Abstract

Adaptive optics wavefront controllers are tractably synthesized using loopshaping and internal model control principles. Modal responses at low and high temporal frequencies can thus be specified distinctly using pairs of open-loop reconstructors. Theoretical examples and parametric simulations illustrate the stability, robustness, and flexibility of the method, which incorporates several existing techniques.

© 2006 Optical Society of America

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References

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  1. M. Le Louarn and M. Tallon, "Analysis of modes and behavior of a multiconjugate adaptive optics system," J. Opt. Soc. Am. A 19, 912-925 (2002).
    [CrossRef]
  2. M. Lloyd-Hart and N. M. Milton, "Fundamental limits on isoplanatic correction with multiconjugate adaptive optics," J. Opt. Soc. Am. A 20, 1949-1957 (2003).
    [CrossRef]
  3. S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design (John Wiley & Sons, 1996).
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    [CrossRef]
  5. D. Redding, S. Basinger, G. Brack, R. Dekany, and B. Oppenheimer, "Adaptive optics reconstruction utilizing super-sampled deformable mirror influence functions," in Adaptive Optical System Technologies, D. Bonaccini and R. K. Tyson, eds., Proc. SPIE 3353, 543-552 (1998).
    [CrossRef]
  6. B. L. Ellerbroek and C. R. Vogel, "Simulations of closed-loop wavefront reconstruction for multi-conjugate adaptive optics on giant telescopes," in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson and M. Lloyd-Hart, eds., Proc. SPIE 5169, 206-217 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. L. H. Lee, "Loopshaped Wavefront Control using Pairs of Open-Loop Reconstructors," presented at Adaptive Optics: Analysis and Methods, Charlotte, North Carolina, June 6-8, 2005.
  12. M. Morari and E. Zafiriou, Robust Process Control (Prentice-Hall, 1989).
  13. B. L. Ellerbroek, C. van Loan, N. P. Pitsianis, and R. J. Plemmons, "Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths," J. Opt. Soc. Am. A 11, 2871-2886 (1994).
    [CrossRef]
  14. K. J. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design (Prentice Hall, 1997).
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    [CrossRef]
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    [CrossRef]
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2005 (2)

2003 (1)

2002 (2)

1994 (1)

1983 (1)

Ellerbroek, B.

Ellerbroek, B. L.

Gilles, L.

Le Louarn, M.

Lloyd-Hart, M.

Milton, N. M.

Piatrou, P.

Pitsianis, N. P.

Plemmons, R. J.

Tallon, M.

van Loan, C.

Wallner, E. P.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Other (10)

S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design (John Wiley & Sons, 1996).

L. Saddlemyer, J. Dunn, M. Smith, G. Herriot, and J.-P. Véran, "Performance results of the reconstructor for Altair, the Gemini North AO system," in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 981-988 (2003).
[CrossRef]

D. Redding, S. Basinger, G. Brack, R. Dekany, and B. Oppenheimer, "Adaptive optics reconstruction utilizing super-sampled deformable mirror influence functions," in Adaptive Optical System Technologies, D. Bonaccini and R. K. Tyson, eds., Proc. SPIE 3353, 543-552 (1998).
[CrossRef]

B. L. Ellerbroek and C. R. Vogel, "Simulations of closed-loop wavefront reconstruction for multi-conjugate adaptive optics on giant telescopes," in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson and M. Lloyd-Hart, eds., Proc. SPIE 5169, 206-217 (2003).
[CrossRef]

G. A. Hyver and R. M. Blankinship, "ALI high power beam control," in American Astronautical Society Guidance and Control 1995, R. D. Culp and J. D. Medbery, eds., Advances in the Astronautical Sciences 88, 445-462 (1995).

L. A. Poyneer and B. Macintosh, "Wave-front control for extreme adaptive optics," in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson and M. Lloyd-Hart, eds., Proc. SPIE 5169, 190-200 (2003).
[CrossRef]

L. H. Lee, "Loopshaped Wavefront Control using Pairs of Open-Loop Reconstructors," presented at Adaptive Optics: Analysis and Methods, Charlotte, North Carolina, June 6-8, 2005.

M. Morari and E. Zafiriou, Robust Process Control (Prentice-Hall, 1989).

K. J. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design (Prentice Hall, 1997).

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York, 1998).

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Figures (5)

Fig. 1.
Fig. 1.

Feedback control system (top) and its feedforward equivalent (bottom).

Fig. 2.
Fig. 2.

Loopshaping internal model control (IMC) system.

Fig. 3.
Fig. 3.

Frequency responses of noise rejection by pseudoinverse leaky-integral (upper left), regularized loopshaped-IMC (upper right), mildly and strongly regularized leaky-integral (middle and lower left), and mildly and strongly regularized POLC/Blankinship-IMC (middle and lower right) controllers for various modes.

Fig. 4.
Fig. 4.

Frequency responses of disturbance rejection by pseudoinverse leaky-integral (upper left), regularized loopshaped-IMC (upper right), mildly and strongly regularized leaky-integral (middle and lower left), and mildly and strongly regularized POLC/Blankinship-IMC (middle and lower right) controllers for various modes.

Fig. 5.
Fig. 5.

Frequency responses of numerical error rejection by pseudoinverse leaky-integral (upper left), regularized loopshaped-IMC (upper right), mildly and strongly regularized leaky-integral (middle and lower left), and mildly and strongly regularized POLC/Blankinship-IMC (middle and lower right) controllers for various modes.

Tables (4)

Tables Icon

Table 1. Monte Carlo 1-σ RMS wavefront error (μm) due to static aberrations vs. q 1 and q 0

Tables Icon

Table 2. Monte Carlo 1-σ RMS wavefront error (μm) due to random WFS biases vs. q 1 and q 0

Tables Icon

Table 3. Monte Carlo 1-σ RMS wavefront error (μm) due to dynamic aberrations vs. q 1 and q 0

Tables Icon

Table 4. Monte Carlo 1-σ RMS wavefront error (μm) due to WFS noise vs. q 1 and q 0

Equations (17)

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e ( z ) = G ( z ) u ( z ) + w ( z )
y ( z ) = H ( z ) G ( z ) u ( z ) + H ( z ) w ( z ) + v ( z )
u ( z ) = F ( I + C ( z ) M ( z ) ) 1 C ( z ) E y ( z )
Q ( z ) = [ I + C ( z ) ( E H ( z ) G ( z ) F + M ( z ) ) ] 1 C ( z ) ,
u ( z ) = R ( z ) H ( z ) w ( z ) R ( z ) v ( z )
e ( z ) = ( I G ( z ) R ( z ) H ( z ) ) w ( z ) G ( z ) R ( z ) v ( z )
0 = det ( I + C ( z ) ( E H ( z ) G ( z ) F + M ( z ) ) ) .
R ( z ) = F [ I + C ( z ) ( J ( z ) + E Δ ( z ) F ) ] 1 C ( z ) E
0 = det ( I + C ( z ) ( J ( z ) + E Δ ( z ) F ) ) ,
R ( z ) = k z z ( 1 k ) F E
R ( z ) = F [ z I ( I k j ) ] 1 z k E 1
Q ( s ) = [ s I + ω ( E H + m I ) ] 1 ω I
Q ( s ) = ( s I + ω J ) 1 ω I
E 1 = ( H T W H + q 1 D ) 1 H T W
E 0 = ( H T W H + q 0 D ) 1 H T W
J = ( H T W H + q 1 D ) 1 ( H T W H + q 0 D ) .
max ( diag ( D ) ) = max ( diag ( H T W H ) ) ,

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