Abstract

We present a comprehensive analysis of the linear quadratic Gaussian control approach applied to adaptive optics (AO) and multiconjugated AO (MCAO) based on numerical and experimental validations. The structure of the control law is presented and its main properties discussed. We then propose an extended experimental validation of this control law in AO and a simplified MCAO configuration. Performance is compared with end-to-end numerical simulations. Sensitivity of the performance regarding tuning parameters is tested. Finally, extension to full MCAO and laser tomographic AO (LTAO) through numerical simulation is presented and analyzed.

© 2009 Optical Society of America

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2008 (3)

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Minimum variance control in presence of actuator saturation in adaptive optics,” Proc. SPIE 7015, 70151G-1-70151G-8 (2008).
[Crossref]

C. Correia Da Silva, H.-F. Raynaud, and C. Kulcsár, “Globally optimal minimum-variance control in adaptive optics systems with mirrors dynamics,” Proc. SPIE 7015, 70151F-1-70151F-12 (2008).

D. P. Looze, “Structure of a hybrid signal LQG controller for adaptive optics,” Proc. SPIE 7015, 701536-1-701536-10 (2008).
[Crossref]

2007 (3)

2006 (3)

2005 (5)

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

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]

E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

2004 (3)

2003 (1)

D. P. Looze, M. Kasper, S. Hippler, O. Beker, and R. Weiss, “Optimal compensation and implementation for adaptive optics systems,” ESA Bull. 15, 67-88 (2003).

2002 (3)

D. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890-901 (2002).
[Crossref]

M. Le Louarn, “Multi-conjugate adaptive optics with laser guide stars: performance in the infra-red and the visible,” Mon. Not. R. Astron. Soc. 334, 865-874 (2002).
[Crossref]

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

2001 (1)

1995 (1)

1994 (1)

E. Gendron and P. Léna, “Astronomical adaptive optics: I. Modal control optimization,” Astron. Astrophys. 291, 337-346 (1994).

1993 (1)

1983 (1)

1975 (1)

R. H. Dicke, “Phase-contrast detection of telescope seeing and their correction,” Astron. J. 198, 605-615 (1975).

1974 (1)

Y. Bar-Shalom and E. Tse, “Dual effect, certainty equivalence and separation in stochastic control,” IEEE Trans. Autom. Control 19, 494-500 (1974).
[Crossref]

1961 (1)

P. D. Joseph and J. T. Tou, “On linear control theory,” AIEE Trans. Appl. Indus. , 80, 193-196 (1961).

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[Crossref]

Amorin, A.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Anderson, B. D. O.

B. D. O. Anderson and J. B. Moore, Optimal Control, Linear Quadratic Methods (Prentice-Hall, 1990).

Anderson, D.

Assémat, F.

E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
[Crossref]

Baade, D.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[Crossref]

Balestra, A.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Bar-Shalom, Y.

Y. Bar-Shalom and E. Tse, “Dual effect, certainty equivalence and separation in stochastic control,” IEEE Trans. Autom. Control 19, 494-500 (1974).
[Crossref]

Beker, O.

D. P. Looze, M. Kasper, S. Hippler, O. Beker, and R. Weiss, “Optimal compensation and implementation for adaptive optics systems,” ESA Bull. 15, 67-88 (2003).

Beuzit, J. L.

T. Fusco, C. Petit, G. Rousset, J. F. Sauvage, A. Blanc, J. M. Conan, and J. L. Beuzit, “Optimization of the pre-compensation of non-common path aberrations for adaptive optics systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2005), paper AWB 2.
[PubMed]

Beuzit, J.-L.

Blanc, A.

T. Fusco, C. Petit, G. Rousset, J. F. Sauvage, A. Blanc, J. M. Conan, and J. L. Beuzit, “Optimization of the pre-compensation of non-common path aberrations for adaptive optics systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2005), paper AWB 2.
[PubMed]

Butler, D. J.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Carbillet, M.

B. Le Roux and M. Carbillet, “Optimal control law in state-space formalism for extreme adaptive optics,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2005), paper AWC 3.
[PubMed]

Cavadore, C.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Charton, J.

Chemla, F.

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
[Crossref]

Conan, J. M.

