Abstract

We have proposed a discrete-layout bimorph piezoelectric deformable mirror (DBPDM) and developed its realistic electromechanical model. Compared with the conventional piezoelectric deformable mirror (CPDM) and the bimorph piezoelectric deformable mirror (BPDM), the DBPDM has both a larger stroke and a higher resonance frequency by integrating the strengths of the CPDM and the BPDM. To verify the advancement, a 21-elements DBPDM is studied in this paper. The results have suggested that the stroke of the DBPDM is larger than 10 microns and its resonance frequency is 53.3 kHz. Furthermore, numerical simulation is conducted on the deformation of the mirror using the realistic electromechanical model, and the dependence of the influence function upon the size of the radius of push pad is analyzed.

© 2017 Optical Society of America

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References

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  1. P. Y. Lin, H. T. Hsieh, and G. D. J. Su, “Design and fabrication of a large-stroke MEMS deformable mirror for wavefront control,” J. Opt. 13(5), 055404 (2011).
    [Crossref]
  2. H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
    [Crossref]
  3. H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
    [Crossref]
  4. N. Woolf, “Adaptive optics,” in IAU Colloq. 79: Very Large Telescopes, their Instrumentation and Programs (1984), 221–233.
  5. R. Tyson, Principles of Adaptive Optics (CRC Press, 2010).
  6. S. Bonora and L. Poletto, “Push-pull membrane mirrors for adaptive optics,” Opt. Express 14(25), 11935–11944 (2006).
    [Crossref] [PubMed]
  7. A. Haber, A. Polo, S. Ravensbergen, H. P. Urbach, and M. Verhaegen, “Identification of a dynamical model of a thermally actuated deformable mirror,” Opt. Lett. 38(16), 3061–3064 (2013).
    [Crossref] [PubMed]
  8. R. Wilson, F. Franza, and L. Noethe, “Active optics: I. a system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).
    [Crossref]
  9. C. L. Hom, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 700–708 (1999).
    [Crossref]
  10. X. D. Lin, C. Xue, X. Y. Liu, J. l. Wang, and P. F. Wei, “Current status and research development of wavefront correctors for adaptive optics,” Chinese Optics 4, 337–351 (2012).
  11. P. Y. Madec, “Overview of deformable mirror technologies for adaptive optics and astronomy,” in SPIE Astronomical Telescopes + Instrumentation, 844705 (International Society for Optics and Photonics, 2012), pp. 5–18.
  12. H. Hofer, L. Chen, G.-Y. Yoon, B. Singer, Y. Yamauchi, and D. R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberrations,” Opt. Express 8(11), 631–643 (2001).
    [Crossref] [PubMed]
  13. A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. Hebert, and M. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
    [Crossref] [PubMed]
  14. Y. Zhang, J. Rha, R. Jonnal, and D. Miller, “Adaptive optics parallel spectral domain optical coherence tomography for imaging the living retina,” Opt. Express 13(12), 4792–4811 (2005).
    [Crossref] [PubMed]
  15. C. L. Hom, P. D. Dean, and S. R. Winzer, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
    [Crossref]
  16. Y. Ning, W. Jiang, N. Ling, and C. Rao, “Response function calculation and sensitivity comparison analysis of various bimorph deformable mirrors,” Opt. Express 15(19), 12030–12038 (2007).
    [Crossref] [PubMed]
  17. R. J. Zawadzki, S. M. Jones, S. S. Olivier, M. Zhao, B. A. Bower, J. A. Izatt, S. Choi, S. Laut, and J. S. Werner, “Adaptive-optics optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express 13(21), 8532–8546 (2005).
    [Crossref] [PubMed]
  18. J. Zhao, F. Xiao, J. Kang, H. Zhao, Y. Dai, and Y. Zhang, “Quantifying intraocular scatter with near diffraction-limited double-pass point spread function,” Biomed. Opt. Express 7(11), 4595–4604 (2016).
    [Crossref] [PubMed]
  19. J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
    [Crossref]
  20. P. Wnuk, C. Radzewicz, and J. Krasiński, “Bimorph piezo deformable mirror for femtosecond pulse shaping,” Opt. Express 13(11), 4154–4159 (2005).
    [Crossref] [PubMed]
  21. E. J. Fernández, L. Vabre, B. Hermann, A. Unterhuber, B. Povazay, and W. Drexler, “Adaptive optics with a magnetic deformable mirror: applications in the human eye,” Opt. Express 14(20), 8900–8917 (2006).
    [Crossref] [PubMed]
  22. H. Wang and S. Yang, “Modeling and analysis of the thermal effects of a circular bimorph piezoelectric actuator,” Appl. Opt. 55(4), 873–878 (2016).
    [Crossref] [PubMed]
  23. H. Wang, M. Hu, and Z. Li, “Modelling and analysis of circular bimorph piezoelectric actuator for deformable mirror,” Appl. Math. Mech. 37(5), 639–646 (2016).
    [Crossref]
  24. H. Wang, “Analytical analysis of a beam Flexural-Mode Piezoelectric Actuator for Deformable Mirrors,” J. Astron. Telesc. Instrum. Syst. 14, 049001 (2015).
  25. S. Jiang, X. Li, S. Guo, Y. Hu, J. Yang, and Q. Jiang, “Performance of a piezoelectric bimorph for scavenging vibration energy,” Smart Mater. Struct. 14(4), 769–774 (2005).
    [Crossref]
  26. J. S. Yang and H. Y. Fang, “Analysis of a rotating elastic beam with piezoelectric films as an angular rate sensor,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 798–804 (2002).
    [Crossref] [PubMed]
  27. T. Low and W. Guo, “Modeling of a three-layer piezoelectric bimorph beam with hysteresis,” J. Microelectromech. Syst. 4(4), 230–237 (1995).
    [Crossref]
  28. H. Wang, X. Xie, Y. Hu, and J. Wang, “Nonlinear analysis of a 5-layer beam-like piezoelectric transformer near resonance,” Guti Lixue Xuebao 27, 195–201 (2014).
  29. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Cambridge University Press, 2013), Vol. 1.
  30. B. A. Auld, Acoustic Fields and Waves in Solids (Рипол Классик, 1973).

