Abstract

The actuator pattern of an adaptive mirror determines the amplitudes and the fidelities of the mirror deformations that can be achieved. In this study, we analyze and compare different electrode patterns of piezoelectric unimorph deformable mirrors using a numerical finite element model. The analysis allows us to determine the optimum actuator pattern, and it is also applicable to bimorph mirrors. The model is verified by comparing its predictions with experimental results of our prototype of a novel unimorph deformable mirror.

© 2010 Optical Society of America

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  1. E. Steinhaus and S. G. Lipson,” Bimorph adaptive mirrors and curvature sensing,” J. Opt. Soc. Am. 69, 478–481 (1979).
    [CrossRef]
  2. J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
    [CrossRef]
  3. D. A. Horsley, H. K. Park, S. P. Laut, and J. S. Werner, “Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry,” Proc. SPIE 5688, 133–144 (2005).
    [CrossRef]
  4. C. S. Long, P. W. Loveday, and A. Forbes, “Development of a piezoelectric adaptive mirror for laser beam control,” in Proceedings of ACTUATOR 2008, 11th International Conference on New Actuators (HVG Hanseatische Veranstaltungs GmbH, 2008), pp. 584–587.
  5. P. Welp, H.-M. Heuck, and U. Wittrock, “Intracavity adaptive optics optimization of an end-pumped Nd:YVO4 laser,” in Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine, C.Dainty, ed. (Imperial College Press2008), pp. 413–418.
    [CrossRef]
  6. J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
    [CrossRef]
  7. J. Porter, A. Guirao, I. Cox, and D. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001).
    [CrossRef]
  8. E. Dalimier and C. Dainty, “Comparative analysis of deformable mirrors for ocular adaptive optics,” Opt. Express 13, 4275–4285 (2005).
    [CrossRef] [PubMed]
  9. E. J. Fernández and P. Artal, “Membrane deformable mirror for adaptive optics: performance limits in visual optics,” Opt. Express 11, 1056–1069 (2003).
    [CrossRef] [PubMed]
  10. G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
    [CrossRef]
  11. V. Piefort, “Finite element modeling of piezoelectric active structures,” Ph.D. dissertation (Université Libre de Bruxelles, 2001).
  12. E. M. Ellis, “Low-cost bimorph mirrors in adaptive optics,” Ph.D. dissertation (Imperial College of Science, Technology and Medicine—University of London, 1999).
  13. Y. Ning, W. Jiang, N. Ling, and C. Rao, “Response function calculation and sensitivity comparison analysis of various bimorph deformable mirrors,” Opt. Express 15, 12030–12038 (2007).
    [CrossRef] [PubMed]
  14. C. Schwartz, E. Ribak, and S. G. Lipson, “Bimorph adaptive mirrors and curvature sensing,” J. Opt. Soc. Am. A 11, 895–902 (1994).
    [CrossRef]
  15. A. Kudryashov and V. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
    [CrossRef]
  16. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R.R.Shannon and J.C.Wyant, eds. (1992), pp. 1–53.
  17. S. Bonora and L. Poletto, “Push-pull membrane mirrors for adaptive optics,” Opt. Express 14, 11935–11944 (2006).
    [CrossRef] [PubMed]
  18. G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev,” Correction of low order aberrations using continuous deformable mirrors,” Opt. Express 16, 2859–2866 (2008).
    [CrossRef] [PubMed]
  19. F. Roddier, “Adaptive optics in astronomy,” 1st ed. (Cambridge U. Press, 1999).

2009 (1)

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

2008 (3)

C. S. Long, P. W. Loveday, and A. Forbes, “Development of a piezoelectric adaptive mirror for laser beam control,” in Proceedings of ACTUATOR 2008, 11th International Conference on New Actuators (HVG Hanseatische Veranstaltungs GmbH, 2008), pp. 584–587.

P. Welp, H.-M. Heuck, and U. Wittrock, “Intracavity adaptive optics optimization of an end-pumped Nd:YVO4 laser,” in Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine, C.Dainty, ed. (Imperial College Press2008), pp. 413–418.
[CrossRef]

G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev,” Correction of low order aberrations using continuous deformable mirrors,” Opt. Express 16, 2859–2866 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

2005 (2)

E. Dalimier and C. Dainty, “Comparative analysis of deformable mirrors for ocular adaptive optics,” Opt. Express 13, 4275–4285 (2005).
[CrossRef] [PubMed]

D. A. Horsley, H. K. Park, S. P. Laut, and J. S. Werner, “Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry,” Proc. SPIE 5688, 133–144 (2005).
[CrossRef]

2004 (1)

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

2003 (1)

2001 (2)

J. Porter, A. Guirao, I. Cox, and D. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001).
[CrossRef]

V. Piefort, “Finite element modeling of piezoelectric active structures,” Ph.D. dissertation (Université Libre de Bruxelles, 2001).

2000 (1)

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

1999 (2)

E. M. Ellis, “Low-cost bimorph mirrors in adaptive optics,” Ph.D. dissertation (Imperial College of Science, Technology and Medicine—University of London, 1999).

