Abstract

New astronomical challenges revolve around the observation of faint galaxies, nearby star-forming regions and the direct imaging of exoplanets. The technologies required to progress in these fields of research rely on the development of custom Adaptive Optics (AO) instruments such as Multi-Object AO (MOAO) or Extreme AO (ExAO). Many obstacles remain in the development of these new technologies. A major barrier to the implementation of MOAO is the utilisation of deformable mirrors (DMs) in an open-loop control system. Micro-Electro-Mechanical-System (MEMS) DMs show promise for application in both MOAO and ExAO. Despite recent encouraging laboratory results, it remains an immature technology which has yet to be demonstrated on a fully operational on-sky AO system. Much of the research in this area focuses on the development of an accurate model of the MEMS DMs. In this paper, a thorough characterization process of a MEMS DM is performed, with the goal of developing an open-loop control strategy free of computationally heavy modelling (such as the use of plate equations). Instead, a simpler approach, based on the additivity of the influence functions, is chosen. The actuator stroke-voltage relationship and the actuator influence functions are carefully calibrated. For 100 initial phase screens with a mean rms of 97 nm (computer generated following a Von Karman statistic), the resulting mean residual open-loop rms error is 16.5 nm, the mean fitting error rms is 13.3 nm and the mean DM error rms is 10.8 nm (error reflecting the performances of the model under test in this paper). This corresponds to 11% of residual DM error.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Perreault, T. Bifano, B. M. Levine, and M. Harenstein, "Adaptive optic correction using microelectromechnical deformable mirrors," Opt. Eng. 41(3), 561-566 (2002).
    [CrossRef]
  2. M. N. Horenstein, T. Bifano, R. Krishnamoorthy, and N. Vandelli, "Electrostatic effects in micromachined actuators for adaptive optics," J. Electrostatics 42, 69-81 (1997).
    [CrossRef]
  3. B. P. Wallace, P. Hampton, C. Bradley, and R. Conan, "Evaluation of a MEMS deformable mirror for an adaptive optics test bench," Opt. Express 14(22), 10132 (2006).
    [CrossRef] [PubMed]
  4. K. M. Morzinski, D. T. Gavel, A. P. Norton, D. R. Dillon, and M. R. Reinig, "Characterizing MEMS deformable mirrors for open-loop operation: High-resolution measurements of thin-plate behavior," Proc. SPIE MEMS Adaptive Optics II 6888, 68880S (2008).
  5. T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
    [CrossRef]
  6. K. M. Morzinski, J. W. Evans, S. Severson, B. Macintosh, D. Dillon, D. Gavel, C. Max, and D. Palmer, "Characterizing the potential of MEMS deformable mirrors for astronomical adaptive optics," Proc. SPIE Advances in Adaptive Optics II 6272, 627221 (2006).
  7. C. Blain, R. Conan, O. Guyon, C. Bradley, and C. Vogel, "Characterization of influence function non-additivities for a 1024-actuator MEMS DM," in press (2009).
  8. S. A. Cornelissen, P. A. Bierden, and T. G. Bifano, "Development of a 4096 element MEMS continuous membrane deformable mirror for high contrast astronomical imaging," Proc. SPIE Advanced wavefront control: methods, devices and applications IV 6306, 630606 (2006).
  9. B. Macintosh, J. Graham, D. Palmer, R. Doyon, D. Gavel, J. Larkin,  et al., "The Gemini Planet Imager," Proc. SPIE Advances in Adaptive Optics II 6272, 62720L (2006).
  10. F. Assemat, E. Gendron, and F. Hammer, "The FALCON concept: Multi-Object adaptive optics and atmospheric tomography for integral field spectroscopy-principle and performance on a 8-m telescope," MNRAS 376, 287-312 (2007).
    [CrossRef]
  11. O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).
  12. T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, P. Baudoz, and P. Puget, "High-order adaptive optics requirement for direct detection of extrasolar planets: Application to the SPHERE Instrument," Opt. Express 14(17), 7515-7534 (2006).
    [CrossRef] [PubMed]
  13. J. W. Evans, K. Morzinski, S. Severson, L. Poyneer, B. Macintosh, D. Dillon, L. Reza, D. Gavel, D. Palmer, S. Olivier, and P. Bierden, "Extreme Adaptive Optics testbed: performance and characterization of a 1024 deformable mirror," Proc. SPIE MEMS/MOEMS Components and their applications III 6113, 131-136 (2006).
  14. L. A. Poyneer and D. Dillon, "MEMS adaptive optics for the Gemini Planet Imager: control methods and validation," Proc. SPIE Advances in Adaptive Optics II 6888, 68880H (2008).
  15. E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).
  16. F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).
  17. D. Gavel, S. Severson, B. Bauman, D. Dillon, M. Reinig, C. Lockwood, D. Palmer, K. Morzinski, M. Ammons, E. Gates, and B. Grigsby,"Villages: An on-sky visible wavelength astronomy AO experiment using MEMS deformable mirror," Proc. SPIE Photonics West 3888-03, (2008).
  18. C. Blain, O. Guyon, R. Conan, and C. Bradley, "Simple iterative method for open-loop control of MEMS deformable mirrors," Proc. SPIE Adaptive Optics Systems 7015, 701534 (2008).
  19. K. Morzinski, K. B. Harpsoe, D. Gavel, and S. M. Ammons,"The open-loop control of MEMS: Modeling and experimental results," Proc. SPIE MEMS Adaptive Optics 6467, 64670G (2007).
  20. J. B. Stewart, A. Diouf, Y. Zhou, and T. Bifano, "Open-Loop control of MEMS deformable mirror for largeamplitude wavefront control," J. Opt. Soc. Am. 24(12), 3827-3833 (2007).
    [CrossRef]
  21. 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(5), 1074-1081 (2006).
    [CrossRef]
  22. M. C. Roggemann and B. Welsh, "Imaging through turbulence."
  23. J. Nelson and G. H. Sanders, "The status of the Thirty Meter Telescope project," Proc. SPIE Ground-based and Airborne Telescopes II 7012, 70121A (2008).

