Abstract

We present an iterative learning control (ILC) algorithm for controlling the shape of a membrane deformable mirror (DM). We furthermore give a physical interpretation of the design parameters of the ILC algorithm. On the basis of this insight, we derive a simple tuning procedure for the ILC algorithm that, in practice, guarantees stable and fast convergence of the membrane to the desired shape. In order to demonstrate the performance of the algorithm, we have built an experimental setup that consists of a commercial membrane DM, a wavefront sensor, and a real-time controller. The experimental results show that, by using the ILC algorithm, we are able to achieve a relatively small error between the real and desired shape of the DM while at the same time we are able to control the saturation of the actuators. Moreover, we show that the ILC algorithm outperforms other control algorithms available in the literature.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  23. M. Verhaegen and V. Verdult, Filtering and System Identification, A Least Squares Approach (Cambridge, 2007).

2013 (1)

S. K. Ravensbergen, P. C. J. N. Rosielle, and M. Steinbuch, “Deformable mirrors with thermo-mechanical actuators for extreme ultraviolet lithography, design, realization and validation,” Precision Engineering 37, 353–363 (2013).
[CrossRef]

2012 (4)

A. Polo, V. Kutchoukov, F. Bociort, S. F. Pereira, and H. P. Urbach, “Determination of wavefront structure for a Hartmann wavefront sensor using a phase-retrieval method,” Opt. Express 20, 237–246 (2012).

A. Haber, R. Fraanje, and M. Verhaegen, “Linear computational complexity robust ilc for lifted systems,” Automatica 48, 1102–1110 (2012).
[CrossRef]

J. Antonello, M. Verhaegen, R. Fraanje, T. van Werkhoven, H. C. Gerritsen, and C. U. Keller, “Semidefinite programming for model-based sensorless adaptive optics,” J Opt. Soc. Am. A 29, 2428–2438 (2012).
[CrossRef]

A. Polo, A. Haber, S. F. Pereira, M. Verhaegen, and H. P. Urbach, “An innovative and efficient method to control the shape of push-pull membrane deformable mirror,” Opt. Express 20, 27922–27932 (2012).
[CrossRef]

2011 (1)

A. Haber, P. R. Fraanje, and M. Verhaegen, “Fast and robust iterative learning control for lifted systems,” World Congress 18, 3617–3622 (2011).

2010 (1)

2007 (1)

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

2006 (1)

2005 (1)

2003 (1)

2002 (2)

A. Roorda, F. Romero-Borja, W. Donnelly, H. Queener, T. Hebert, and M. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10, 405–412 (2002).
[CrossRef]

T. Weyrauch, M. A. Vorontsov, J. Gowens, and T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” Proc. SPIE 4489, 177–184 (2002).

1999 (1)

1995 (1)

Alleyne, A. G.

D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” Control Systems (IEEE, 2006) 26, 96–114.

Antonello, J.

J. Antonello, M. Verhaegen, R. Fraanje, T. van Werkhoven, H. C. Gerritsen, and C. U. Keller, “Semidefinite programming for model-based sensorless adaptive optics,” J Opt. Soc. Am. A 29, 2428–2438 (2012).
[CrossRef]

Artal, P.

Bahk, S.-W.

Bartsch, D. U.

Bifano, T. G.

T. Weyrauch, M. A. Vorontsov, J. Gowens, and T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” Proc. SPIE 4489, 177–184 (2002).

Bociort, F.

A. Polo, V. Kutchoukov, F. Bociort, S. F. Pereira, and H. P. Urbach, “Determination of wavefront structure for a Hartmann wavefront sensor using a phase-retrieval method,” Opt. Express 20, 237–246 (2012).

Bonora, S.

Booth, M. J.

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

Bower, B.

Bristow, D. A.

D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” Control Systems (IEEE, 2006) 26, 96–114.

Campbell, M.

Choi, S.

Donnelly, W.

Fainman, Y.

Fernandez, E.

Fess, E.

Fraanje, P. R.

A. Haber, P. R. Fraanje, and M. Verhaegen, “Fast and robust iterative learning control for lifted systems,” World Congress 18, 3617–3622 (2011).

Fraanje, R.

A. Haber, R. Fraanje, and M. Verhaegen, “Linear computational complexity robust ilc for lifted systems,” Automatica 48, 1102–1110 (2012).
[CrossRef]

J. Antonello, M. Verhaegen, R. Fraanje, T. van Werkhoven, H. C. Gerritsen, and C. U. Keller, “Semidefinite programming for model-based sensorless adaptive optics,” J Opt. Soc. Am. A 29, 2428–2438 (2012).
[CrossRef]

Freeman, W. R.

Gerritsen, H. C.

J. Antonello, M. Verhaegen, R. Fraanje, T. van Werkhoven, H. C. Gerritsen, and C. U. Keller, “Semidefinite programming for model-based sensorless adaptive optics,” J Opt. Soc. Am. A 29, 2428–2438 (2012).
[CrossRef]

Golub, G. H.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996).

Gowens, J.

T. Weyrauch, M. A. Vorontsov, J. Gowens, and T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” Proc. SPIE 4489, 177–184 (2002).

Haber, A.