F. Roddier, “Adaptive optics in astronomy,” 1st ed. (Cambridge U. Press, 1999).

1996 (1)

A. Kudryashov and V. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
[CrossRef]

1994 (1)

1992 (1)

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R.R.Shannon and J.C.Wyant, eds. (1992), pp. 1–53.

1979 (1)

Artal, P.

Bastaits, R.

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

Biereichel, P.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Bonora, S.

Chun, M.

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

Cox, I.

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R.R.Shannon and J.C.Wyant, eds. (1992), pp. 1–53.

Dainty, C.

Dalimier, E.

Delabre, B.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Donaldson, R.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Ellis, E. M.

E. M. Ellis, “Low-cost bimorph mirrors in adaptive optics,” Ph.D. dissertation (Imperial College of Science, Technology and Medicine—University of London, 1999).

Fedrigo, E.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Fernández, E. J.

Forbes, A.

C. S. Long, P. W. Loveday, and A. Forbes, “Development of a piezoelectric adaptive mirror for laser beam control,” in Proceedings of ACTUATOR 2008, 11th International Conference on New Actuators (HVG Hanseatische Veranstaltungs GmbH, 2008), pp. 584–587.

Franza, F.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Gebhardt, S.

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

Gigan, P.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Gojak, D.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Graves, J.

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

Guirao, A.

Heuck, H.-M.

P. Welp, H.-M. Heuck, and U. Wittrock, “Intracavity adaptive optics optimization of an end-pumped Nd:YVO4 laser,” in Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine, C.Dainty, ed. (Imperial College Press2008), pp. 413–418.
[CrossRef]

Horsley, D. A.

D. A. Horsley, H. K. Park, S. P. Laut, and J. S. Werner, “Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry,” Proc. SPIE 5688, 133–144 (2005).
[CrossRef]

Hubin, N.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Jiang, W.

Kasper, M.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Käufl, U.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Kudryashov, A.

A. Kudryashov and V. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
[CrossRef]

Laut, S. P.

D. A. Horsley, H. K. Park, S. P. Laut, and J. S. Werner, “Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry,” Proc. SPIE 5688, 133–144 (2005).
[CrossRef]

Ling, N.

Lipson, S. G.

Lizon, J.-L.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Loktev, M.

Long, C. S.

C. S. Long, P. W. Loveday, and A. Forbes, “Development of a piezoelectric adaptive mirror for laser beam control,” in Proceedings of ACTUATOR 2008, 11th International Conference on New Actuators (HVG Hanseatische Veranstaltungs GmbH, 2008), pp. 584–587.

Loveday, P. W.

C. S. Long, P. W. Loveday, and A. Forbes, “Development of a piezoelectric adaptive mirror for laser beam control,” in Proceedings of ACTUATOR 2008, 11th International Conference on New Actuators (HVG Hanseatische Veranstaltungs GmbH, 2008), pp. 584–587.

Ning, Y.

Northcott, M.

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

O’Connor, D.

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

Oberti, S.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Park, H. K.

D. A. Horsley, H. K. Park, S. P. Laut, and J. S. Werner, “Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry,” Proc. SPIE 5688, 133–144 (2005).
[CrossRef]

Paufique, J.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Piefort, V.

V. Piefort, “Finite element modeling of piezoelectric active structures,” Ph.D. dissertation (Université Libre de Bruxelles, 2001).

Pirard, J.-F.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Poletto, L.

Porter, J.

Potter, D.

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

Pozna, E.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Preumont, A.

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

Rao, C.

Ribak, E.

Rigaut, F.

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

Roddier, C.

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

Roddier, F.

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

F. Roddier, “Adaptive optics in astronomy,” 1st ed. (Cambridge U. Press, 1999).

Rodrigues, G.

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

Roose, S.

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

Samokhin, A.

Santos, J.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Schönecker, A.

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

Schwartz, C.

Shmalhausen, V.

A. Kudryashov and V. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
[CrossRef]

Soloviev, O.

Steinhaus, E.

Stockman, Y.

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

Stroebele, S.

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

Vdovin, G.

Villon, P.

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

Welp, P.

P. Welp, H.-M. Heuck, and U. Wittrock, “Intracavity adaptive optics optimization of an end-pumped Nd:YVO4 laser,” in Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine, C.Dainty, ed. (Imperial College Press2008), pp. 413–418.
[CrossRef]

Werner, J. S.

D. A. Horsley, H. K. Park, S. P. Laut, and J. S. Werner, “Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry,” Proc. SPIE 5688, 133–144 (2005).
[CrossRef]

Williams, D.

Wittrock, U.

P. Welp, H.-M. Heuck, and U. Wittrock, “Intracavity adaptive optics optimization of an end-pumped Nd:YVO4 laser,” in Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine, C.Dainty, ed. (Imperial College Press2008), pp. 413–418.
[CrossRef]

Wyant, J. C.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R.R.Shannon and J.C.Wyant, eds. (1992), pp. 1–53.

