Abstract

We present a variant of the model introduced by Vogel and Yang [J. Opt. Soc. Am. A23, 1074 (2006)] for point-actuated deformable mirrors (DMs) with continuous facesheets, and we describe a robust efficient regularized- output least-squares computational scheme to estimate the parameters in the model, given noisy discrete observations of the DM response to known actuation. We demonstrate the effectiveness of this approach with experimental data obtained from a pair of DMs—a piezo-actuated prototype DM built by CILAS for the Thirty Meter Telescope Project and an electrostatically actuated commercial micro-electro-mechanical systems (MEMS) DM produced by Boston Micromachines Corporation.

© 2010 Optical Society of America

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  1. C. R. Vogel and Q. Yang, “Modeling, simulation, and open-loop control of a continuous facesheet MEMS deformable mirror,” J. Opt. Soc. Am. A 23, 1074–1081 (2006).
    [CrossRef]
  2. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1959).
  3. J.-C. Sinquin, J.-M. Luron, and C. Guillemard, “Deformable mirror technologies for astronomy at CILAS,” Proc. SPIE 7015, 7015–7023 (2008).
  4. J. B. Stewart, A. Doiuf, Y. Zhou, and T. G. Bifano, “Open-loop control of a MEMS deformable mirror for large-amplitude wavefront control,” J. Opt. Soc. Am. A 24, 3827–3833 (2007).
    [CrossRef]
  5. F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy,” Mon. Not. R. Astron. Soc. 376, 287–312 (2008).
    [CrossRef]
  6. B. L. Ellerbroek and C. R. Vogel, “Topical review: Inverse problems in atmospheric adaptive optics,” Inverse Probl. 25, 063001 (2009).
    [CrossRef]
  7. L. Gilles, “Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multi-conjugate adaptive optics,” Appl. Opt. 44, 993–1002 (2005).
    [CrossRef]
  8. K. M. Morzinski, K. B. W. Harpse, D. T. Gavel, and S. M. Ammons, “The open-loop control of MEMS: Modeling and experimental results,” Proc. SPIE 6467, 64670G (2007).
    [CrossRef]
  9. C. R. Vogel, Computational Methods for Inverse Problems (SIAM, 2002).
  10. H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems (Birkhuser, 1989).
  11. C. R. Vogel and J. J. Heys, “Fast multigrid solution of biharmonic operator equations,” preprint, Department of Mathematical Sciences, Montana State University, 2009.
  12. MATLAB, The Mathworks, Natick, Mass., USA.
  13. C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.
  14. C. Blain, R. Conan, C. Bradley, O. Guyon, and C. R. Vogel, “Characterization of the influence function non-additivities for a 1024-actuator MEMS deformable mirror,” in Proceedings of First AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, Y.Clenet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2010), 06009.

2010 (1)

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. R. Vogel, “Characterization of the influence function non-additivities for a 1024-actuator MEMS deformable mirror,” in Proceedings of First AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, Y.Clenet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2010), 06009.

2009 (2)

C. R. Vogel and J. J. Heys, “Fast multigrid solution of biharmonic operator equations,” preprint, Department of Mathematical Sciences, Montana State University, 2009.

B. L. Ellerbroek and C. R. Vogel, “Topical review: Inverse problems in atmospheric adaptive optics,” Inverse Probl. 25, 063001 (2009).
[CrossRef]

2008 (2)

J.-C. Sinquin, J.-M. Luron, and C. Guillemard, “Deformable mirror technologies for astronomy at CILAS,” Proc. SPIE 7015, 7015–7023 (2008).

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy,” Mon. Not. R. Astron. Soc. 376, 287–312 (2008).
[CrossRef]

2007 (3)

C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.

J. B. Stewart, A. Doiuf, Y. Zhou, and T. G. Bifano, “Open-loop control of a MEMS deformable mirror for large-amplitude wavefront control,” J. Opt. Soc. Am. A 24, 3827–3833 (2007).
[CrossRef]

K. M. Morzinski, K. B. W. Harpse, D. T. Gavel, and S. M. Ammons, “The open-loop control of MEMS: Modeling and experimental results,” Proc. SPIE 6467, 64670G (2007).
[CrossRef]

2006 (1)

2005 (1)

2002 (1)

C. R. Vogel, Computational Methods for Inverse Problems (SIAM, 2002).

1989 (1)

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems (Birkhuser, 1989).

1959 (1)

S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1959).

Ammons, S. M.

K. M. Morzinski, K. B. W. Harpse, D. T. Gavel, and S. M. Ammons, “The open-loop control of MEMS: Modeling and experimental results,” Proc. SPIE 6467, 64670G (2007).
[CrossRef]

Assémat, F.

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy,” Mon. Not. R. Astron. Soc. 376, 287–312 (2008).
[CrossRef]

Banks, H. T.

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems (Birkhuser, 1989).

Bifano, T. G.

Blain, C.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. R. Vogel, “Characterization of the influence function non-additivities for a 1024-actuator MEMS deformable mirror,” in Proceedings of First AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, Y.Clenet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2010), 06009.

C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.

Bradley, C.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. R. Vogel, “Characterization of the influence function non-additivities for a 1024-actuator MEMS deformable mirror,” in Proceedings of First AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, Y.Clenet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2010), 06009.

C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.