T. Fusco, C. Petit, G. Rousset, J. F. Sauvage, A. Blanc, J. M. Conan, and J. L. Beuzit, “Optimization of the pre-compensation of non-common path aberrations for adaptive optics systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2005), paper AWB 2.
[PubMed]

Conan, J.-M.

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Minimum variance control in presence of actuator saturation in adaptive optics,” Proc. SPIE 7015, 70151G-1-70151G-8 (2008).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87-97 (2007).
[Crossref]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464-7476 (2006).
[Crossref] [PubMed]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, 62721T (2006).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261-1276 (2004).
[Crossref]

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, “Kalman Filter based control loop for adaptive optics,” Proc. SPIE 5490, 1414-1425 (2004).
[Crossref]

T. Fusco, J.-M. Conan, G. Rousset, L. M. Mugnier, and V. Michau, “Optimal wavefront reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527-2538 (2001).
[Crossref]

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wavefront temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559-1570 (1995).
[Crossref]

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Can LQG adaptive optics control cope with actuator saturation?” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2007), paper PMA1.
[PubMed]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Performance of LQG control for VLT-type MCAO systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2007), paper JTuA3.
[PubMed]

Conan, R.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Correia Da Silva, C.

C. Correia Da Silva, H.-F. Raynaud, and C. Kulcsár, “Globally optimal minimum-variance control in adaptive optics systems with mirrors dynamics,” Proc. SPIE 7015, 70151F-1-70151F-12 (2008).

Delabre, B.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Dessenne, C.

C. Dessenne, “Commande modale et prédictive en optique adaptative classique,” Ph.D. thesis (Université Paris VII, 1998).

Dicke, R. H.

R. H. Dicke, “Phase-contrast detection of telescope seeing and their correction,” Astron. J. 198, 605-615 (1975).

Diolaiti, E.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Doelman, N.

Dohlen, K.

Donaldson, R.

E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
[Crossref]

Farinato, J.

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E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
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C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261-1276 (2004).
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C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, “Kalman Filter based control loop for adaptive optics,” Proc. SPIE 5490, 1414-1425 (2004).
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T. Fusco, J.-M. Conan, G. Rousset, L. M. Mugnier, and V. Michau, “Optimal wavefront reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527-2538 (2001).
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T. Fusco, C. Petit, G. Rousset, J. F. Sauvage, A. Blanc, J. M. Conan, and J. L. Beuzit, “Optimization of the pre-compensation of non-common path aberrations for adaptive optics systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2005), paper AWB 2.
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E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
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E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
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C. Correia Da Silva, H.-F. Raynaud, and C. Kulcsár, “Globally optimal minimum-variance control in adaptive optics systems with mirrors dynamics,” Proc. SPIE 7015, 70151F-1-70151F-12 (2008).

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87-97 (2007).
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C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464-7476 (2006).
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C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, 62721T (2006).
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C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261-1276 (2004).
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C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, “Kalman Filter based control loop for adaptive optics,” Proc. SPIE 5490, 1414-1425 (2004).
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C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Performance of LQG control for VLT-type MCAO systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2007), paper JTuA3.
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B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261-1276 (2004).
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E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
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E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
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E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
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C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

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C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Minimum variance control in presence of actuator saturation in adaptive optics,” Proc. SPIE 7015, 70151G-1-70151G-8 (2008).
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C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87-97 (2007).
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C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464-7476 (2006).
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C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, 62721T (2006).
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C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, “Kalman Filter based control loop for adaptive optics,” Proc. SPIE 5490, 1414-1425 (2004).
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C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Performance of LQG control for VLT-type MCAO systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2007), paper JTuA3.
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Quiros-Pacheco, F.

