Abstract

A low cost adaptive optics system constructed almost entirely of commercially available components is presented. The system uses a 37 actuator membrane mirror and operates at frame rates up to 800 Hz using a single processor. Numerical modelling of the membrane mirror is used to optimize parameters of the system. The dynamic performance of the system is investigated in detail using a diffractive wavefront generator based on a ferroelectric spatial light modulator. This is used to produce wavefronts with time-varying aberrations. The ability of the system to correct for Kolmogorov turbulence with different strengths and effective wind speeds is measured experimentally using the wavefront generator.

©2000 Optical Society of America

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References

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2000 (1)

1998 (2)

1997 (1)

1995 (1)

1993 (1)

A. Glindemann, R. G. Lane, and J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[Crossref]

1986 (1)

1979 (1)

1977 (1)

Baker, J.

Bareket, N.

Biliotti, V.

D. Bonaccini, G. Brusa, S. Esposito, P. Salinari, P. Stefanini, and V. Biliotti, “Adaptive optics wave-front corrector using addressable liquid-crystal retarders.2.,” In Active and adaptive optical components, Proc. SPIE1543, 133–143 (Osserv Astrofis Arcetri, I-50125 Florence, Italy, 1992).

Bonaccini, D.

D. Bonaccini, G. Brusa, S. Esposito, P. Salinari, P. Stefanini, and V. Biliotti, “Adaptive optics wave-front corrector using addressable liquid-crystal retarders.2.,” In Active and adaptive optical components, Proc. SPIE1543, 133–143 (Osserv Astrofis Arcetri, I-50125 Florence, Italy, 1992).

Booth, M. J.

Browne, S.

Brusa, G.

D. Bonaccini, G. Brusa, S. Esposito, P. Salinari, P. Stefanini, and V. Biliotti, “Adaptive optics wave-front corrector using addressable liquid-crystal retarders.2.,” In Active and adaptive optical components, Proc. SPIE1543, 133–143 (Osserv Astrofis Arcetri, I-50125 Florence, Italy, 1992).

Claflin, E. S.

Dainty, J. C.

J. C. Dainty, A. V. Koryabin, and A. V. Kudryashov, “Low-order adaptive deformable mirror,” Appl. Opt. 37, 4663–4668 (1998).
[Crossref]

A. Glindemann, R. G. Lane, and J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[Crossref]

Dayton, D.

Esposito, S.

D. Bonaccini, G. Brusa, S. Esposito, P. Salinari, P. Stefanini, and V. Biliotti, “Adaptive optics wave-front corrector using addressable liquid-crystal retarders.2.,” In Active and adaptive optical components, Proc. SPIE1543, 133–143 (Osserv Astrofis Arcetri, I-50125 Florence, Italy, 1992).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, Cambridge, 1992).

Gallegos, J.

Glindemann, A.

A. Glindemann, R. G. Lane, and J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[Crossref]

Gonglewski, J.

Grosso, R. P.

Koryabin, A. V.

Kudryashov, A. V.

Lane, R. G.

A. Glindemann, R. G. Lane, and J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[Crossref]

Lipson, S. G.

Love, G. D.

McDermott, S.

Neil, M. A. A.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, Cambridge, 1992).

Restaino, S.

Roddier, F.

F. Roddier, “The problematic of adaptive optics design,” in Adaptive optics for astronomy, D.M. Alloin and J. M. Mariotti, eds., (Kluwer Academic, 1994), pp. 89–111.

Rogers, S.

Salinari, P.

D. Bonaccini, G. Brusa, S. Esposito, P. Salinari, P. Stefanini, and V. Biliotti, “Adaptive optics wave-front corrector using addressable liquid-crystal retarders.2.,” In Active and adaptive optical components, Proc. SPIE1543, 133–143 (Osserv Astrofis Arcetri, I-50125 Florence, Italy, 1992).

Sarro, P. M.

Shilko, M.

Stefanini, P.

D. Bonaccini, G. Brusa, S. Esposito, P. Salinari, P. Stefanini, and V. Biliotti, “Adaptive optics wave-front corrector using addressable liquid-crystal retarders.2.,” In Active and adaptive optical components, Proc. SPIE1543, 133–143 (Osserv Astrofis Arcetri, I-50125 Florence, Italy, 1992).

Steinhaus, E.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, Cambridge, 1992).

Vdovin, G.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, Cambridge, 1992).

Wilson, T.

Yellin, M.

Appl. Opt. (3)

J. Mod. Opt. (1)

A. Glindemann, R. G. Lane, and J. C. Dainty, “Simulation of time-evolving speckle patterns using Kolmogorov statistics,” J. Mod. Opt. 40, 2381–2388 (1993).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Lett. (1)

Other (4)

F. Roddier, “The problematic of adaptive optics design,” in Adaptive optics for astronomy, D.M. Alloin and J. M. Mariotti, eds., (Kluwer Academic, 1994), pp. 89–111.

http://okotech.com/mirrors/technical/index.html

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, Cambridge, 1992).

D. Bonaccini, G. Brusa, S. Esposito, P. Salinari, P. Stefanini, and V. Biliotti, “Adaptive optics wave-front corrector using addressable liquid-crystal retarders.2.,” In Active and adaptive optical components, Proc. SPIE1543, 133–143 (Osserv Astrofis Arcetri, I-50125 Florence, Italy, 1992).

Supplementary Material (1)

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the adaptive optical system

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Fig. 2.
Fig. 2.

Data flow for the adaptive optical system

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Fig. 3.
Fig. 3.

Singular values of the membrane mirror influence matrix

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Fig. 4.
Fig. 4.

Two modes of the membrane mirror corresponding to the largest (mode 1) and smallest (mode 37) singular values.

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Fig. 5.
Fig. 5.

Singular values of the membrane mirror influence matrix weighted for Kolmogorov statistics

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Fig. 6.
Fig. 6.

Mean Strehl, S=exp(-σ 2), correcting for Kolmogorov turbulence using the membrane mirror. (Monte Carlo with λ=633 nm, maximum actuator voltage V max=200V, maximum membrane deflection was 7.5 µm with all electrodes set to V max).

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Fig. 7.
Fig. 7.

Video showing the output image with the adaptive optics system correcting for turbulence with D/r 0=6 and v/r 0=25Hz (nominal). (1.89Mb movie)

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Fig. 8.
Fig. 8.

Plot of Strehl ratio v. number of spatial modes. [Exposure time 4 seconds, D/r 0=6, v/r 0=25Hz (nominal)]

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Fig. 9.
Fig. 9.

Experimental performance of the AO system for quasi-Kolmogorov turbulence of different strengths and wind speeds. (g=-0.52, frame rate=800 s-1, 24 spatial correction modes)

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Fig. 10.
Fig. 10.

The ratio of the measured wavefront sensor signal variances for the AO system off and on for sinusoidally varying input signals.

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Equations (9)

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

∇ 2 z ( x , y ) = − P ( x , y ) ⁄ T = − ε 0 V 2 ⁄ T d 2 ,
ϕ m = A m x m ,
x 0 = A m − 1 ϕ 0 ,
A m − 1 = V S − 1 U T ,
C − 1 ⁄ 2 ϕ = ( C − 1 ⁄ 2 A m ) x
ϕ e = A m L ( A m − 1 ϕ 0 ) − ϕ 0
L ( x ) = { x ∣ x ∣ ≤ x max x max x ⁄ ∣ x ∣ ∣ x ∣ > x max
σ e 2 = 〈 ϕ e 2 〉 = ϕ e T ϕ e
x n = ( 1 − β ) x n − 1 + g Ms n

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