Abstract

Adaptive optics systems and control algorithms can be tested in the laboratory with controlled disturbances. We have a micromachined deformable mirror that we use as a programmable aberration generator. We present a method of programming the actuator amplitudes so that the wave front reflecting from the surface will simulate atmospheric turbulence. We present experimental results that show that we can simulate the Kolmogorov spatial spectrum within the constraints of the useful region of the deformable mirror.

© 2001 Optical Society of America

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References

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  1. R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, Boston, Mass., 1997).
  2. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. G. Vdovin, “Current performance limits for micromachined membrane deformable mirrors,” in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. Love, ed. (World Scientific, Singapore, 2000), pp. 118–122.
    [CrossRef]
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    [CrossRef]

2000

1999

1998

1992

D. P. Greenwood, C. A. Primmerman, “Adaptive optics research at Lincoln Laboratory,” Lincoln Lab. J. 5(1), 3–24 (1992).

1990

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

1979

1977

1976

Bartsch, D.

Booth, M. J.

Cagigal, M. P.

Canales, V. F.

Dainty, J. C.

Fainman, Y.

Freeman, W. R.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Greenwood, D. P.

D. P. Greenwood, C. A. Primmerman, “Adaptive optics research at Lincoln Laboratory,” Lincoln Lab. J. 5(1), 3–24 (1992).

D. P. Greenwood, “Bandwidth specification for adaptive optics systems,” J. Opt. Soc. Am. 67, 390–393 (1977).
[CrossRef]

Harding, C. M.

Johnston, R. A.

Lane, R. G.

Levine, M.

M. Levine, Adaptive Optics Associates, Inc., Cambridge, Mass. (personal communication, 2000).

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

Munro, I.

Neil, M. A. A.

Noll, R. J.

Paterson, C.

Primmerman, C. A.

D. P. Greenwood, C. A. Primmerman, “Adaptive optics research at Lincoln Laboratory,” Lincoln Lab. J. 5(1), 3–24 (1992).

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Sun, P.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, Boston, Mass., 1997).

Valley, G.

Vdovin, G.

G. Vdovin, Adaptive Mirror Micromachined in Silicon (Delft U. Press, Delft, The Netherlands, 1996).

G. Vdovin, “Current performance limits for micromachined membrane deformable mirrors,” in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. Love, ed. (World Scientific, Singapore, 2000), pp. 118–122.
[CrossRef]

Wandzura, S.

Wilson, T.

Zhu, L.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Lincoln Lab. J.

D. P. Greenwood, C. A. Primmerman, “Adaptive optics research at Lincoln Laboratory,” Lincoln Lab. J. 5(1), 3–24 (1992).

Opt. Eng.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Opt. Express

Opt. Lett.

Other

miniWavescope Users Manual (Adaptive Optics Associates, Inc., Cambridge, Mass., 1999).

M. Levine, Adaptive Optics Associates, Inc., Cambridge, Mass. (personal communication, 2000).

G. Vdovin, Adaptive Mirror Micromachined in Silicon (Delft U. Press, Delft, The Netherlands, 1996).

G. Vdovin, “Current performance limits for micromachined membrane deformable mirrors,” in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. Love, ed. (World Scientific, Singapore, 2000), pp. 118–122.
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, Boston, Mass., 1997).

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

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Figures (5)

Fig. 1
Fig. 1

Optical test configuration used to measure the wave front imparted by the aberration generator. For this experiment, the Xinetics DM was replaced by a flat. The OKO DM is the aberration generator. The imaging optics are not used. WFS, wave-front sensor.

Fig. 2
Fig. 2

Influence function of a central actuator of the OKO DM. The peak is approximately 0.5 µm. When unpowered, the mirror exhibits some tilt, focus, and astigmatism. These were removed through calibration and small adjustments to the 1× relay lenses.

Fig. 3
Fig. 3

Influence function of an edge actuator of the OKO DM. The peak is approximately 0.4 µm.

Fig. 4
Fig. 4

Wave front when the atmospheric turbulence actuator commands were applied. The rms wave-front error for this realization is approximately 0.80 µm.

Fig. 5
Fig. 5

Measured phase structure functions for a few realizations of atmospheric wave fronts compared with the theoretical value (solid curve).

Equations (9)

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

Dϕr=6.88r/r05/3.
Dϕr=ϕr1-ϕ(r1-r2,
Z=U-1·B,
surfacer, θ=n=1N anInr, θ,
n=1N anInr, θ
k=1M zkZkr, θ,
 n=1N anInr, θ-k=1M zkZkr, θ2rdrdθ.
an= Inr, θk=1M zkZkr, θrdrdθ In2r, θrdrdθ.
Inr, θ=1an,calk=1M zknZkr, θ

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