2009 (2)

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).

2007 (2)

J. B. Stewart, A. Diouf, Y. Zhou, and T. Bifano, "Open-Loop control of MEMS deformable mirror for largeamplitude wavefront control," J. Opt. Soc. Am. 24(12), 3827-3833 (2007).
[CrossRef]

F. Assemat, E. Gendron, and F. Hammer, "The FALCON concept: Multi-Object adaptive optics and atmospheric tomography for integral field spectroscopy-principle and performance on a 8-m telescope," MNRAS 376, 287-312 (2007).
[CrossRef]

2006 (3)

2005 (1)

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

2002 (1)

J. A. Perreault, T. Bifano, B. M. Levine, and M. Harenstein, "Adaptive optic correction using microelectromechnical deformable mirrors," Opt. Eng. 41(3), 561-566 (2002).
[CrossRef]

1997 (2)

M. N. Horenstein, T. Bifano, R. Krishnamoorthy, and N. Vandelli, "Electrostatic effects in micromachined actuators for adaptive optics," J. Electrostatics 42, 69-81 (1997).
[CrossRef]

T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
[CrossRef]

Assemat, F.

F. Assemat, E. Gendron, and F. Hammer, "The FALCON concept: Multi-Object adaptive optics and atmospheric tomography for integral field spectroscopy-principle and performance on a 8-m telescope," MNRAS 376, 287-312 (2007).
[CrossRef]

Baudoz, P.

Belikov, R.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

Beuzit, J.-L.

Bifano, T.

J. B. Stewart, A. Diouf, Y. Zhou, and T. Bifano, "Open-Loop control of MEMS deformable mirror for largeamplitude wavefront control," J. Opt. Soc. Am. 24(12), 3827-3833 (2007).
[CrossRef]

J. A. Perreault, T. Bifano, B. M. Levine, and M. Harenstein, "Adaptive optic correction using microelectromechnical deformable mirrors," Opt. Eng. 41(3), 561-566 (2002).
[CrossRef]

M. N. Horenstein, T. Bifano, R. Krishnamoorthy, and N. Vandelli, "Electrostatic effects in micromachined actuators for adaptive optics," J. Electrostatics 42, 69-81 (1997).
[CrossRef]

Bifano, T. G.