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C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, 62721T (2006).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

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E. Marchetti, N. Hubin, E. Fedrigo, R. Donaldson, R. Conan, M. Le Louarn, B. Delabre, F. Franza, D. Baade, C. Cavadore, A. Balestra, J.-L. Lizon, R. Ragazzoni, J. Farinato, E. Vernet-Viard, E. Diolaiti, D. J. Butler, S. Hippler, and A. Amorin, “MAD, the ESO multiconjugate adaptive optics demonstrator,” Proc. SPIE 4839, 317-328 (2002).
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C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Minimum variance control in presence of actuator saturation in adaptive optics,” Proc. SPIE 7015, 70151G-1-70151G-8 (2008).
[Crossref]

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C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87-97 (2007).
[Crossref]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464-7476 (2006).
[Crossref] [PubMed]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, 62721T (2006).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261-1276 (2004).
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C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, “Kalman Filter based control loop for adaptive optics,” Proc. SPIE 5490, 1414-1425 (2004).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Performance of LQG control for VLT-type MCAO systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2007), paper JTuA3.
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C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Can LQG adaptive optics control cope with actuator saturation?” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2007), paper PMA1.
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C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, “Kalman Filter based control loop for adaptive optics,” Proc. SPIE 5490, 1414-1425 (2004).
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T. Fusco, C. Petit, G. Rousset, J. F. Sauvage, A. Blanc, J. M. Conan, and J. L. Beuzit, “Optimization of the pre-compensation of non-common path aberrations for adaptive optics systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2005), paper AWB 2.
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D. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890-901 (2002).
[Crossref]

D. Wiberg and D. T. Gavel, “A spatial non-dynamic LQG controller: Part I, Application to adaptive optics,” in IEEE Conference on Decision and Control (IEEE, 2004), Vol. 3, pp. 3326-3332.

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E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
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AIEE Trans. Appl. Indus. (1)

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C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” C. R. Acad. Sci., Ser. IV Phys. Astrophys. 6, 1059-1069 (2005).

C. R. Phys. (1)

E. Gendron, F. Assémat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco and N. Hubin, “FALCON: Multi-object,” C. R. Phys. 6, 1110-1117 (2005).
[Crossref]

ESA Bull. (1)

D. P. Looze, M. Kasper, S. Hippler, O. Beker, and R. Weiss, “Optimal compensation and implementation for adaptive optics systems,” ESA Bull. 15, 67-88 (2003).

IEEE Trans. Autom. Control (1)

Y. Bar-Shalom and E. Tse, “Dual effect, certainty equivalence and separation in stochastic control,” IEEE Trans. Autom. Control 19, 494-500 (1974).
[Crossref]

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[Crossref]

Opt. Express (3)

Proc. SPIE (8)

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla and D. Rabaud, “Off-axis adaptive optics with optimal control: Experimental and numerical validation,” Proc. SPIE 5903, 227-235 (2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, 62721T (2006).
[Crossref]

D. P. Looze, “Structure of a hybrid signal LQG controller for adaptive optics,” Proc. SPIE 7015, 701536-1-701536-10 (2008).
[Crossref]

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Minimum variance control in presence of actuator saturation in adaptive optics,” Proc. SPIE 7015, 70151G-1-70151G-8 (2008).
[Crossref]

C. Correia Da Silva, H.-F. Raynaud, and C. Kulcsár, “Globally optimal minimum-variance control in adaptive optics systems with mirrors dynamics,” Proc. SPIE 7015, 70151F-1-70151F-12 (2008).

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, “Kalman Filter based control loop for adaptive optics,” Proc. SPIE 5490, 1414-1425 (2004).
[Crossref]

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[Crossref]

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[Crossref]

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D. Wiberg and D. T. Gavel, “A spatial non-dynamic LQG controller: Part I, Application to adaptive optics,” in IEEE Conference on Decision and Control (IEEE, 2004), Vol. 3, pp. 3326-3332.

D. Wiberg and D. T. Gavel, “A spatial non-dynamic LQG controller: Part II, Theory,” IEEE Conference on Decision and Control (IEEE, 2004) Vol. 3, pp. 3333-3338.

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Performance of LQG control for VLT-type MCAO systems,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2007), paper JTuA3.
[PubMed]

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C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Can LQG adaptive optics control cope with actuator saturation?” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, Technical Digest (Optical Society of America, 2007), paper PMA1.
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Figures (15)

Fig. 1
Fig. 1

(a) Block diagram of AO closed-loop. (b) Temporal diagram of the system process.

Fig. 2
Fig. 2

Principle of a MCAO system. Turbulence is composed of L layers and analyzed in n g s directions via n g s WFSs conjugated with GS. Correction is performed by M DMs (two here) conjugated at M altitudes in n obj directions of interest.

