Abstract

Many next-generation adaptive optics (AO) systems for vision will have two deformable mirrors (DMs) instead of one: a high-stroke, low-resolution mirror (the woofer) and a low-stroke, high-resolution mirror (the tweeter). We developed a zonal wavefront-control algorithm and validated it using simulations. Rather than separating the woofer and tweeter corrections into two independent control processes or using a modal decomposition, the algorithm we proposed uses wavefront slope measurements from a single Shack–Hartmann wavefront sensor to generate control signals for both deformable mirrors within a single zonal control. A Lagrange multiplier is chosen to integrate two DMs into a single-DM wavefront control, and a damped least-squares control is employed to suppress the correlation between the two DMs.

© 2008 Optical Society of America

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References

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2007 (4)

2006 (2)

S. Hu, B. Xu, X. Zhang, J. Hou, J. Wu, and W. Jiang, Appl. Opt. 45, 2638 (2006).
[CrossRef] [PubMed]

T. J. Brennan and T. A. Rhoadarmer, Proc. SPIE 6306, 63060B1 (2006).

2002 (3)

2001 (1)

J. S. McLellan, S. Marcos, and S. A. Burns, Invest. Ophthalmol. Visual Sci. 42, 1390 (2001).

1994 (1)

K. Levenberg, J. Appl. Math. 2, 164 (1994).

1976 (1)

1974 (1)

D. Q. Su and Y. N. Wang, Acta Astron. Sin. 15, 51 (1974).

Barchers, J. D.

Blain, C.

Bradley, C.

Brennan, T. J.

T. J. Brennan and T. A. Rhoadarmer, Proc. SPIE 6306, 63060B1 (2006).

Burns, S. A.

J. S. McLellan, S. Marcos, and S. A. Burns, Invest. Ophthalmol. Visual Sci. 42, 1390 (2001).

Chen, D. C.

Conan, R.

Hampton, P.

Hilton, A.

Hou, J.

Hu, S.

Jiang, W.

Jones, S. M.

Keskin, O.

Levenberg, K.

K. Levenberg, J. Appl. Math. 2, 164 (1994).

Liu, G.

Marcos, S.

J. S. McLellan, S. Marcos, and S. A. Burns, Invest. Ophthalmol. Visual Sci. 42, 1390 (2001).

McLellan, J. S.

J. S. McLellan, S. Marcos, and S. A. Burns, Invest. Ophthalmol. Visual Sci. 42, 1390 (2001).

Noll, R. J.

Olivier, S. S.

Rao, C.

Rhoadarmer, T. A.

T. J. Brennan and T. A. Rhoadarmer, Proc. SPIE 6306, 63060B1 (2006).

Silva, D. A.

Su, D. Q.

D. Q. Su and Y. N. Wang, Acta Astron. Sin. 15, 51 (1974).

Wang, Y. N.

D. Q. Su and Y. N. Wang, Acta Astron. Sin. 15, 51 (1974).

Wu, J.

Xu, B.

Yang, H.

Zhang, W.

Zhang, X.

Zhang, Y.

Zou, W.

W. Zou, Opt. Eng. (Bellingham) 41, 2338 (2002).
[CrossRef]

Acta Astron. Sin. (1)

D. Q. Su and Y. N. Wang, Acta Astron. Sin. 15, 51 (1974).

Appl. Opt. (2)

Chin. Opt. Lett. (2)

Invest. Ophthalmol. Visual Sci. (1)

J. S. McLellan, S. Marcos, and S. A. Burns, Invest. Ophthalmol. Visual Sci. 42, 1390 (2001).

J. Appl. Math. (1)

K. Levenberg, J. Appl. Math. 2, 164 (1994).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Eng. (Bellingham) (1)

W. Zou, Opt. Eng. (Bellingham) 41, 2338 (2002).
[CrossRef]

Proc. SPIE (1)

T. J. Brennan and T. A. Rhoadarmer, Proc. SPIE 6306, 63060B1 (2006).

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Figures (4)

Fig. 1
Fig. 1

(a) Mapping of the DM 1 (Mirao) actuators and lenslet array. (b) Mapping of the DM 2 (BMC) actuators and lenslet array. (c) Influence function of a DM 1 actuator at (4.25, 4.25) ( σ = 1 , Gaussian). (d) Influence function of a DM 2 actuator at point (3.75, 3.25) ( σ = 0.2 , Gaussian).

Fig. 2
Fig. 2

(a) Input wavefront error map ( RMS = 2.9491 μ m ) . (b) 3D map of the DM 1 wavefront correction ( RMS = 3.0946 μ m ) . (c) 3D map of the DM 2 wavefront correction ( RMS = 1.2368 μ m ) . (d) Residual wavefront error map ( RMS = 0.4557 μ m ) . (e) Wavefront error comparisons quantified by Zernike order.

Fig. 3
Fig. 3

(a) 3D map of the DM 2 wavefront correction (no damping, RMS = 3.1881 μ m ). (b) Residual wavefront error map ( RMS = 2.5556 μ m ) . (c) Wavefront error comparisons quantified by Zernike order. (d) Single- DM 2 wavefront correction with conventional SVD method ( RMS = 3.1893 μ m ) .

Fig. 4
Fig. 4

(a) 3D map of the (Color on line) DM 1 wavefront correction (no damping, RMS = 3.0184 μ m ). (b) Residual wavefront error map ( RMS = 0.5707 μ m ) . (c) Wavefront error comparisons quantified by Zernike order. (d) Single- DM 1 wavefront correction with conventional SVD method ( RMS = 2.9956 μ m ) .

Equations (5)

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ψ ( X , Y ) = ρ 2 [ A X + λ B Y , S ] = A X + λ B Y S 2 2 ,
{ A T ( A X + λ B Y S ) = 0 B T ( A X + λ B Y S ) = 0 } .
C T C P = C T S ,
P = [ X Y ] = [ A T A + β 1 λ A T B λ B T A λ 2 B T B + β 2 ] 1 [ A T λ B T ] S ,
[ λ 1 A 1 T λ 2 A 2 T λ t A t T ] [ λ 1 A 1 λ 2 A 2 λ t A t ] [ F 1 F 2 F t ] = [ λ 1 A 1 T λ 2 A 2 T λ t A t T ] S ,

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