T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
[CrossRef]

Blain, C.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

Bradley, C.

Charton, J.

Conan, R.

Diouf, A.

J. B. Stewart, A. Diouf, Y. Zhou, and T. Bifano, "Open-Loop control of MEMS deformable mirror for largeamplitude wavefront control," J. Opt. Soc. Am. 24(12), 3827-3833 (2007).
[CrossRef]

Dohlen, K.

Dorton, J. K.

T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
[CrossRef]

Fusco, T.

Galicher, R.

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

Garrel, V.

F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).

Gendron, E.

F. Assemat, E. Gendron, and F. Hammer, "The FALCON concept: Multi-Object adaptive optics and atmospheric tomography for integral field spectroscopy-principle and performance on a 8-m telescope," MNRAS 376, 287-312 (2007).
[CrossRef]

Guyon, O.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

Hammer, F.

F. Assemat, E. Gendron, and F. Hammer, "The FALCON concept: Multi-Object adaptive optics and atmospheric tomography for integral field spectroscopy-principle and performance on a 8-m telescope," MNRAS 376, 287-312 (2007).
[CrossRef]

Hampton, P.

Harenstein, M.

J. A. Perreault, T. Bifano, B. M. Levine, and M. Harenstein, "Adaptive optic correction using microelectromechnical deformable mirrors," Opt. Eng. 41(3), 561-566 (2002).
[CrossRef]

Horenstein, M. N.

M. N. Horenstein, T. Bifano, R. Krishnamoorthy, and N. Vandelli, "Electrostatic effects in micromachined actuators for adaptive optics," J. Electrostatics 42, 69-81 (1997).
[CrossRef]

T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
[CrossRef]

Kasper, M.

Krishnamoorthy, R.

M. N. Horenstein, T. Bifano, R. Krishnamoorthy, and N. Vandelli, "Electrostatic effects in micromachined actuators for adaptive optics," J. Electrostatics 42, 69-81 (1997).
[CrossRef]

Levine, B. M.

J. A. Perreault, T. Bifano, B. M. Levine, and M. Harenstein, "Adaptive optic correction using microelectromechnical deformable mirrors," Opt. Eng. 41(3), 561-566 (2002).
[CrossRef]

Lozi, J.

F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).

Mali, R. K.

T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
[CrossRef]

Martinache, F.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

Matsuo, T.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

Mouillet, D.

Nicolle, M.

Perreault, J.

T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
[CrossRef]

Perreault, J. A.

J. A. Perreault, T. Bifano, B. M. Levine, and M. Harenstein, "Adaptive optic correction using microelectromechnical deformable mirrors," Opt. Eng. 41(3), 561-566 (2002).
[CrossRef]

Petit, C.

Pluzhnik, E.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

Pluzhnik, E. A.

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

Puget, P.

Ridgway, S.

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

Rousset, G.

Sauvage, J.-F.

Sivo, G.

F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).

Stewart, J. B.

J. B. Stewart, A. Diouf, Y. Zhou, and T. Bifano, "Open-Loop control of MEMS deformable mirror for largeamplitude wavefront control," J. Opt. Soc. Am. 24(12), 3827-3833 (2007).
[CrossRef]

Tanaka, S.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

Totems, J.

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

Vandelli, N.

T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
[CrossRef]

M. N. Horenstein, T. Bifano, R. Krishnamoorthy, and N. Vandelli, "Electrostatic effects in micromachined actuators for adaptive optics," J. Electrostatics 42, 69-81 (1997).
[CrossRef]

Vogel, C. R.

Wallace, B. P.

Woodruff, R.

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

Yang, Q.

Zhou, Y.

J. B. Stewart, A. Diouf, Y. Zhou, and T. Bifano, "Open-Loop control of MEMS deformable mirror for largeamplitude wavefront control," J. Opt. Soc. Am. 24(12), 3827-3833 (2007).
[CrossRef]

J. Electrostatics (1)

M. N. Horenstein, T. Bifano, R. Krishnamoorthy, and N. Vandelli, "Electrostatic effects in micromachined actuators for adaptive optics," J. Electrostatics 42, 69-81 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. B. Stewart, A. Diouf, Y. Zhou, and T. Bifano, "Open-Loop control of MEMS deformable mirror for largeamplitude wavefront control," J. Opt. Soc. Am. 24(12), 3827-3833 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

Laboratory System Validation (1)

O. Guyon, E. Pluzhnik, F. Martinache, J. Totems, S. Tanaka, T. Matsuo, C. Blain, and R. Belikov "High Contrast Imaging and Wavefront Control with a PIAA Coronagraph: Laboratory System Validation," in press (2009).