Fig. 3
Fig. 3

Example of comparison of integrator (left) versus LQG (right) corrected PSFs recorded on October 27th. The respective SRs are 89.5% and 91.5%. For the integrator the four peaks related to the waffle amplification are circled in black.

Fig. 4
Fig. 4

Principle of OAAO: we consider a single turbulent layer at altitude h and two stars with angular separation β. The projections in the turbulent layer of the entrance pupil in each direction define an on-axis (diagonal pattern) and an off-axis (horizontal pattern) footprint. The footprints’ relative separation is denoted by n = β h D . The 2 β FoV defines a metapupil encircling both footprints.

Fig. 5
Fig. 5

Experimental performance results of LQG control (diamonds) in the closed-loop OAAO setup configuration compared with a classic integrator AO (stars). The SR is given for the off-axis star according to the footprints’ relative separation in %. Results are compared with end-to-end numerical simulations. Solid curve is the numerical LQG control performance; dashed curve is obtained with a classic integrator.

Fig. 6
Fig. 6

PSF of on-axis star (left) and off-axis star (right) for a relative separation n = 20 % , in open loop (top), with integrator (middle), and with off-axis LQG control (bottom). The left/right SR are respectively: top, 7%–7%, middle, 93%–34%, bottom, 43%–81% (experimental results on BOA).

Fig. 7
Fig. 7

Left: Experimental results on BOA, performance in SR (in %) of off-axis correction as a function of noise variance for different relative footprint separations. Note that noise values below 0.001 pixels 2 are not considered as the system becomes unstable. Right: End-to-end simulations, performance in SR of off-axis correction as a function of noise variance for different relative footprint separations.

Fig. 8
Fig. 8

Impact of the number of estimated modes on PSF (experimental results on BOA) with LQG control. Left: cut of the PSF with 80 modes estimated. Right: zoom of the left figure, comparison of PSFs obtained with integrator and 80 or 120 mode LQG control. Note the reduction of the aliasing effect around λ 2 d = 4 λ D .

Fig. 9
Fig. 9

Impact of estimated mode number. Left: Experimental performance in SR of off-axis correction as a function of the number of estimated modes in the altitude layer for a n = 20 % relative separation. Right: End-to-end simulation; performance of off-axis correction as a function of the number of estimated modes in the altitude layer for different relative footprint separations.

Fig. 10
Fig. 10

Left: Scheme of the MCAO configuration composed of a three layer atmosphere, three WFSs, and two DMs. Right: guide stars (diamonds) and directions of interest (stars) in the 2 arcmin FoV.

Fig. 11
Fig. 11

Left: SR map in the FoV for an integral controller. SR ranks from 9% in the center to a 66% SR on the guide star. Right: performance in terms of PSF in the 21 directions of interest. PSFs have been artificially brought closer.

Fig. 12
Fig. 12

Left: SR map in the FoV for a classic integrator controller. SR ranks from 32% in the center to a 55% average SR on the guide stars (stars). Right: performance in terms of PSF in the 21 directions of interest. PSFs have been artificially brought closer.

Fig. 13
Fig. 13

Left: performance obtained with LQG control. SR is nearly flat, reaching a 55% average in the entire FoV. White dots are the directions of interest. Right: performance in terms of PSF in the 21 directions of interest. PSFs have been artificially brought closer.

Fig. 14
Fig. 14

Left: performance obtained with integrator controller in a NTAO configuration. SR is nearly flat (GLAO type correction), with a 20% average in the FoV. White dot is the direction of interest. Right: performance in terms of PSF in the FoV. PSFs have been artificially brought closer.

Fig. 15
Fig. 15

Left: performance obtained with LQG control. SR reaches 55% average in the center of the FoV. White dot is the direction of interest and thus of optimization. Right: performance in terms of PSFs in the FoV. PSFs have been artificially brought closer.