2016 (3)

2015 (1)

H. Wang, “Analytical analysis of a beam Flexural-Mode Piezoelectric Actuator for Deformable Mirrors,” J. Astron. Telesc. Instrum. Syst. 14, 049001 (2015).

2014 (1)

H. Wang, X. Xie, Y. Hu, and J. Wang, “Nonlinear analysis of a 5-layer beam-like piezoelectric transformer near resonance,” Guti Lixue Xuebao 27, 195–201 (2014).

2013 (2)

J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
[Crossref]

A. Haber, A. Polo, S. Ravensbergen, H. P. Urbach, and M. Verhaegen, “Identification of a dynamical model of a thermally actuated deformable mirror,” Opt. Lett. 38(16), 3061–3064 (2013).
[Crossref] [PubMed]

2012 (1)

X. D. Lin, C. Xue, X. Y. Liu, J. l. Wang, and P. F. Wei, “Current status and research development of wavefront correctors for adaptive optics,” Chinese Optics 4, 337–351 (2012).

2011 (1)

P. Y. Lin, H. T. Hsieh, and G. D. J. Su, “Design and fabrication of a large-stroke MEMS deformable mirror for wavefront control,” J. Opt. 13(5), 055404 (2011).
[Crossref]

2007 (1)

2006 (2)

2005 (4)

2002 (2)

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. Hebert, and M. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[Crossref] [PubMed]

J. S. Yang and H. Y. Fang, “Analysis of a rotating elastic beam with piezoelectric films as an angular rate sensor,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 798–804 (2002).
[Crossref] [PubMed]

2001 (1)

1999 (2)

C. L. Hom, P. D. Dean, and S. R. Winzer, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[Crossref]

C. L. Hom, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 700–708 (1999).
[Crossref]

1995 (1)

T. Low and W. Guo, “Modeling of a three-layer piezoelectric bimorph beam with hysteresis,” J. Microelectromech. Syst. 4(4), 230–237 (1995).
[Crossref]

1987 (1)

R. Wilson, F. Franza, and L. Noethe, “Active optics: I. a system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).
[Crossref]

1953 (2)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

Bonora, S.

