Abstract

This paper presents the first-ever experimental evaluation of a closed-loop adaptive optics system based on a magnetic fluid deformable mirror (MFDM). MFDMs are a new type of wavefront correctors used in adaptive optics systems to compensate for complex optical aberrations. They have been found particularly suitable for ophthalmic imaging systems where they can be used to compensate for the aberrations in the eye that lead to blurry retinal images. However, their practical implementation in clinical devices requires effective methods to control the shape of their deformable surface. This paper presents one such control method which is based on an innovative technique used to linearize the response of the MFDM surface shape. The design of the controller is based on a DC-decoupled model of the multi-input multi-output system and on considering a decentralized PI controller. Experimental results showing the performance of the closed-loop system comprising the developed controller and a 19-channel prototype MFDM are presented.

© 2009 OSA

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2008

2007

D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
[CrossRef] [PubMed]

D. A. Horsleya, H. Parka, S. P. Lautb, and J. S. Wernerb, “Characterization of a bimorph deformable mirror using stroboscopic phase-shifting interferometry,” Sensor. Actuat, A-Phys. 134, 221–230 (2007).
[CrossRef]

P. A. Piers, S. Manzanera, P. M. Prieto, N. Gorceix, and P. Artal, “Use of adaptive optics to determine the optimal ocular spherical aberration,” J. Cataract Refract. Surg. 33(10), 1721–1726 (2007).
[CrossRef] [PubMed]

I. W. Jung, Y. A. Peter, E. Carr, J. S. Wang, and O. Solgaard, “Single-crystal-silicon continuous membrane deformable mirror array for adaptive optics in space-based telescopes,” IEEE J. Sel. Top. Quantum Electron. 13(2), 162–167 (2007).
[CrossRef]

2006

2005

E. Dalimier and C. Dainty, “Comparative analysis of deformable mirrors for ocular adaptive optics,” Opt. Express 13(11), 4275–4285 (2005).
[CrossRef] [PubMed]

A. Liotard, S. Muraret, F. Zamkotsian, and J. Y. Fourniols, “Static and dynamic microdeformable mirror characterization by phase-shifting and time-averaged interferometry,” Proc. SPIE 5716, 207–217 (2005).
[CrossRef]

2003

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

2002

A. Tuantranont and V. M. Bright, “Segmented silicon-micromachined microelectromechanical deformable mirrors for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 8(1), 33–45 (2002).
[CrossRef]

J. A. Perreault, T. G. Bifano, B. M. Levine, and M. N. Horenstein, “Adaptive optic correction using microelectromechanical deformable mirrors,” Opt. Eng. 41(3), 561–566 (2002).
[CrossRef]

N. Doble, G. Yoon, L. Chen, P. Bierden, B. Singer, S. Olivier, and D. R. Williams, “Use of a microelectromechanical mirror for adaptive optics in the human eye,” Opt. Lett. 27(17), 1537–1539 (2002).
[CrossRef]

2001

D. C. Dayton, J. D. Mansell, J. D. Gonglewski, and S. R. Restino, “Novel micromachined membrane mirror characterization and closed-loop demonstration,” Opt. Commun. 200(1-6), 99–105 (2001).
[CrossRef]

1953

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

Artal, P.

P. A. Piers, S. Manzanera, P. M. Prieto, N. Gorceix, and P. Artal, “Use of adaptive optics to determine the optimal ocular spherical aberration,” J. Cataract Refract. Surg. 33(10), 1721–1726 (2007).
[CrossRef] [PubMed]

Arzelier, D.

Babcock, H. W.

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

Baudouin, L.

Ben Amara, F.

A. Iqbal and F. Ben Amara, “Modeling and experimental evaluation of a circular magnetic-fluid deformable mirror,” Int. J. Optomechatronics 2(2), 126–143 (2008).
[CrossRef]

Bergamasco, R.

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Berube, V.

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Bierden, P.

Bifano, T. G.

J. A. Perreault, T. G. Bifano, B. M. Levine, and M. N. Horenstein, “Adaptive optic correction using microelectromechanical deformable mirrors,” Opt. Eng. 41(3), 561–566 (2002).
[CrossRef]

Bogart, G.

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

Borra, E. F.

D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
[CrossRef] [PubMed]

P. Laird, N. Caron, M. Rioux, E. F. Borra, and A. R. Ritcey, “Ferrofluidic adaptive mirrors,” Appl. Opt. 45(15), 3495–3500 (2006).
[CrossRef] [PubMed]

S. Thibault, D. Brousseau, M. Rioux, S. Senkow, J. P. Dery, E. F. Borra, and A. R. Ritcey, “Nanoengineered ferrofluid deformable mirror: A progress report,” Proc. SPIE 6272, 627231 (2006).