Tables (2)

Tables Icon

Table 1 Integrator Performance on BOA in SR a

Tables Icon

Table 2 Comparison of Integrator versus LQG Performance on BOA in SR a

Equations (45)

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y n = 1 T ( n 2 ) T ( n 1 ) T D ϕ ( t ) d t + w n 1 .
ϕ cor ( t ) = N u n ,
ϕ res ( t ) = ϕ tur ( t ) ϕ cor ( t ) = ϕ tur ( t ) N u n .
ϕ n res = 1 T ( n 1 ) T n T ϕ res ( s ) d s ,
y n = D ϕ n 1 res + w n 1 ,
ϕ n + 1 cor = N u n ,
ϕ n + 1 res = ϕ n + 1 tur N u n .
J ( u ) ao = lim t + 1 t 0 t ϕ res ( s ) 2 d s .
J ( u ) ao = lim n + 1 n ( j = 1 n 1 T ( j 1 ) T j T ϕ tur ( s ) ϕ j tur 2 d s ) + lim n + 1 n j = 1 n ϕ j tur N u j 1 2 = J res , 1 + J res , 2 .
φ n tur = [ ( φ 1 , n tur ) T , ( φ 2 , n tur ) T , , ( φ L , n tur ) T ] T .
ϕ γ 1 , n tur ( r ) = i = 1 L φ i , n tur ( r + h i γ 1 ) ,
ϕ γ 1 , n tur = M γ 1 L φ n tur ,
ϕ γ , n tur = [ ( ϕ γ 1 , n tur ) T , ( ϕ γ 2 , n tur ) T , , ( ϕ γ p , n tur ) T ] T = ( M γ L φ n tur ) T ,
M γ L = [ ( M γ 1 L ) T , ( M γ 2 L ) T , , ( M γ p L ) T ] T .
u n = ( u 1 , n T , u 2 , n T , , u M , n T ) T .
φ n corr = [ ( φ 1 , n corr ) T , ( φ 2 , n corr ) T , , ( φ M , n corr ) T ] T = N u n 1 ,
ϕ γ , n corr = M γ M φ n corr .
y n = D ( M α L φ n 1 tur M α M N u n 2 ) + w n ,
ϕ n res = M β L φ n tur M β M N u n 1 .
J ( u ) mcao = lim n + 1 n j = 1 n M β L φ j tur M β M N u j 1 2 .
u n = P φ n + 1 tur = [ ( M β M N ) T M β M N ] ( M β M N ) T M β L φ n + 1 tur ,
u n = P φ ̂ n + 1 n tur = [ ( M β M N ) T M β M N ] ( M β M N ) T M β L φ ̂ n + 1 n tur ,
φ i , n + 1 tur = A i φ i , n tur + ν n ,
A i j j = exp { 0.3 [ n ( j ) + 1 ] V T D } ,
φ n + 1 tur = A tur φ n tur + ν n ,
X n = [ ( φ n tur ) T , ( φ n 1 tur ) T , ( u n 1 ) T , ( u n 2 ) T ] T ,
X n + 1 = A X n + B u n + v n ,
y n = C X n + w n ,
A = [ A tur 0 0 0 I d 0 0 0 0 0 0 0 0 0 I d 0 ] , B = ( 0 0 I d 0 ) ,
C = ( 0 D M α L 0 D M α M N ) ,
v n = ( I d , 0 , 0 , 0 ) T ν n .
X ̂ n n = X ̂ n n 1 + H ( y n C X ̂ n n 1 ) ,
X ̂ n + 1 n = A X ̂ n n + B u n .
H = ( A tur H opt H opt 0 0 ) ,
H opt = Σ C m T ( C m Σ C m T + Σ w ) 1 ,
Σ = A tur Σ ( A tur ) T + Σ v A tur Σ C m T ( C m Σ C m T + Σ w ) 1 C m Σ ( A tur ) T .
u n = P φ ̂ n + 1 n tur = P A tur φ ̂ n n tur ,
u n = K X ̂ n n ,
J ( u ) mcao = lim n + 1 n j = 1 n X n T Q X n = lim n + 1 n j = 1 n X n T ( C p T C p ) X n
C p = ( M β L 0 M β M N 0 ) .
φ ̂ n n tur = φ ̂ n n 1 tur + A tur H opt ( y n y ̂ n n 1 ) ,
φ ̂ n + 1 n tur = A tur φ ̂ n n tur ,
u n = P φ ̂ n + 1 n tur .
x c = λ f ml 2 π S sspup ϕ x d x d y ,
x c = λ f ml 2 π L x ϕ x max ϕ x min ,

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