Bower, B. A.

Campbell, M.

Chen, L.

Choi, S.

Chu, J.

J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
[Crossref]

Dai, Y.

Dean, P. D.

C. L. Hom, P. D. Dean, and S. R. Winzer, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[Crossref]

Donnelly Iii, W.

Drexler, W.

Fang, H. Y.

J. S. Yang and H. Y. Fang, “Analysis of a rotating elastic beam with piezoelectric films as an angular rate sensor,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 798–804 (2002).
[Crossref] [PubMed]

Fernández, E. J.

Franza, F.

R. Wilson, F. Franza, and L. Noethe, “Active optics: I. a system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).
[Crossref]

Guo, S.

S. Jiang, X. Li, S. Guo, Y. Hu, J. Yang, and Q. Jiang, “Performance of a piezoelectric bimorph for scavenging vibration energy,” Smart Mater. Struct. 14(4), 769–774 (2005).
[Crossref]

Guo, W.

T. Low and W. Guo, “Modeling of a three-layer piezoelectric bimorph beam with hysteresis,” J. Microelectromech. Syst. 4(4), 230–237 (1995).
[Crossref]

Haber, A.

Hebert, T.

Hermann, B.

Hofer, H.

Hom, C. L.

C. L. Hom, P. D. Dean, and S. R. Winzer, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[Crossref]

C. L. Hom, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 700–708 (1999).
[Crossref]

Hsieh, H. T.

P. Y. Lin, H. T. Hsieh, and G. D. J. Su, “Design and fabrication of a large-stroke MEMS deformable mirror for wavefront control,” J. Opt. 13(5), 055404 (2011).
[Crossref]

Hu, M.

H. Wang, M. Hu, and Z. Li, “Modelling and analysis of circular bimorph piezoelectric actuator for deformable mirror,” Appl. Math. Mech. 37(5), 639–646 (2016).
[Crossref]

Hu, Y.

H. Wang, X. Xie, Y. Hu, and J. Wang, “Nonlinear analysis of a 5-layer beam-like piezoelectric transformer near resonance,” Guti Lixue Xuebao 27, 195–201 (2014).

J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
[Crossref]

S. Jiang, X. Li, S. Guo, Y. Hu, J. Yang, and Q. Jiang, “Performance of a piezoelectric bimorph for scavenging vibration energy,” Smart Mater. Struct. 14(4), 769–774 (2005).
[Crossref]

Izatt, J. A.

Jiang, Q.

S. Jiang, X. Li, S. Guo, Y. Hu, J. Yang, and Q. Jiang, “Performance of a piezoelectric bimorph for scavenging vibration energy,” Smart Mater. Struct. 14(4), 769–774 (2005).
[Crossref]

Jiang, S.

S. Jiang, X. Li, S. Guo, Y. Hu, J. Yang, and Q. Jiang, “Performance of a piezoelectric bimorph for scavenging vibration energy,” Smart Mater. Struct. 14(4), 769–774 (2005).
[Crossref]

Jiang, W.

Jones, S. M.

Jonnal, R.

Kang, J.

Krasinski, J.

Laut, S.

Li, B.

J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
[Crossref]

Li, X.

S. Jiang, X. Li, S. Guo, Y. Hu, J. Yang, and Q. Jiang, “Performance of a piezoelectric bimorph for scavenging vibration energy,” Smart Mater. Struct. 14(4), 769–774 (2005).
[Crossref]

Li, Z.

H. Wang, M. Hu, and Z. Li, “Modelling and analysis of circular bimorph piezoelectric actuator for deformable mirror,” Appl. Math. Mech. 37(5), 639–646 (2016).
[Crossref]

Lin, P. Y.

P. Y. Lin, H. T. Hsieh, and G. D. J. Su, “Design and fabrication of a large-stroke MEMS deformable mirror for wavefront control,” J. Opt. 13(5), 055404 (2011).
[Crossref]

Lin, X. D.