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Bright, V. M.

A. Tuantranont and V. M. Bright, “Segmented silicon-micromachined microelectromechanical deformable mirrors for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 8(1), 33–45 (2002).
[CrossRef]

Brousseau, D.

D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
[CrossRef] [PubMed]

S. Thibault, D. Brousseau, M. Rioux, S. Senkow, J. P. Dery, E. F. Borra, and A. R. Ritcey, “Nanoengineered ferrofluid deformable mirror: A progress report,” Proc. SPIE 6272, 627231 (2006).

Caron, N.

Carr, E.

I. W. Jung, Y. A. Peter, E. Carr, J. S. Wang, and O. Solgaard, “Single-crystal-silicon continuous membrane deformable mirror array for adaptive optics in space-based telescopes,” IEEE J. Sel. Top. Quantum Electron. 13(2), 162–167 (2007).
[CrossRef]

Chen, L.

da Silva, L. V.

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Dainty, C.

Dalimier, E.

Dayton, D. C.

D. C. Dayton, J. D. Mansell, J. D. Gonglewski, and S. R. Restino, “Novel micromachined membrane mirror characterization and closed-loop demonstration,” Opt. Commun. 200(1-6), 99–105 (2001).
[CrossRef]

Dery, J. P.

S. Thibault, D. Brousseau, M. Rioux, S. Senkow, J. P. Dery, E. F. Borra, and A. R. Ritcey, “Nanoengineered ferrofluid deformable mirror: A progress report,” Proc. SPIE 6272, 627231 (2006).

Doble, N.

Fourniols, J. Y.

A. Liotard, S. Muraret, F. Zamkotsian, and J. Y. Fourniols, “Static and dynamic microdeformable mirror characterization by phase-shifting and time-averaged interferometry,” Proc. SPIE 5716, 207–217 (2005).
[CrossRef]

Gonglewski, J. D.

D. C. Dayton, J. D. Mansell, J. D. Gonglewski, and S. R. Restino, “Novel micromachined membrane mirror characterization and closed-loop demonstration,” Opt. Commun. 200(1-6), 99–105 (2001).
[CrossRef]

Gorceix, N.

P. A. Piers, S. Manzanera, P. M. Prieto, N. Gorceix, and P. Artal, “Use of adaptive optics to determine the optimal ocular spherical aberration,” J. Cataract Refract. Surg. 33(10), 1721–1726 (2007).
[CrossRef] [PubMed]

Guignard, F.

Horenstein, M. N.

J. A. Perreault, T. G. Bifano, B. M. Levine, and M. N. Horenstein, “Adaptive optic correction using microelectromechanical deformable mirrors,” Opt. Eng. 41(3), 561–566 (2002).
[CrossRef]

Horsleya, D. A.

D. A. Horsleya, H. Parka, S. P. Lautb, and J. S. Wernerb, “Characterization of a bimorph deformable mirror using stroboscopic phase-shifting interferometry,” Sensor. Actuat, A-Phys. 134, 221–230 (2007).
[CrossRef]

Iqbal, A.

A. Iqbal and F. Ben Amara, “Modeling and experimental evaluation of a circular magnetic-fluid deformable mirror,” Int. J. Optomechatronics 2(2), 126–143 (2008).
[CrossRef]

Jung, I. W.

I. W. Jung, Y. A. Peter, E. Carr, J. S. Wang, and O. Solgaard, “Single-crystal-silicon continuous membrane deformable mirror array for adaptive optics in space-based telescopes,” IEEE J. Sel. Top. Quantum Electron. 13(2), 162–167 (2007).
[CrossRef]

Kurczynski, P.

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

Lai, W.

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

Laird, P.

P. Laird, N. Caron, M. Rioux, E. F. Borra, and A. R. Ritcey, “Ferrofluidic adaptive mirrors,” Appl. Opt. 45(15), 3495–3500 (2006).
[CrossRef] [PubMed]

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Lautb, S. P.

D. A. Horsleya, H. Parka, S. P. Lautb, and J. S. Wernerb, “Characterization of a bimorph deformable mirror using stroboscopic phase-shifting interferometry,” Sensor. Actuat, A-Phys. 134, 221–230 (2007).
[CrossRef]

Levine, B. M.

J. A. Perreault, T. G. Bifano, B. M. Levine, and M. N. Horenstein, “Adaptive optic correction using microelectromechanical deformable mirrors,” Opt. Eng. 41(3), 561–566 (2002).
[CrossRef]

Lifton, V.