MNRAS (1)

F. Assemat, E. Gendron, and F. Hammer, "The FALCON concept: Multi-Object adaptive optics and atmospheric tomography for integral field spectroscopy-principle and performance on a 8-m telescope," MNRAS 376, 287-312 (2007).
[CrossRef]

Opt. Eng. (2)

J. A. Perreault, T. Bifano, B. M. Levine, and M. Harenstein, "Adaptive optic correction using microelectromechnical deformable mirrors," Opt. Eng. 41(3), 561-566 (2002).
[CrossRef]

T. G. Bifano, R. K. Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, and D. A. Castanon, "Continuous-membrane surface-micromachined silicon deformable mirror," Opt. Eng. 36(5), 1354-1360 (1997).
[CrossRef]

Opt. Express (2)

Science and Techniques (1)

E. A. Pluzhnik, O. Guyon, S. Ridgway, R. Woodruff, C. Blain, F. Martinache, and R. Galicher, "The Phase Induced Aplitude Apodization Coronagraph: an overview of simulations and laboratory effort," IAU, Direct Imaging of Exoplanets: Science and Techniques 200, (2005).

The Subaru Coronagraphic Extreme AO Project (1)

F. Martinache, O. Guyon, J. Lozi, V. Garrel, C. Blain, and G. Sivo, "The Subaru Coronagraphic Extreme AO Project," in press (2009).

Other (12)

D. Gavel, S. Severson, B. Bauman, D. Dillon, M. Reinig, C. Lockwood, D. Palmer, K. Morzinski, M. Ammons, E. Gates, and B. Grigsby,"Villages: An on-sky visible wavelength astronomy AO experiment using MEMS deformable mirror," Proc. SPIE Photonics West 3888-03, (2008).

C. Blain, O. Guyon, R. Conan, and C. Bradley, "Simple iterative method for open-loop control of MEMS deformable mirrors," Proc. SPIE Adaptive Optics Systems 7015, 701534 (2008).

K. Morzinski, K. B. Harpsoe, D. Gavel, and S. M. Ammons,"The open-loop control of MEMS: Modeling and experimental results," Proc. SPIE MEMS Adaptive Optics 6467, 64670G (2007).

J. W. Evans, K. Morzinski, S. Severson, L. Poyneer, B. Macintosh, D. Dillon, L. Reza, D. Gavel, D. Palmer, S. Olivier, and P. Bierden, "Extreme Adaptive Optics testbed: performance and characterization of a 1024 deformable mirror," Proc. SPIE MEMS/MOEMS Components and their applications III 6113, 131-136 (2006).

L. A. Poyneer and D. Dillon, "MEMS adaptive optics for the Gemini Planet Imager: control methods and validation," Proc. SPIE Advances in Adaptive Optics II 6888, 68880H (2008).

K. M. Morzinski, D. T. Gavel, A. P. Norton, D. R. Dillon, and M. R. Reinig, "Characterizing MEMS deformable mirrors for open-loop operation: High-resolution measurements of thin-plate behavior," Proc. SPIE MEMS Adaptive Optics II 6888, 68880S (2008).

K. M. Morzinski, J. W. Evans, S. Severson, B. Macintosh, D. Dillon, D. Gavel, C. Max, and D. Palmer, "Characterizing the potential of MEMS deformable mirrors for astronomical adaptive optics," Proc. SPIE Advances in Adaptive Optics II 6272, 627221 (2006).

C. Blain, R. Conan, O. Guyon, C. Bradley, and C. Vogel, "Characterization of influence function non-additivities for a 1024-actuator MEMS DM," in press (2009).

S. A. Cornelissen, P. A. Bierden, and T. G. Bifano, "Development of a 4096 element MEMS continuous membrane deformable mirror for high contrast astronomical imaging," Proc. SPIE Advanced wavefront control: methods, devices and applications IV 6306, 630606 (2006).

