Loopshaped wavefront control using open-loop reconstructors

Lawton H. Lee

doi:10.1364/OE.14.007477

Loopshaped wavefront control using open-loop reconstructors

Lawton H. Lee

Optics Express
Vol. 14,
Issue 17,
pp. 7477-7486
(2006)
•https://doi.org/10.1364/OE.14.007477

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Lawton H. Lee, "Loopshaped wavefront control using open-loop reconstructors," Opt. Express 14, 7477-7486 (2006)

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Related Topics
Table of Contents Category
- Focus Issue: Adaptive Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Active or adaptive optics (010.1080)
- Wave-front sensing (010.7350)

About this Article
History
- Original Manuscript: March 7, 2006
- Revised Manuscript: April 27, 2006
- Manuscript Accepted: May 1, 2006
- Published: August 21, 2006

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Open Access

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.

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References

View by:
Article Order
|
Year
|
Author
|
Publication

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]
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]
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]
L. Gilles, “Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics,” Appl. Opt. 44, 993–1002 (2005).
[Crossref] [PubMed]
P. Piatrou and L. Gilles, “Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics,” Appl. Opt. 44, 1003–1010 (2005).
[Crossref] [PubMed]
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).
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]
K. J. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design (Prentice Hall, 1997).
E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983).
[Crossref]
B. Ellerbroek, “Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1803–1816 (2002).
[Crossref]
J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York, 1998).

2005 (2)

P. Piatrou and L. Gilles, “Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics,” Appl. Opt. 44, 1003–1010 (2005).
[Crossref] [PubMed]

L. Gilles, “Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics,” Appl. Opt. 44, 993–1002 (2005).
[Crossref] [PubMed]

2003 (4)

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]

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]

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]

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]

2002 (2)

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]

B. Ellerbroek, “Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1803–1816 (2002).
[Crossref]

1998 (1)

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]

1995 (1)

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).

1994 (1)

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]

1983 (1)

E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983).
[Crossref]

Åström, K. J.

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

Basinger, S.

Blankinship, R. M.

Brack, G.

Dekany, R.

Dunn, J.

Ellerbroek, B.

B. Ellerbroek, “Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1803–1816 (2002).
[Crossref]

Ellerbroek, B. L.

Gilles, L.

P. Piatrou and L. Gilles, “Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics,” Appl. Opt. 44, 1003–1010 (2005).
[Crossref] [PubMed]

Hardy, J. W.

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

Herriot, G.

Hyver, G. A.

Le Louarn, M.

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]

Lee, L. H.

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.

Lloyd-Hart, M.

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]

Macintosh, B.

Milton, N. M.

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]

Morari, M.

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

Oppenheimer, B.

Piatrou, P.

P. Piatrou and L. Gilles, “Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics,” Appl. Opt. 44, 1003–1010 (2005).
[Crossref] [PubMed]

Pitsianis, N. P.

Plemmons, R. J.

Postlethwaite, I.

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

Poyneer, L. A.

Redding, D.

Saddlemyer, L.

Skogestad, S.

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

Smith, M.

Tallon, M.

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]

van Loan, C.

Véran, J.-P.

Vogel, C. R.

Wallner, E. P.

E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983).
[Crossref]

Wittenmark, B.

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

Zafiriou, E.

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

Advances in the Astronautical Sciences (1)

Proc. SPIE (4)

Other (5)

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).

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

Cited By

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Fig. 1. Feedback control system (top) and its feedforward equivalent (bottom).

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Fig. 2. Loopshaping internal model control (IMC) system.

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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.

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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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

Tables (4)

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

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

View Table | View all tables in this article

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

View Table | View all tables in this article

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

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Equations (17)

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

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) = \frac{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)),

	10^-2	10^-1	10⁰	10⁺¹	10⁺²
q ₁:
10^-2	0.05	—	—	—	—
10^-1	0.05	0.05	—	—	—
10⁰	0.05	0.05	0.10	—	—
10⁺¹	0.09	0.10	0.11	0.29	—
10⁺²	0.20	0.22	0.20	0.31	0.41

	10^-2	10^-1	10⁰	10⁺¹	10⁺²
q ₁
10^-2	0.41	—	—	—	—
10^-1	0.38	0.38	—	—	—
10⁰	0.34	0.33	0.32	—	—
10⁺¹	0.20	0.19	0.18	0.16	—
10⁺²	0.07	0.07	0.07	0.05	0.03

	10^-2	10^-1	10⁰	10⁺¹	10⁺²
q ₁:
10^-2	0.05	—	—	—	—
10^-1	0.05	0.05	—	—	—
10⁰	0.05	0.05	0.10	—	—
10⁺¹	0.09	0.10	0.11	0.29	—
10⁺²	0.20	0.22	0.20	0.31	0.41

	10^-2	10^-1	10⁰	10⁺¹	10⁺²
q ₁
10^-2	0.41	—	—	—	—
10^-1	0.38	0.38	—	—	—
10⁰	0.34	0.33	0.32	—	—
10⁺¹	0.20	0.19	0.18	0.16	—
10⁺²	0.07	0.07	0.07	0.05	0.03

Abstract

References

2005 (2)

2003 (4)

2002 (2)

1998 (1)

1995 (1)

1994 (1)

1983 (1)

Åström, K. J.

Basinger, S.

Blankinship, R. M.

Brack, G.

Dekany, R.

Dunn, J.

Ellerbroek, B.

Ellerbroek, B. L.

Gilles, L.

Hardy, J. W.

Herriot, G.

Hyver, G. A.

Le Louarn, M.

Lee, L. H.

Lloyd-Hart, M.

Macintosh, B.

Milton, N. M.

Morari, M.

Oppenheimer, B.

Piatrou, P.

Pitsianis, N. P.

Plemmons, R. J.

Postlethwaite, I.

Poyneer, L. A.

Redding, D.

Saddlemyer, L.

Skogestad, S.

Smith, M.

Tallon, M.

van Loan, C.

Véran, J.-P.

Vogel, C. R.

Wallner, E. P.

Wittenmark, B.

Zafiriou, E.

Advances in the Astronautical Sciences (1)

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Proc. SPIE (4)

Other (5)

Cited By

Figures (5)

Tables (4)

Equations (17)

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