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

Liotard, A.

A. Liotard, S. Muraret, F. Zamkotsian, and J. Y. Fourniols, “Static and dynamic microdeformable mirror characterization by phase-shifting and time-averaged interferometry,” Proc. SPIE 5716, 207–217 (2005).
[CrossRef]

Looze, D. P.

Mansell, J. D.

D. C. Dayton, J. D. Mansell, J. D. Gonglewski, and S. R. Restino, “Novel micromachined membrane mirror characterization and closed-loop demonstration,” Opt. Commun. 200(1-6), 99–105 (2001).
[CrossRef]

Mansfield, W.

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

Manzanera, S.

P. A. Piers, S. Manzanera, P. M. Prieto, N. Gorceix, and P. Artal, “Use of adaptive optics to determine the optimal ocular spherical aberration,” J. Cataract Refract. Surg. 33(10), 1721–1726 (2007).
[CrossRef] [PubMed]

Muraret, S.

A. Liotard, S. Muraret, F. Zamkotsian, and J. Y. Fourniols, “Static and dynamic microdeformable mirror characterization by phase-shifting and time-averaged interferometry,” Proc. SPIE 5716, 207–217 (2005).
[CrossRef]

Olivier, S.

Parka, H.

D. A. Horsleya, H. Parka, S. P. Lautb, and J. S. Wernerb, “Characterization of a bimorph deformable mirror using stroboscopic phase-shifting interferometry,” Sensor. Actuat, A-Phys. 134, 221–230 (2007).
[CrossRef]

Perreault, J. A.

J. A. Perreault, T. G. Bifano, B. M. Levine, and M. N. Horenstein, “Adaptive optic correction using microelectromechanical deformable mirrors,” Opt. Eng. 41(3), 561–566 (2002).
[CrossRef]

Peter, Y. A.

I. W. Jung, Y. A. Peter, E. Carr, J. S. Wang, and O. Solgaard, “Single-crystal-silicon continuous membrane deformable mirror array for adaptive optics in space-based telescopes,” IEEE J. Sel. Top. Quantum Electron. 13(2), 162–167 (2007).
[CrossRef]

Piers, P. A.

P. A. Piers, S. Manzanera, P. M. Prieto, N. Gorceix, and P. Artal, “Use of adaptive optics to determine the optimal ocular spherical aberration,” J. Cataract Refract. Surg. 33(10), 1721–1726 (2007).
[CrossRef] [PubMed]

Prieto, P. M.

P. A. Piers, S. Manzanera, P. M. Prieto, N. Gorceix, and P. Artal, “Use of adaptive optics to determine the optimal ocular spherical aberration,” J. Cataract Refract. Surg. 33(10), 1721–1726 (2007).
[CrossRef] [PubMed]

Prieur, C.

Restino, S. R.

D. C. Dayton, J. D. Mansell, J. D. Gonglewski, and S. R. Restino, “Novel micromachined membrane mirror characterization and closed-loop demonstration,” Opt. Commun. 200(1-6), 99–105 (2001).
[CrossRef]

Rioux, M.

S. Thibault, D. Brousseau, M. Rioux, S. Senkow, J. P. Dery, E. F. Borra, and A. R. Ritcey, “Nanoengineered ferrofluid deformable mirror: A progress report,” Proc. SPIE 6272, 627231 (2006).

P. Laird, N. Caron, M. Rioux, E. F. Borra, and A. R. Ritcey, “Ferrofluidic adaptive mirrors,” Appl. Opt. 45(15), 3495–3500 (2006).
[CrossRef] [PubMed]

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Ritcey, A. R.

P. Laird, N. Caron, M. Rioux, E. F. Borra, and A. R. Ritcey, “Ferrofluidic adaptive mirrors,” Appl. Opt. 45(15), 3495–3500 (2006).
[CrossRef] [PubMed]

S. Thibault, D. Brousseau, M. Rioux, S. Senkow, J. P. Dery, E. F. Borra, and A. R. Ritcey, “Nanoengineered ferrofluid deformable mirror: A progress report,” Proc. SPIE 6272, 627231 (2006).

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Robitaille, N.

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Sadoulet, B.

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

Scipioni, M.

Senkow, S.

S. Thibault, D. Brousseau, M. Rioux, S. Senkow, J. P. Dery, E. F. Borra, and A. R. Ritcey, “Nanoengineered ferrofluid deformable mirror: A progress report,” Proc. SPIE 6272, 627231 (2006).