B. Macintosh, J. Graham, D. Palmer, R. Doyon, D. Gavel, J. Larkin,  et al., "The Gemini Planet Imager," Proc. SPIE Advances in Adaptive Optics II 6272, 62720L (2006).

M. C. Roggemann and B. Welsh, "Imaging through turbulence."

J. Nelson and G. H. Sanders, "The status of the Thirty Meter Telescope project," Proc. SPIE Ground-based and Airborne Telescopes II 7012, 70121A (2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1:
Fig. 1:

(a) Non-additivity of the influence functions of two neighboring actuators and (b) compensation of the non-additivity when the actuators are set on a push-pull configuration (one up, one down).

Fig. 2:
Fig. 2:

(a) Diagram of the experimental setup and (b) DM’s active area (light green square). The interferometer mask is set to cover the 17 by 17 array of actuators.

Fig. 3:
Fig. 3:

Stroke-voltage relationship plots for the 324 actuators. In this figure, the x axis represents the squared voltages and the y axis represents the stroke (in nm). All actuators have a maximum stroke of approximately 800 nm excepts for the actuator coupled with the defective actuator which only has a maximum stroke of 400 nm.

Fig. 4:
Fig. 4:

(a) Normalised influence function for actuator # 171 and (b) transversal cut along x axis, y axis and the main diagonal of influence function # 171. The interferometer spatial resolution is 6.2 pixels per actuator. The slight asymmetry observed in (a) is due to a pixelisation effect.

Fig. 5:
Fig. 5:

(a) original sample phase screen φ generated with Matlab, (b) corresponding fitted phase φ ˜ obtained by the multiplication of the influence function F and the stroke coefficients ak , (c) stroke map (ak coefficients obtained by projection of the original phase φ onto the influence functions F), (d) voltage map (vertical scale in Volt) obtained with Eq. (6), (e) projection of the original phase screen φ onto the DM (phase φm measured by the interferometer) and (f) “open-loop” error or “measurement” error = φ - φm . This error map incorporates both the fitting error and the DM error (non-linear effects such as the mechanical coupling between neighbouring actuators). Vertical scales for (a), (b), (c), (e), and (f) are in nm.

Fig. 6:
Fig. 6:

(a) Diagram of the open-loop control process and (b) error estimation. The original phase screens φ are generated using Matlab. The influence functions F and the SVRs are measured during the DM calibration. The stroke maps (ak coefficients) are computed using Eq. (4). The voltage maps [obtained using Eq. (6)] are sent to the DM and the interferometer measures the DM membrane deflection (named the measurement phase screen φm ). φm is the projection of the original phase φ onto the DM.

Fig. 7:
Fig. 7:

(a) Fitting error versus the size of the interferometer mask. When the size of the mask is decreased, the phase screen is rescaled to match the interferometer mask size. As the mask get smaller, the number of actuators available to reproduce the phase screen decreases, and the fitting error increases as a result. The fitting error is minimum when the mask edges are positioned at the center of the edge actuators of the DM’s active area (b) Diagram of the interferometer mask size relative to the first three outer actuator coronas.

Fig. 8:
Fig. 8:

Histogram representation of the statistical study over 100 generated phase screens. (a) distribution of the original phase screen rms (vary from 56 nm to 155 nm), (b) distribution of the stroke map or ak coefficients rms, (c), (d), (e) and (f) illustrate the variation between option A and B for the open-loop error rms and the DM error rms. “x-axis” represents the rms wavefront error (nm surface), “y-axis” represents the number of corresponding phase screens.

Tables (2)

Tables Icon

Table 1: Mean and standard deviation rms of the fitting errors. All values are given in nm.

Tables Icon

Table 2: Mean and standard deviation rms of the measurement errors. All numbers are given in nm except for the ratio values given in %.

Equations (6)

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

stroke ( k ) = gain ( k ) · V ( k ) 2 + off set ( k )
φ x y = k = 1 324 a k · F k x y
φ = F · a
a = F · φ with F = ( F T F ) 1 F T
F · a = φ ˜
V ( k ) = a k offset ( k ) gain ( k )

Metrics