X. D. Lin, C. Xue, X. Y. Liu, J. l. Wang, and P. F. Wei, “Current status and research development of wavefront correctors for adaptive optics,” Chinese Optics 4, 337–351 (2012).

Ling, N.

Liu, X. Y.

X. D. Lin, C. Xue, X. Y. Liu, J. l. Wang, and P. F. Wei, “Current status and research development of wavefront correctors for adaptive optics,” Chinese Optics 4, 337–351 (2012).

Liu, Y.

J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
[Crossref]

Low, T.

T. Low and W. Guo, “Modeling of a three-layer piezoelectric bimorph beam with hysteresis,” J. Microelectromech. Syst. 4(4), 230–237 (1995).
[Crossref]

Ma, J.

J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
[Crossref]

Miller, D.

Ning, Y.

Noethe, L.

R. Wilson, F. Franza, and L. Noethe, “Active optics: I. a system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).
[Crossref]

Olivier, S. S.

Poletto, L.

Polo, A.

Povazay, B.

Queener, H.

Radzewicz, C.

Rao, C.

Ravensbergen, S.

Rha, J.

Romero-Borja, F.

Roorda, A.

Singer, B.

Su, G. D. J.

P. Y. Lin, H. T. Hsieh, and G. D. J. Su, “Design and fabrication of a large-stroke MEMS deformable mirror for wavefront control,” J. Opt. 13(5), 055404 (2011).
[Crossref]

Unterhuber, A.

Urbach, H. P.

Vabre, L.

Verhaegen, M.

Wang, H.

H. Wang and S. Yang, “Modeling and analysis of the thermal effects of a circular bimorph piezoelectric actuator,” Appl. Opt. 55(4), 873–878 (2016).
[Crossref] [PubMed]

H. Wang, M. Hu, and Z. Li, “Modelling and analysis of circular bimorph piezoelectric actuator for deformable mirror,” Appl. Math. Mech. 37(5), 639–646 (2016).
[Crossref]

H. Wang, “Analytical analysis of a beam Flexural-Mode Piezoelectric Actuator for Deformable Mirrors,” J. Astron. Telesc. Instrum. Syst. 14, 049001 (2015).

H. Wang, X. Xie, Y. Hu, and J. Wang, “Nonlinear analysis of a 5-layer beam-like piezoelectric transformer near resonance,” Guti Lixue Xuebao 27, 195–201 (2014).

Wang, J.

H. Wang, X. Xie, Y. Hu, and J. Wang, “Nonlinear analysis of a 5-layer beam-like piezoelectric transformer near resonance,” Guti Lixue Xuebao 27, 195–201 (2014).

Wang, J. l.

X. D. Lin, C. Xue, X. Y. Liu, J. l. Wang, and P. F. Wei, “Current status and research development of wavefront correctors for adaptive optics,” Chinese Optics 4, 337–351 (2012).

Wei, P. F.

X. D. Lin, C. Xue, X. Y. Liu, J. l. Wang, and P. F. Wei, “Current status and research development of wavefront correctors for adaptive optics,” Chinese Optics 4, 337–351 (2012).

Werner, J. S.

Williams, D. R.

Wilson, R.

R. Wilson, F. Franza, and L. Noethe, “Active optics: I. a system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).
[Crossref]

Winzer, S. R.

C. L. Hom, P. D. Dean, and S. R. Winzer, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[Crossref]

Wnuk, P.

Xiao, F.

Xie, X.

H. Wang, X. Xie, Y. Hu, and J. Wang, “Nonlinear analysis of a 5-layer beam-like piezoelectric transformer near resonance,” Guti Lixue Xuebao 27, 195–201 (2014).

Xu, C.

J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
[Crossref]

Xue, C.

X. D. Lin, C. Xue, X. Y. Liu, J. l. Wang, and P. F. Wei, “Current status and research development of wavefront correctors for adaptive optics,” Chinese Optics 4, 337–351 (2012).

Yamauchi, Y.

Yang, J.

