Fig. 2
Fig. 2

Cross section in directions X and Y of the influence function for the central actuator.

Fig. 3
Fig. 3

Former three eigenmode orders of the MMDM and their corresponding former 24-order Zernike polynomial coefficient (tile removed) (unit: 1 μm).C2. “Zernike Coefficient(Micron)” to “Zernike Coefficient (μm)” (3x). Fix cutoff type of “Zernike Order”; “No.” to “Number” (3x); “Eigen Mode” to “Eigenmode” (3x)

Fig. 4
Fig. 4

Fitting defocusing, 45° astigmatism, and 90° astigmatism of the MMDM (unit: 1 μm).

Fig. 5
Fig. 5

Schematic diagram of the experimental setup based on the MMDM.

Fig. 6
Fig. 6

Wavefront variations in a closed-loop and an open-loop process (unit: 1 μm).

Fig. 7
Fig. 7

Far-field variations in a closed-loop and an open-loop process.

Tables (1)

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Table 1 Data Contrast

Equations (9)

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ϕ ( x , y ) = i = 1 n V i F i ( x , y ) ,
C ( i , j ) = F i ( x , y ) × F j ( x , y ) d x d y .
C = U S U T ,
E j ( x , y ) = i = 1 n U ( i , j ) × F i ( x , y ) .
ϕ ( x , y ) = i = 1 n α i × E i ( x , y ) + δ ,
E ( x , y ) = i = 1 n A i Z i ( x , y ) + ζ ,
Z j ( x , y ) = i = 1 n A i E i ( x , y ) + φ ( x , y ) .
[ φ ( x , y ) i = 1 n α i E i ( x , y ) ] 2 d x d y > ξ ,
Z j ( x , y ) = i = 1 n ( A i + α i ) . E i ( x , y ) + ξ .

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