Abstract

We propose an improvement to the electrostatic membrane deformable mirror technique introducing push-pull capability that increases the performance in the correction of optical aberrations. The push-pull effect is achieved by the addition of some transparent electrodes on the top of the device. The transparent electrode is an indium-tin-oxide coated glass. The improvement of the mirror in generating surfaces is demonstrated by the comparison with a pull membrane mirror. The control is carried out in open loop by the knowledge of the response of each single electrode. An effective iterative strategy for the clipping management is presented. The performances are evaluated both in terms of Zernike polynomials generation and in terms of aberrations compensation based on the statistics of human eyes.

©2006 Optical Society of America

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References

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  1. G. Vdovin and P. M. Sarro, “Flexible mirror micromachined in silicon,” App. Opt. 34, 2968–2972 (1995).
    [Crossref]
  2. 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]
  3. E. J. Fernández, I. Iglesias, and P. Artal “Closed-loop adaptive optics in the human eye,” Opt. Lett. 26, 746–748 (2001).
    [Crossref]
  4. E. Dalimier and C. Dainty “Comparative analysis of deformable mirrors for ocular adaptive optics,” Opt. Express 13, 4275–4285 (2005).
    [Crossref] [PubMed]
  5. P. Kurczynski, H. M. Dyson, B. Sadoulet, J. E. Bower, W. Y.-C. Lai, W. M. Mansfield, and J. A. Taylor “Fabrication and measurement of low-stress membrane mirrors for adaptive optics,” Appl. Opt. 43, 3573–3580 (2004).
    [Crossref] [PubMed]
  6. P. Kurczynski, H. M. Dyson, and B. Sadoulet, “Large amplitude wavefront generation and correction with membrane mirrors,” Opt. Express 14, 509 (2006).
    [Crossref] [PubMed]
  7. E. M. Vuelban, N. Bhattacharya, and J. J. M. Braat, “Liquid deformable mirror for high-order wavefront correction,” Opt. Lett. 31, 1717 (2006).
    [Crossref] [PubMed]
  8. S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, “Wavefront active control by a DSP-Driven deformable membrane mirror,” to be publiched on Review of scientific instruments (Accepted 24th July 2006).
  9. E. S. Clafin and N. Bareket “Configuring an electrostatic membrane mirror by least-squares fitting with analytically derived influence functions,” J. Opt. Soc. Am. A,  3, 1833–1839, (1986).
    [Crossref]
  10. J. F. Castejon-Mochon, N. Lopez-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611–1617 (2002).
    [Crossref] [PubMed]
  11. L. Zhu, P.-C. Sun, and Y. Fainman, “Aberration free dynamic focusing with a multichannel micromachined membrane deformable mirror,” Appl. Opt. 38, 5350–5354 (1999).
    [Crossref]
  12. L. Zhu, P.-C. Sun, D.-U. Bratsch, W. R. Freeman, and Y. Fainman, “Adaptive control of micromachined continuous membrane deformable mirror for aberration compensation,” Appl. Opt,  38, 168–176, (1999).
    [Crossref]
  13. L. Zhu, P. Sun, D. Bartsch, W. R. Freeman, and Y. Fainman, “Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror,” Appl. Opt.,  38, 1510–1518 (1999).
    [Crossref]
  14. R. K. Tyson and B. W. Frazier, “Microelectromechanical system programmable aberration generator for adaptive optics,” Appl. Opt. 40, 2063–2067 (2001).
    [Crossref]

2006 (2)

2005 (1)

2004 (1)

2003 (1)

2002 (1)

J. F. Castejon-Mochon, N. Lopez-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611–1617 (2002).
[Crossref] [PubMed]

2001 (2)

1999 (3)

L. Zhu, P.-C. Sun, and Y. Fainman, “Aberration free dynamic focusing with a multichannel micromachined membrane deformable mirror,” Appl. Opt. 38, 5350–5354 (1999).
[Crossref]

L. Zhu, P.-C. Sun, D.-U. Bratsch, W. R. Freeman, and Y. Fainman, “Adaptive control of micromachined continuous membrane deformable mirror for aberration compensation,” Appl. Opt,  38, 168–176, (1999).
[Crossref]

L. Zhu, P. Sun, D. Bartsch, W. R. Freeman, and Y. Fainman, “Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror,” Appl. Opt.,  38, 1510–1518 (1999).
[Crossref]

1995 (1)

G. Vdovin and P. M. Sarro, “Flexible mirror micromachined in silicon,” App. Opt. 34, 2968–2972 (1995).
[Crossref]

1986 (1)

Artal, P.