S. Jiang, X. Li, S. Guo, Y. Hu, J. Yang, and Q. Jiang, “Performance of a piezoelectric bimorph for scavenging vibration energy,” Smart Mater. Struct. 14(4), 769–774 (2005).
[Crossref]

Yang, J. S.

J. S. Yang and H. Y. Fang, “Analysis of a rotating elastic beam with piezoelectric films as an angular rate sensor,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 798–804 (2002).
[Crossref] [PubMed]

Yang, S.

Yoon, G.-Y.

Zawadzki, R. J.

Zhang, Y.

Zhao, H.

Zhao, J.

Zhao, M.

Appl. Math. Mech. (1)

H. Wang, M. Hu, and Z. Li, “Modelling and analysis of circular bimorph piezoelectric actuator for deformable mirror,” Appl. Math. Mech. 37(5), 639–646 (2016).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (1)

Chinese Optics (1)

X. D. Lin, C. Xue, X. Y. Liu, J. l. Wang, and P. F. Wei, “Current status and research development of wavefront correctors for adaptive optics,” Chinese Optics 4, 337–351 (2012).

Guti Lixue Xuebao (1)

H. Wang, X. Xie, Y. Hu, and J. Wang, “Nonlinear analysis of a 5-layer beam-like piezoelectric transformer near resonance,” Guti Lixue Xuebao 27, 195–201 (2014).

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

J. S. Yang and H. Y. Fang, “Analysis of a rotating elastic beam with piezoelectric films as an angular rate sensor,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49(6), 798–804 (2002).
[Crossref] [PubMed]

J. Astron. Telesc. Instrum. Syst. (1)

H. Wang, “Analytical analysis of a beam Flexural-Mode Piezoelectric Actuator for Deformable Mirrors,” J. Astron. Telesc. Instrum. Syst. 14, 049001 (2015).

J. Microelectromech. Syst. (1)

T. Low and W. Guo, “Modeling of a three-layer piezoelectric bimorph beam with hysteresis,” J. Microelectromech. Syst. 4(4), 230–237 (1995).
[Crossref]

J. Mod. Opt. (1)

R. Wilson, F. Franza, and L. Noethe, “Active optics: I. a system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).
[Crossref]

J. Opt. (1)

P. Y. Lin, H. T. Hsieh, and G. D. J. Su, “Design and fabrication of a large-stroke MEMS deformable mirror for wavefront control,” J. Opt. 13(5), 055404 (2011).
[Crossref]

Opt. Eng. (1)

J. Ma, Y. Liu, Y. Hu, C. Xu, B. Li, and J. Chu, “Low-cost unimorph deformable mirror with high actuator count for astronomical adaptive optics,” Opt. Eng. 52(1), 016602 (2013).
[Crossref]

Opt. Express (8)

H. Hofer, L. Chen, G.-Y. Yoon, B. Singer, Y. Yamauchi, and D. R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberrations,” Opt. Express 8(11), 631–643 (2001).
[Crossref] [PubMed]

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. Hebert, and M. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[Crossref] [PubMed]

P. Wnuk, C. Radzewicz, and J. Krasiński, “Bimorph piezo deformable mirror for femtosecond pulse shaping,” Opt. Express 13(11), 4154–4159 (2005).
[Crossref] [PubMed]

Y. Zhang, J. Rha, R. Jonnal, and D. Miller, “Adaptive optics parallel spectral domain optical coherence tomography for imaging the living retina,” Opt. Express 13(12), 4792–4811 (2005).
[Crossref] [PubMed]

R. J. Zawadzki, S. M. Jones, S. S. Olivier, M. Zhao, B. A. Bower, J. A. Izatt, S. Choi, S. Laut, and J. S. Werner, “Adaptive-optics optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express 13(21), 8532–8546 (2005).
[Crossref] [PubMed]

E. J. Fernández, L. Vabre, B. Hermann, A. Unterhuber, B. Povazay, and W. Drexler, “Adaptive optics with a magnetic deformable mirror: applications in the human eye,” Opt. Express 14(20), 8900–8917 (2006).
[Crossref] [PubMed]