Conan, R.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. R. Vogel, “Characterization of the influence function non-additivities for a 1024-actuator MEMS deformable mirror,” in Proceedings of First AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, Y.Clenet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2010), 06009.

C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.

Doiuf, A.

Ellerbroek, B. L.

B. L. Ellerbroek and C. R. Vogel, “Topical review: Inverse problems in atmospheric adaptive optics,” Inverse Probl. 25, 063001 (2009).
[CrossRef]

Gavel, D. T.

K. M. Morzinski, K. B. W. Harpse, D. T. Gavel, and S. M. Ammons, “The open-loop control of MEMS: Modeling and experimental results,” Proc. SPIE 6467, 64670G (2007).
[CrossRef]

Gendron, E.

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy,” Mon. Not. R. Astron. Soc. 376, 287–312 (2008).
[CrossRef]

Gilles, L.

Guillemard, C.

J.-C. Sinquin, J.-M. Luron, and C. Guillemard, “Deformable mirror technologies for astronomy at CILAS,” Proc. SPIE 7015, 7015–7023 (2008).

Guyon, O.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. R. Vogel, “Characterization of the influence function non-additivities for a 1024-actuator MEMS deformable mirror,” in Proceedings of First AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, Y.Clenet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2010), 06009.

Hammer, F.

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy,” Mon. Not. R. Astron. Soc. 376, 287–312 (2008).
[CrossRef]

Hampton, P.

C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.

Harpse, K. B. W.

K. M. Morzinski, K. B. W. Harpse, D. T. Gavel, and S. M. Ammons, “The open-loop control of MEMS: Modeling and experimental results,” Proc. SPIE 6467, 64670G (2007).
[CrossRef]

Heys, J. J.

C. R. Vogel and J. J. Heys, “Fast multigrid solution of biharmonic operator equations,” preprint, Department of Mathematical Sciences, Montana State University, 2009.

Hilton, A.

C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.

Keskin, O.

C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.

Kunisch, K.

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems (Birkhuser, 1989).

Luron, J. -M.

J.-C. Sinquin, J.-M. Luron, and C. Guillemard, “Deformable mirror technologies for astronomy at CILAS,” Proc. SPIE 7015, 7015–7023 (2008).

Morzinski, K. M.

K. M. Morzinski, K. B. W. Harpse, D. T. Gavel, and S. M. Ammons, “The open-loop control of MEMS: Modeling and experimental results,” Proc. SPIE 6467, 64670G (2007).
[CrossRef]

Sinquin, J. -C.

J.-C. Sinquin, J.-M. Luron, and C. Guillemard, “Deformable mirror technologies for astronomy at CILAS,” Proc. SPIE 7015, 7015–7023 (2008).

Stewart, J. B.

Timoshenko, S.

S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1959).

Vogel, C. R.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. R. Vogel, “Characterization of the influence function non-additivities for a 1024-actuator MEMS deformable mirror,” in Proceedings of First AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, Y.Clenet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2010), 06009.

B. L. Ellerbroek and C. R. Vogel, “Topical review: Inverse problems in atmospheric adaptive optics,” Inverse Probl. 25, 063001 (2009).
[CrossRef]

C. R. Vogel and J. J. Heys, “Fast multigrid solution of biharmonic operator equations,” preprint, Department of Mathematical Sciences, Montana State University, 2009.

C. R. Vogel and Q. Yang, “Modeling, simulation, and open-loop control of a continuous facesheet MEMS deformable mirror,” J. Opt. Soc. Am. A 23, 1074–1081 (2006).
[CrossRef]

C. R. Vogel, Computational Methods for Inverse Problems (SIAM, 2002).

Woinowsky-Krieger, S.

S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1959).

Yang, Q.

Zhou, Y.

Appl. Opt. (1)

Inverse Probl. (1)

B. L. Ellerbroek and C. R. Vogel, “Topical review: Inverse problems in atmospheric adaptive optics,” Inverse Probl. 25, 063001 (2009).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy,” Mon. Not. R. Astron. Soc. 376, 287–312 (2008).
[CrossRef]

Proc. SPIE (2)

J.-C. Sinquin, J.-M. Luron, and C. Guillemard, “Deformable mirror technologies for astronomy at CILAS,” Proc. SPIE 7015, 7015–7023 (2008).

K. M. Morzinski, K. B. W. Harpse, D. T. Gavel, and S. M. Ammons, “The open-loop control of MEMS: Modeling and experimental results,” Proc. SPIE 6467, 64670G (2007).
[CrossRef]

Other (7)

C. R. Vogel, Computational Methods for Inverse Problems (SIAM, 2002).

H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems (Birkhuser, 1989).

C. R. Vogel and J. J. Heys, “Fast multigrid solution of biharmonic operator equations,” preprint, Department of Mathematical Sciences, Montana State University, 2009.

MATLAB, The Mathworks, Natick, Mass., USA.

C. Blain, R. Conan, C. Bradley, O. Keskin, P. Hampton, and A. Hilton, “Magnetic ALPAO and piezo-stack CILAS deformable mirrors characterization,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis, Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ATuC6.

C. Blain, R. Conan, C. Bradley, O. Guyon, and C. R. Vogel, “Characterization of the influence function non-additivities for a 1024-actuator MEMS deformable mirror,” in Proceedings of First AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, Y.Clenet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2010), 06009.

S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1959).

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