Abstract

A deformable mirror based on internal reflection from an electrostatically deformable liquid–air interface is proposed and investigated. A differential equation describing the static behavior of such a mirror is analyzed and solved numerically. Stable closed-loop operation of an adaptive optical system with a liquid deformable mirror is demonstrated, including forming and the correction of low-order aberrations described by Zernike polynomials and the real-time correction of dynamically changing aberrations.

© 2009 Optical Society of America

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References

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    [CrossRef]
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2008 (1)

2007 (1)

2006 (1)

2004 (1)

S. Kuiper and B. Hendriks, Appl. Phys. Lett. 85, 1128 (2004).
[CrossRef]

2001 (1)

2000 (1)

1996 (1)

Bhattacharya, N.

Borra, E. F.

Braat, J. J. M.

Brousseau, D.

Dipper, N.

Dyson, H.

Hendriks, B.

S. Kuiper and B. Hendriks, Appl. Phys. Lett. 85, 1128 (2004).
[CrossRef]

Jamar, C. A.

Kuiper, S.

S. Kuiper and B. Hendriks, Appl. Phys. Lett. 85, 1128 (2004).
[CrossRef]

Loktev, M.

Ninane, N. M.

Samokhin, A.

Saranin, V. A.

V. A. Saranin, Equilibrum of Liquids and Its Stability (Institute of Computer Research, 2002).

Sharples, R.

Soloviev, O.

Thibault, S.

Tremblay, G.

Vdovin, G.

Vuelban, E. M.

Supplementary Material (1)

» Media 1: MOV (900 KB)     

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Figures (5)

Fig. 1
Fig. 1

Schematic of a deformable mirror based on full internal reflection (FIR) from the liquid interface.

Fig. 2
Fig. 2

Calculated response caused by V = 100 V applied to a circular electrode of 2 mm in diameter, positioned 0.5 mm over the liquid surface, for different electrode positions.

Fig. 3
Fig. 3

Closed-loop adaptive optical system for the investigation of the properties of a liquid deformable mirror.

Fig. 4
Fig. 4

Live interferograms of the of the influence functions of the liquid corrector: zero (top left), nonzero control voltage applied to different electrodes (top right and bottom left), and computer simulation (bottom right). The responses are axially symmetrical, and the observed elliptic shape is caused by the tilted incidence.

Fig. 5
Fig. 5

Live interferograms obtained in a closed loop AO system: tilt (top left), defocus (top right), astigmatism (second row left), coma (second row right), trifoil (third row left), catastrophic instability (third row right), aberration introduced with AO loop open (bottom row left), aberration corrected with AO loop closed (bottom row right). See Media 1 for the dynamics of the closed-loop AO system behavior.

Equations (4)

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Δ U ( x , y ) = ε ε 0 V ( x , y ) 2 2 d 2 ρ g U ( x , y ) k U ( x , y ) T ,
U max = ε ε 0 V max 2 2 ( ρ g + k ) d 2 .
U i , j = T ( U i 1 , j + U i + 1 , j + U i , j 1 + U i , j + 1 ) ε ε 0 V i , j 2 δ 2 2 d 2 ( ρ g + k ) δ 2 + 4 T .
( V d ) 2 < 2 ε 0 ρ g T .

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