Singer, B.

Solgaard, O.

I. W. Jung, Y. A. Peter, E. Carr, J. S. Wang, and O. Solgaard, “Single-crystal-silicon continuous membrane deformable mirror array for adaptive optics in space-based telescopes,” IEEE J. Sel. Top. Quantum Electron. 13(2), 162–167 (2007).
[CrossRef]

Thibault, S.

D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
[CrossRef] [PubMed]

S. Thibault, D. Brousseau, M. Rioux, S. Senkow, J. P. Dery, E. F. Borra, and A. R. Ritcey, “Nanoengineered ferrofluid deformable mirror: A progress report,” Proc. SPIE 6272, 627231 (2006).

P. Laird, R. Bergamasco, V. Berube, E. F. Borra, A. R. Ritcey, M. Rioux, N. Robitaille, S. Thibault, L. V. da Silva, and H. Yockell-Lelivre, “Ferrofluid-based deformable mirrors: a new approach to adaptive optics using liquid mirrors,” Proc. SPIE 4839, 733–740 (2003).
[CrossRef]

Tuantranont, A.

A. Tuantranont and V. M. Bright, “Segmented silicon-micromachined microelectromechanical deformable mirrors for adaptive optics,” IEEE J. Sel. Top. Quantum Electron. 8(1), 33–45 (2002).
[CrossRef]

Tyson, J.

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

Tyson, R. K.

Viegas, J.

Wang, J. S.

I. W. Jung, Y. A. Peter, E. Carr, J. S. Wang, and O. Solgaard, “Single-crystal-silicon continuous membrane deformable mirror array for adaptive optics in space-based telescopes,” IEEE J. Sel. Top. Quantum Electron. 13(2), 162–167 (2007).
[CrossRef]

Wernerb, J. S.

D. A. Horsleya, H. Parka, S. P. Lautb, and J. S. Wernerb, “Characterization of a bimorph deformable mirror using stroboscopic phase-shifting interferometry,” Sensor. Actuat, A-Phys. 134, 221–230 (2007).
[CrossRef]

Williams, D. R.

P. Kurczynski, G. Bogart, W. Lai, V. Lifton, W. Mansfield, J. Tyson, B. Sadoulet, and D. R. Williams, “Electrostatically actuated membrane mirrors for adaptive optics,” Proc. SPIE 4983, 250–258 (2003).
[CrossRef]

N. Doble, G. Yoon, L. Chen, P. Bierden, B. Singer, S. Olivier, and D. R. Williams, “Use of a microelectromechanical mirror for adaptive optics in the human eye,” Opt. Lett. 27(17), 1537–1539 (2002).
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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of an adaptive optics system.

Fig. 2
Fig. 2

Schematic diagram of a typical MFDM.

Fig. 3
Fig. 3

Schematic diagram of the modified MFDM.

Fig. 4
Fig. 4

Closed-loop AO system: (a) Typical system, (b) Equivalent simulated system.

Fig. 5
Fig. 5

Block diagram of the closed-loop system.

Fig. 6
Fig. 6

Optical side of the experimental setup.

Fig. 7
Fig. 7

Tracking of the generalized wavefront shape: (a) Wavefront shape, (b) RMS error.

Fig. 8
Fig. 8

The point spread function (computed from the obtained data) of the static wavefront error before and after applying the AO correction: (a) Before correction, (b) After correction.

Fig. 9, part 1
Fig. 9, part 1

Zernike mode shapes generated using the MFDM: (a) desired shapes, (b) acquired shapes, (c) error surface.

Fig. 9, part 2
Fig. 9, part 2

Zernike mode shapes generated using the MFDM: (a) desired shapes, (b) acquired shapes, (c) error surface.

Fig. 10
Fig. 10

RMS error for the Zernike mode shapes generated using the MFDM.

Equations (9)

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ζ s = ζ a b e r r a t e d 2 ζ
e = r y s
x ( k + 1 ) = A g x ( k ) + B g u ( k ) y s ( k ) = C g x ( k )
G 0 = C g ( I A g ) 1 B g
G ¯ ( z ) = G ( z ) G 0 1
K = G 0 1 K ¯ = k G 0 1
k ( z ) = k p + k i z z 1
k p = 0.025 , k i = 0.056
r = [ 2.0 , 4.0 , 5.0 , 1.0 , 5.5 , 0.5 , 3.5 , 8.5 , 6.0 , 3.0 , 2.5 , 2.0 , 3.0 , 4.0 , 2.0 , 4.0 , 5.0 , 1.0 , 6.0 ] T ( μ m )

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