Abstract

A simple but effective decoupling control algorithm based on Zernike mode decomposition for adaptive optics systems with dual deformable mirrors is proposed. One of the two deformable mirrors is characterized with a large stroke (woofer) and the other with high spatial resolutions (tweeter). The algorithm works as follows: wavefront gradient vector is decoupled using the Zernike modes at first, and then the control vector for the woofer is generated with low order Zernike coefficients to eliminate high order modes. At the same time the control vector for the tweeter is reset by a constraint matrix in order to avoid coupling error accumulation. Simulation indicates the algorithm could get better performance compared with traditional Zernike mode decomposition control algorithms. Experiments demonstrate that this algorithm can effectively compensate for phase distortions and significantly suppress the coupling between the woofer and tweeter.

© 2013 Optical Society of America

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References

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2012 (2)

2011 (1)

2010 (2)

2009 (3)

2008 (2)

2007 (4)

2006 (1)

Agathoklis, P.

Blain, C.

Bradley, C.

Brown, J. M.

Burns, S. A.

Cense, B.

Chen, B.

Chen, D. C.

Choi, S.

Conan, R.

Dong, L.

Gao, W.

Guan, C.

Hampton, P.

Hampton, P. J.

Hilton, A.

Hou, J.

Hu, S.

Ivers, K. M.

Jiang, W.

Jones, S. M.

Jonnal, R. S.

Keskin, O.

Kocaoglu, O. P.

Koperda, E.

Lavigne, J. F.

Lei, X.

Li, C.

Liu, G.

Liu, W.

Miller, D. T.

Ning, Y.

Oliver, S. S.

Olivier, S. S.

Porter, J.

Qi, X.

Queener, H.

Rao, C.

Silva, D. A.

Sredar, N.

Véran, J. P.

Wang, S.

Werner, J. S.

Wu, J.

Xu, B.

Yan, H.

Yang, H.

Yang, P.

Yu, H.

Zawadzki, R.

Zhang, X.

Zhang, Y.

Zhou, H.

Zou, W.

Appl. Opt. (4)

Biomed. Opt. Express (1)

Chin. Opt. Lett. (1)

J. Opt. Soc. Am. A (4)

Opt. Express (4)

Opt. Lett. (1)

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Figures (13)

Fig. 1
Fig. 1

A typical dual deformable mirrors adaptive optics system.

Fig. 2
Fig. 2

Configurations of the Hartmann-Shack wavefront sensor’s sub-apertures and the DM’s actuators: (a) woofer; (b) tweeter.

Fig. 3
Fig. 3

Zernike coefficients of the phase aberration.

Fig. 4
Fig. 4

(a) RMS of the residual wavefront during correction; (b) Coupling coefficient during the correction.

Fig. 5
Fig. 5

Schematic diagram of the experiment system.

Fig. 6
Fig. 6

Actuator geometry and the clear aperture of deformable mirrors used in the experiments: (a) woofer; (b) tweeter.

Fig. 7
Fig. 7

(a) RMS of the residual wavefront during correction; (b) Wavefront error composition quantified by Zernike order.

Fig. 8
Fig. 8

(a) The initial aberrations (RMS = 0.665λ), (b) The residual wavefront after correction only by the woofer to compensate defocus (RMS = 0. 373λ), (c) The residual wavefront corrected only by the tweeter to compensate aberrations except defocus (RMS = 0. 568λ), (d) The residual wavefront corrected by woofer and tweeter together (RMS = 0.021λ).

Fig. 9
Fig. 9

(a) RMS of the residual wavefront during correction; (b) Wavefront error composition quantified by Zernike order.

Fig. 10
Fig. 10

(a) The initial aberrations (RMS = 0.672λ), (b) The residual wavefront after correction only by the woofer to compensate 0° astigmatism (RMS = 0. 618λ), (c) The residual wavefront corrected only by the tweeter to compensate aberrations except 0° astigmatism (RMS = 0. 305λ), (d) The residual wavefront corrected by woofer and tweeter together (RMS = 0.019λ).

Fig. 11
Fig. 11

(a) RMS of the residual wavefront during correction; (b) Wavefront error composition quantified by Zernike order.

Fig. 12
Fig. 12

(a) The initial aberrations (RMS = 0.673λ), (b) The residual wavefront after correction only by the woofer to compensate defocus and astigmatisms (RMS = 0. 120λ), (c) The residual wavefront corrected only by the tweeter to compensate aberrations except defocus and astigmatisms (RMS = 0. 665λ), (d) The residual wavefront corrected by woofer and tweeter together (RMS = 0.031λ).

Fig. 13
Fig. 13

The coupling coefficient during the longtime experiment.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

g=Za,
a= Z + g,
a w = I w Z + g,
A w (k+1)=pid_a× A w (k)+pid_b× a w (k),
V w =T A w ,
g= R w v w =Za,
v w = R w + Za,
T= R w + Z,
g t =gZ I w Z + g=(IZ I w Z + )g,
v t = R t + g t ,
V t '(k+1)=pid_a× V t (k)+pid_b× v t (k),
V t '= V t +ΔVI V t ,
0= R m V t ,
R m ( i,j )=k V i (x,y) Z j (x,y) Z j (x,y) Z j (x,y) ,
[ V t ' 0 ]=[ V t +ΔV 0 ][ I R m ] V t ,
C= [ I R m ] + ,
V t [ I R m ] + [ V t +ΔV 0 ]= [ I R m ] + [ V t ' 0 ]=C[ V t ' 0 ],
V i (x,y)=exp[lnω ( (x x i ) 2 + (y y i ) 2 /d) α ],
r= | S w S t ds | S w S w ds S t S t ds ,

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