Abstract

Magnetic-liquid deformable mirrors (MLDMs) were introduced by our group in 2004 and numerous developments have been made since then. The usefulness of this type of mirror in various applications has already been shown, but experimental data on their dynamics are still lacking. A complete theoretical modeling of MLDM dynamics is a complex task because it requires an approach based on magnetohydrodynamics. A purpose of this paper is to present and analyze new experimental data of the dynamics of these mirrors from open-loop step response measurements and show that a basic transfer function modeling is adequate to achieve closed-loop control. Also, experimental data on the eigenmodes dynamic is presented and a modal-based control approach is suggested.

© 2014 Optical Society of America

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References

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    [CrossRef]
  2. D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15, 18190–18199 (2007).
    [CrossRef]
  3. A. Iqbal and F. B. Amara, “Modeling of a magnetic-fluid deformable mirror for retinal imaging adaptive optics systems,” Int. J. Optomechatron. 1, 180–208 (2007).
    [CrossRef]
  4. D. Brousseau, E. F. Borra, M. Rochette, and D. Bouffard-Landry, “Linearization of the response of a 91-actuator magnetic liquid deformable mirror,” Opt. Express 18, 8239–8250 (2010).
    [CrossRef]
  5. D. Brousseau, J. Drapeau, M. Piché, and E. F. Borra, “Generation of Bessel beams using a magnetic liquid deformable mirror,” Appl. Opt. 50, 4005–4010 (2011).
    [CrossRef]
  6. S. Thibault, D. Brousseau, and E. F. Borra, “Liquid deformable mirror for advanced sub-optical system testing,” Proc. SPIE 7739, 773910 (2010).
    [CrossRef]
  7. J. Parent, E. F. Borra, D. Brousseau, A. M. Ritcey, J.-P. Déry, and S. Thibault, “Dynamic response of ferrofluidic deformable mirrors,” Appl. Opt. 48, 1–6 (2009).
    [CrossRef]
  8. J. Clerk-Maxwell, Treatise on Electricity and Magnetism (Clarendon, 1873).
  9. F. Boyer and E. Falcon, “Wave turbulence on the surface of a ferrofluid in a magnetic field,” Phys. Rev. Lett. 101, 244502 (2008).
    [CrossRef]
  10. A. Visioli, Practical PID Control (Springer, 2006).
  11. T. Ruppel, “Model-based feed forward control of large deformable mirrors,” Eur. J. Control 3, 261–272 (2011).

2012 (1)

2011 (2)

T. Ruppel, “Model-based feed forward control of large deformable mirrors,” Eur. J. Control 3, 261–272 (2011).

D. Brousseau, J. Drapeau, M. Piché, and E. F. Borra, “Generation of Bessel beams using a magnetic liquid deformable mirror,” Appl. Opt. 50, 4005–4010 (2011).
[CrossRef]

2010 (2)

D. Brousseau, E. F. Borra, M. Rochette, and D. Bouffard-Landry, “Linearization of the response of a 91-actuator magnetic liquid deformable mirror,” Opt. Express 18, 8239–8250 (2010).
[CrossRef]

S. Thibault, D. Brousseau, and E. F. Borra, “Liquid deformable mirror for advanced sub-optical system testing,” Proc. SPIE 7739, 773910 (2010).
[CrossRef]

2009 (1)

2008 (1)

F. Boyer and E. Falcon, “Wave turbulence on the surface of a ferrofluid in a magnetic field,” Phys. Rev. Lett. 101, 244502 (2008).
[CrossRef]

2007 (2)

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

A. Iqbal and F. B. Amara, “Modeling of a magnetic-fluid deformable mirror for retinal imaging adaptive optics systems,” Int. J. Optomechatron. 1, 180–208 (2007).
[CrossRef]

Amara, F. B.

A. Iqbal and F. B. Amara, “Modeling of a magnetic-fluid deformable mirror for retinal imaging adaptive optics systems,” Int. J. Optomechatron. 1, 180–208 (2007).
[CrossRef]

Borra, E. F.

Bouffard-Landry, D.

Boyer, F.

F. Boyer and E. Falcon, “Wave turbulence on the surface of a ferrofluid in a magnetic field,” Phys. Rev. Lett. 101, 244502 (2008).
[CrossRef]

Brousseau, D.

Clerk-Maxwell, J.