Bareket, N.

Bartsch, D.

L. Zhu, P. Sun, D. Bartsch, W. R. Freeman, and Y. Fainman, “Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror,” Appl. Opt.,  38, 1510–1518 (1999).
[Crossref]

Benito, A.

J. F. Castejon-Mochon, N. Lopez-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611–1617 (2002).
[Crossref] [PubMed]

Bhattacharya, N.

Bonora, S.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, “Wavefront active control by a DSP-Driven deformable membrane mirror,” to be publiched on Review of scientific instruments (Accepted 24th July 2006).

Bower, J. E.

Braat, J. J. M.

Bratsch, D.-U.

L. Zhu, P.-C. Sun, D.-U. Bratsch, W. R. Freeman, and Y. Fainman, “Adaptive control of micromachined continuous membrane deformable mirror for aberration compensation,” Appl. Opt,  38, 168–176, (1999).
[Crossref]

Capraro, I.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, “Wavefront active control by a DSP-Driven deformable membrane mirror,” to be publiched on Review of scientific instruments (Accepted 24th July 2006).

Castejon-Mochon, J. F.

J. F. Castejon-Mochon, N. Lopez-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611–1617 (2002).
[Crossref] [PubMed]

Clafin, E. S.

Dainty, C.

Dalimier, E.

Dyson, H. M.

Fainman, Y.

L. Zhu, P. Sun, D. Bartsch, W. R. Freeman, and Y. Fainman, “Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror,” Appl. Opt.,  38, 1510–1518 (1999).
[Crossref]

L. Zhu, P.-C. Sun, and Y. Fainman, “Aberration free dynamic focusing with a multichannel micromachined membrane deformable mirror,” Appl. Opt. 38, 5350–5354 (1999).
[Crossref]

L. Zhu, P.-C. Sun, D.-U. Bratsch, W. R. Freeman, and Y. Fainman, “Adaptive control of micromachined continuous membrane deformable mirror for aberration compensation,” Appl. Opt,  38, 168–176, (1999).
[Crossref]

Fernández, E. J.

Frazier, B. W.

Freeman, W. R.

L. Zhu, P. Sun, D. Bartsch, W. R. Freeman, and Y. Fainman, “Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror,” Appl. Opt.,  38, 1510–1518 (1999).
[Crossref]

L. Zhu, P.-C. Sun, D.-U. Bratsch, W. R. Freeman, and Y. Fainman, “Adaptive control of micromachined continuous membrane deformable mirror for aberration compensation,” Appl. Opt,  38, 168–176, (1999).
[Crossref]

Iglesias, I.

Kurczynski, P.

Lai, W. Y.-C.

Lopez-Gil, N.

J. F. Castejon-Mochon, N. Lopez-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611–1617 (2002).
[Crossref] [PubMed]

Mansfield, W. M.

Poletto, L.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, “Wavefront active control by a DSP-Driven deformable membrane mirror,” to be publiched on Review of scientific instruments (Accepted 24th July 2006).

Romanin, M.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, “Wavefront active control by a DSP-Driven deformable membrane mirror,” to be publiched on Review of scientific instruments (Accepted 24th July 2006).

Sadoulet, B.

Sarro, P. M.

G. Vdovin and P. M. Sarro, “Flexible mirror micromachined in silicon,” App. Opt. 34, 2968–2972 (1995).
[Crossref]

Sun, P.

L. Zhu, P. Sun, D. Bartsch, W. R. Freeman, and Y. Fainman, “Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror,” Appl. Opt.,  38, 1510–1518 (1999).
[Crossref]

Sun, P.-C.

L. Zhu, P.-C. Sun, D.-U. Bratsch, W. R. Freeman, and Y. Fainman, “Adaptive control of micromachined continuous membrane deformable mirror for aberration compensation,” Appl. Opt,  38, 168–176, (1999).
[Crossref]

L. Zhu, P.-C. Sun, and Y. Fainman, “Aberration free dynamic focusing with a multichannel micromachined membrane deformable mirror,” Appl. Opt. 38, 5350–5354 (1999).
[Crossref]

Taylor, J. A.