S. Bonora and L. Poletto, “Push-pull membrane mirrors for adaptive optics,” Opt. Express 14(25), 11935–11944 (2006).
[Crossref] [PubMed]

Y. Ning, W. Jiang, N. Ling, and C. Rao, “Response function calculation and sensitivity comparison analysis of various bimorph deformable mirrors,” Opt. Express 15(19), 12030–12038 (2007).
[Crossref] [PubMed]

Opt. Lett. (1)

Publ. Astron. Soc. Pac. (2)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

Smart Mater. Struct. (3)

C. L. Hom, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 700–708 (1999).
[Crossref]

C. L. Hom, P. D. Dean, and S. R. Winzer, “Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis,” Smart Mater. Struct. 8(5), 691–699 (1999).
[Crossref]

S. Jiang, X. Li, S. Guo, Y. Hu, J. Yang, and Q. Jiang, “Performance of a piezoelectric bimorph for scavenging vibration energy,” Smart Mater. Struct. 14(4), 769–774 (2005).
[Crossref]

Other (5)

A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Cambridge University Press, 2013), Vol. 1.

B. A. Auld, Acoustic Fields and Waves in Solids (Рипол Классик, 1973).

P. Y. Madec, “Overview of deformable mirror technologies for adaptive optics and astronomy,” in SPIE Astronomical Telescopes + Instrumentation, 844705 (International Society for Optics and Photonics, 2012), pp. 5–18.

N. Woolf, “Adaptive optics,” in IAU Colloq. 79: Very Large Telescopes, their Instrumentation and Programs (1984), 221–233.

R. Tyson, Principles of Adaptive Optics (CRC Press, 2010).

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Figures (6)

Fig. 1
Fig. 1 The configuration of a discrete-layout bimorph piezoelectric deformable mirror.

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Fig. 2
Fig. 2 (a) A simply-support BBPBA. (b) The cross section of the BBPBA. (c) The dome height of BBPBA and loading a concentrated force. (d)The cross section of the push pad.

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Fig. 3
Fig. 3 (a)The static dome height displacement ds versus the electric field for different stresses of Apad. (b) The . resonance frequency of the whole DBPDM is obtained with the mode analysis of whole finite element model.

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Fig. 4
Fig. 4 A deformable mirror of 21 elements. (a)The locations of No.1, No.2 and No.3 BBPBAs. (b) FEA model of mirror face sheet and pads.

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Fig. 5
Fig. 5 (a) The 3D influence function for a unit voltage of the No.1 BBPBA. (b)The influence function versus normalized radius for different side lengths of pads at No.1 BBPBA.

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Fig. 6
Fig. 6 (a) The influence function versus normalized radius for different side lengths of pads at No.2 BBPBA. (b) The influence function versus normalized radius for different side lengths of pads at No.3 BBPBA.

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Equations (12)

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F= ∫ A T z dS= T ¯ z A pad = w pad 2 T ¯ z .
σ 1 p =− x 3 s 11 −1 ( ∂ 2 u 3 /∂ x 2 )− s 11 −1 d 31 E 3 +F x 3 ( x 1 +L)/(2 I e ),
σ 1 m = x 3 E m ( ∂ 2 u 3 /∂ x 2 )+nF x 3 ( x 1 +L)/(2 I e ).
M= ∫ x 3 σ 1 d x 2 d x 3 =−D ( ∂ 2 u 3 /∂ x 2 )+(h+c) e 31 p V+ΓF( x 1 +L).
∂ 2 M/∂ x 1 2 =−D( ∂ 4 u 3 /∂ x 1 4 )=0.
u 3 (−L)= u 3 (L)=0, M(−L)=M(L)=0.
u 3 = H 1 + H 2 x 1 + H 3 x 1 2 + H 4 x 1 3 .
d s = u 3 (0)= H 1 =−[2 e 31 p V(c+h)+LΓF] L 2 /(4D).
F= k s d s + k v V,
{ F N }=[ K dm M N ]{ d s N − d 0 }.
[ K dm M N ]{ d N − d 0 }= k s { d N }+kv{ V N }.
w(x,y)= ∑ N f N (x,y) d N .

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