J. Clerk-Maxwell, Treatise on Electricity and Magnetism (Clarendon, 1873).

Déry, J.-P.

Drapeau, J.

Falcon, E.

F. Boyer and E. Falcon, “Wave turbulence on the surface of a ferrofluid in a magnetic field,” Phys. Rev. Lett. 101, 244502 (2008).
[CrossRef]

Iqbal, A.

A. Iqbal and F. B. Amara, “Modeling of a magnetic-fluid deformable mirror for retinal imaging adaptive optics systems,” Int. J. Optomechatron. 1, 180–208 (2007).
[CrossRef]

Parent, J.

Piché, M.

Ritcey, A. M.

Rochette, M.

Ruppel, T.

T. Ruppel, “Model-based feed forward control of large deformable mirrors,” Eur. J. Control 3, 261–272 (2011).

ten Have, E. S.

Thibault, S.

Vdovin, G.

Visioli, A.

A. Visioli, Practical PID Control (Springer, 2006).

Appl. Opt. (3)

Eur. J. Control (1)

T. Ruppel, “Model-based feed forward control of large deformable mirrors,” Eur. J. Control 3, 261–272 (2011).

Int. J. Optomechatron. (1)

A. Iqbal and F. B. Amara, “Modeling of a magnetic-fluid deformable mirror for retinal imaging adaptive optics systems,” Int. J. Optomechatron. 1, 180–208 (2007).
[CrossRef]

Opt. Express (2)

Phys. Rev. Lett. (1)

F. Boyer and E. Falcon, “Wave turbulence on the surface of a ferrofluid in a magnetic field,” Phys. Rev. Lett. 101, 244502 (2008).
[CrossRef]

Proc. SPIE (1)

S. Thibault, D. Brousseau, and E. F. Borra, “Liquid deformable mirror for advanced sub-optical system testing,” Proc. SPIE 7739, 773910 (2010).
[CrossRef]

Other (2)

A. Visioli, Practical PID Control (Springer, 2006).

J. Clerk-Maxwell, Treatise on Electricity and Magnetism (Clarendon, 1873).

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Figures (10)

Fig. 1.
Fig. 1.

MLDM setup showing the coupled laser source (SRC) operating at 635 nm, the MLDM, the wavefront sensor (WFS), and the relay optics.

Fig. 2.
Fig. 2.

MLDM actuator array shown with the 120 active actuators and the 27.5-mm diameter pupil overlaid in red.

Fig. 3.
Fig. 3.

MLDM eigenvalues. Mode numbers superior to 30 are discarded due to their low gain relative to the maximum gain.

Fig. 4.
Fig. 4.

MLDM eigenmodes in WFS space.

Fig. 5.
Fig. 5.

Open-loop step response of the MLDM when a command is sent to the central actuator. The blue curve is the measured wavefront PV and the red curve is the mean of the x and y slope maximums as a function of time. Amplitude is given in normalized arbitrary units. The sampling frequency is 100 Hz.

Fig. 6.
Fig. 6.

Open-loop step response of the MLDM when a command is sent to the central actuator and its closest two neighbors are driven with an inverse command of 0.5× the command of the central actuator. The blue curve shows the measured wavefront PV while the red marker shows the mean of the x and y slope maximums as a function of time. Amplitude is given in normalized arbitrary units. The sampling frequency is 100 Hz.

Fig. 7.
Fig. 7.

Modeled open-loop step response of the MLDM central actuator based on transfer function of Eq. (1).

Fig. 8.
Fig. 8.

Wavefront RMS amplitude on the MLDM as a function of time at start of closing the loop using the basic PID controller. The closed-loop frequency is 97 Hz.

Fig. 9.
Fig. 9.

Wavefront PV open-loop step responses of MLDM for modes 1–12. Amplitude is given in normalized arbitrary units.

Fig. 10.
Fig. 10.

Open-loop step response of MLDM mode 30. The blue curve is the measured wavefront PV and the red curve is the mean of the x and y slope maximums as a function of time. Amplitude is given in normalized arbitrary units.

Tables (1)

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Table 1. Best Fit Parameters of MLDM Transfer Function Model

Equations (2)

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HMLDM(s)=g11(1+sT)+g2ω02(s2+2ζω0s+ω02),
u(t)=u(t1)+Kc[e(t)e(t1)]+KcΔtTie(t)+KcTdΔt[e(t)2e(t1)+e(t2)],

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