Trestino, C.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, “Wavefront active control by a DSP-Driven deformable membrane mirror,” to be publiched on Review of scientific instruments (Accepted 24th July 2006).

Tyson, R. K.

Vdovin, G.

G. Vdovin and P. M. Sarro, “Flexible mirror micromachined in silicon,” App. Opt. 34, 2968–2972 (1995).
[Crossref]

Villoresi, P.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, “Wavefront active control by a DSP-Driven deformable membrane mirror,” to be publiched on Review of scientific instruments (Accepted 24th July 2006).

Vuelban, E. M.

Zhu, L.

L. Zhu, P.-C. Sun, D.-U. Bratsch, W. R. Freeman, and Y. Fainman, “Adaptive control of micromachined continuous membrane deformable mirror for aberration compensation,” Appl. Opt,  38, 168–176, (1999).
[Crossref]

L. Zhu, P. Sun, D. Bartsch, W. R. Freeman, and Y. Fainman, “Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror,” Appl. Opt.,  38, 1510–1518 (1999).
[Crossref]

L. Zhu, P.-C. Sun, and Y. Fainman, “Aberration free dynamic focusing with a multichannel micromachined membrane deformable mirror,” Appl. Opt. 38, 5350–5354 (1999).
[Crossref]

App. Opt. (1)

G. Vdovin and P. M. Sarro, “Flexible mirror micromachined in silicon,” App. Opt. 34, 2968–2972 (1995).
[Crossref]

Appl. Opt (1)

L. Zhu, P.-C. Sun, D.-U. Bratsch, W. R. Freeman, and Y. Fainman, “Adaptive control of micromachined continuous membrane deformable mirror for aberration compensation,” Appl. Opt,  38, 168–176, (1999).
[Crossref]

Appl. Opt. (4)

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

Opt. Express (3)

Opt. Lett. (2)

Vision Res. (1)

J. F. Castejon-Mochon, N. Lopez-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611–1617 (2002).
[Crossref] [PubMed]

Other (1)

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, “Wavefront active control by a DSP-Driven deformable membrane mirror,” to be publiched on Review of scientific instruments (Accepted 24th July 2006).

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Figures (8)

Fig. 1.
Fig. 1. Schematic of the push-pull mirror and picture of the prototype.

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Fig. 2.
Fig. 2. Geometry of the actuators: a) non-transparent electrodes placed under the bottom side of the membrane; b) transparent actuators placed over the top side of the membrane. The red line indicates the size of the membrane. The ITO coated glass is the dashed blue pattern.

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Fig. 3.
Fig. 3. Interferogram of the mirror flat position taken by a Zygo interferometer.

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Fig. 3.
Fig. 3. (a). peak-to-valley amplitude obtained by the NNLS fitting of the first three terms of Zernike polynomials over the active region. The horizontal red lines represent the pad positions of the first, second and third ring. (b) Purity of the first three terms of the Zernike polynomials over the active region.

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Fig. 4.
Fig. 4. Examples of measured influence functions. Surface and interferograms are shown for the electrodes 2, 8, 20, 38, 42.

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Fig. 5.
Fig. 5. interferograms of the main aberrations measured with Zygo interferometer.

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Fig. 6.
Fig. 6. (a). histogram of the Peak to Valley measurements of the main Zernike Polynomials obtained from the model (green) and measured (red). b) comparison between the peak to valley measurements of the Pull mirror (red) and the Push-Pull mirror (green).

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Fig. 7.
Fig. 7. Residual wavefront rms error after fitting with Pull mirror and Push-Pull mirror over a 10mm pupil.

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Tables (1)

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Table 1. results of the aberrations produced with the Push-Pull mirror.

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Equations (5)

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P i = D i D 1 2 + . . . . . + D n 2
D i = < M ( x , y ) • z ̂ i ( x , y ) >
A = [ A 1 . . . . . A 47 ]
p = A − 1 Z ( x , y )
p ″ = A ″ − 1 [ Z ( x , y ) − A ′ p ′ ]

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