J. Opt. Soc. Am. (1)

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

Opt. Eng. (2)

G. Rodrigues, R. Bastaits, S. Roose, Y. Stockman, S. Gebhardt, A. Schönecker, P. Villon, and A. Preumont, “Modular bimorph mirrors for adaptive optics,” Opt. Eng. 48, 034001 (2009).
[CrossRef]

A. Kudryashov and V. Shmalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. 35, 3064–3073 (1996).
[CrossRef]

Opt. Express (5)

Proc. SPIE (3)

J. Graves, M. Northcott, F. Roddier, C. Roddier, D. Potter, D. O’Connor, F. Rigaut, and M. Chun, “First light for Hokupa’a 36 on Gemini North,” Proc. SPIE 4007, 26–30 (2000).
[CrossRef]

J. Paufique, P. Biereichel, R. Donaldson, B. Delabre, E. Fedrigo, F. Franza, P. Gigan, D. Gojak, N. Hubin, M. Kasper, U. Käufl, J.-L. Lizon, S. Oberti, J.-F. Pirard, E. Pozna, J. Santos, and S. Stroebele, “MACAO-CRIRES: a step towards high resolution in infrared,” Proc. SPIE 5490, 216–227 (2004).
[CrossRef]

D. A. Horsley, H. K. Park, S. P. Laut, and J. S. Werner, “Characterization for vision science applications of a bimorph deformable mirror using phase-shifting interferometry,” Proc. SPIE 5688, 133–144 (2005).
[CrossRef]

Other (6)

C. S. Long, P. W. Loveday, and A. Forbes, “Development of a piezoelectric adaptive mirror for laser beam control,” in Proceedings of ACTUATOR 2008, 11th International Conference on New Actuators (HVG Hanseatische Veranstaltungs GmbH, 2008), pp. 584–587.

P. Welp, H.-M. Heuck, and U. Wittrock, “Intracavity adaptive optics optimization of an end-pumped Nd:YVO4 laser,” in Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine, C.Dainty, ed. (Imperial College Press2008), pp. 413–418.
[CrossRef]

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R.R.Shannon and J.C.Wyant, eds. (1992), pp. 1–53.

F. Roddier, “Adaptive optics in astronomy,” 1st ed. (Cambridge U. Press, 1999).

V. Piefort, “Finite element modeling of piezoelectric active structures,” Ph.D. dissertation (Université Libre de Bruxelles, 2001).

E. M. Ellis, “Low-cost bimorph mirrors in adaptive optics,” Ph.D. dissertation (Imperial College of Science, Technology and Medicine—University of London, 1999).

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Figures (9)

Fig. 1
Fig. 1

Sketch of the unimorph mirror geometry used for modeling. The sketch is not to scale: the thickness (z direction) has been magnified by almost an order of magnitude.

Fig. 2
Fig. 2

Optimized FEM mesh with 260,000 elements (left) and surface deformation of the mirror under activation of a single electrode (right).

Fig. 3
Fig. 3

Low-order Zernike modes. The cumulated inflection lines of all previous Zernike modes up to the Zernike mode shown in false shades are indicated.

Fig. 4
Fig. 4

Analyzed electrode patterns. The active optical aperture is shaded red/gray.

Fig. 5
Fig. 5

(a) Prototype mirror, (b) experimentally measured influence functions of the mirror, and (c) FEM simulation of the influence functions. Shown is the deformation generated by a single electrode activated with a voltage of 100 V . The false-shading elevation plots that represent the deformation of the whole mirror are plotted at a position that corresponds to the electrode that is being activated.

Fig. 6
Fig. 6

Comparison of the calculated and experimentally measured amplitudes of the prototype mirror for different Zernike modes.

Fig. 7
Fig. 7

Maximum peak-to-valley Zernike amplitudes for different actuator patterns. The Zernike amplitudes are limited by the Maréchal criterion for the RMS deviation σ Δ s or the voltage limits of the piezoceramic. The 11   bars for each Zernike mode correspond to the 11 electrode patterns shown at the top of the figure.

Fig. 8
Fig. 8

Calculated purity values for the investigated electrode patterns. The purity indicates how well the mirror can create a Zernike mode.

Fig. 9
Fig. 9

Astigmatism Zernike amplitudes and purities of the 22.5 ° electrode pattern with and without an additional outer ring outside of the active optical area. The surface deformation, the corresponding interferogram, and the applied voltages are plotted from top to bottom.

Tables (1)

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Table 1 Material Properties and Dimensions Used in Numerical Models—Also Relevant Data for Unimorph Mirrors We Manufactured

Equations (9)

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s ( x , y ) = i = 1 n v i v test · ϕ i ( x , y ) ,
s ( x , y ) = v i v test · ϕ ( x , y ) T ,
ϕ i ( x , y ) v test = j = 1 90 a i j v test Z j ( x , y ) ,
ϕ ( x , y ) T v test = IM · Z ( x , y ) T ,
v = CM · a target   Z j T .
σ 2 Δ s = 1 A A [ s actual   Z j s target Z j ] 2 d x d y = 1 A A [ Σ j = 1 90 ( a actual   Z j a target Z j ) · Z j ( x , y ) ] 2 d x d y ,
v = CM [ a T target   Z j IM · v ] ,
p j = a ^ target, Z j a T ^ actual , Z j .
2 Z 8 r 2 = 0 ,

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