A. Haber, R. Fraanje, and M. Verhaegen, “Linear computational complexity robust ilc for lifted systems,” Automatica 48, 1102–1110 (2012).
[CrossRef]

A. Polo, A. Haber, S. F. Pereira, M. Verhaegen, and H. P. Urbach, “An innovative and efficient method to control the shape of push-pull membrane deformable mirror,” Opt. Express 20, 27922–27932 (2012).
[CrossRef]

A. Haber, P. R. Fraanje, and M. Verhaegen, “Fast and robust iterative learning control for lifted systems,” World Congress 18, 3617–3622 (2011).

Hebert, T.

Izatt, J.

Jones, S.

Keller, C. U.

J. Antonello, M. Verhaegen, R. Fraanje, T. van Werkhoven, H. C. Gerritsen, and C. U. Keller, “Semidefinite programming for model-based sensorless adaptive optics,” J Opt. Soc. Am. A 29, 2428–2438 (2012).
[CrossRef]

Kruschwitz, B. E.

Kutchoukov, V.

A. Polo, V. Kutchoukov, F. Bociort, S. F. Pereira, and H. P. Urbach, “Determination of wavefront structure for a Hartmann wavefront sensor using a phase-retrieval method,” Opt. Express 20, 237–246 (2012).

Laut, S.

Malacara, D.

D. Malacara, Optical Shop Testing, volume 59, (Wiley, 2007).

Olivier, S.

Pereira, S. F.

A. Polo, A. Haber, S. F. Pereira, M. Verhaegen, and H. P. Urbach, “An innovative and efficient method to control the shape of push-pull membrane deformable mirror,” Opt. Express 20, 27922–27932 (2012).
[CrossRef]

A. Polo, V. Kutchoukov, F. Bociort, S. F. Pereira, and H. P. Urbach, “Determination of wavefront structure for a Hartmann wavefront sensor using a phase-retrieval method,” Opt. Express 20, 237–246 (2012).

Poletto, L.

Polo, A.

A. Polo, A. Haber, S. F. Pereira, M. Verhaegen, and H. P. Urbach, “An innovative and efficient method to control the shape of push-pull membrane deformable mirror,” Opt. Express 20, 27922–27932 (2012).
[CrossRef]

A. Polo, V. Kutchoukov, F. Bociort, S. F. Pereira, and H. P. Urbach, “Determination of wavefront structure for a Hartmann wavefront sensor using a phase-retrieval method,” Opt. Express 20, 237–246 (2012).

Queener, H.

Ravensbergen, S. K.

S. K. Ravensbergen, P. C. J. N. Rosielle, and M. Steinbuch, “Deformable mirrors with thermo-mechanical actuators for extreme ultraviolet lithography, design, realization and validation,” Precision Engineering 37, 353–363 (2013).
[CrossRef]

S. K. Ravensbergen, “Adaptive Optics for Extreme Ultraviolet Lithography, Actuator Design and Validation for Deformable Mirror Concepts,” PhD thesis, Technische Universiteit Eindhoven, 2012.

Roddier, F.

F. Roddier, Adaptive Optics in Astronomy. (Cambridge, 1999).

Romero-Borja, F.

Roorda, A.

Rosielle, P. C. J. N.

S. K. Ravensbergen, P. C. J. N. Rosielle, and M. Steinbuch, “Deformable mirrors with thermo-mechanical actuators for extreme ultraviolet lithography, design, realization and validation,” Precision Engineering 37, 353–363 (2013).
[CrossRef]

Sarro, P. M.

Steinbuch, M.

S. K. Ravensbergen, P. C. J. N. Rosielle, and M. Steinbuch, “Deformable mirrors with thermo-mechanical actuators for extreme ultraviolet lithography, design, realization and validation,” Precision Engineering 37, 353–363 (2013).
[CrossRef]

Sun, P. C.

Tharayil, M.

D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” Control Systems (IEEE, 2006) 26, 96–114.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 3rd ed., Series in Optics and Optoelectronics. (CRC, 2010).

Urbach, H. P.

A. Polo, A. Haber, S. F. Pereira, M. Verhaegen, and H. P. Urbach, “An innovative and efficient method to control the shape of push-pull membrane deformable mirror,” Opt. Express 20, 27922–27932 (2012).
[CrossRef]

A. Polo, V. Kutchoukov, F. Bociort, S. F. Pereira, and H. P. Urbach, “Determination of wavefront structure for a Hartmann wavefront sensor using a phase-retrieval method,” Opt. Express 20, 237–246 (2012).

Van Loan, C. F.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996).

van Werkhoven, T.

J. Antonello, M. Verhaegen, R. Fraanje, T. van Werkhoven, H. C. Gerritsen, and C. U. Keller, “Semidefinite programming for model-based sensorless adaptive optics,” J Opt. Soc. Am. A 29, 2428–2438 (2012).
[CrossRef]

Vdovin, G.

Verdult, V.

M. Verhaegen and V. Verdult, Filtering and System Identification, A Least Squares Approach (Cambridge, 2007).

Verhaegen, M.

A. Polo, A. Haber, S. F. Pereira, M. Verhaegen, and H. P. Urbach, “An innovative and efficient method to control the shape of push-pull membrane deformable mirror,” Opt. Express 20, 27922–27932 (2012).
[CrossRef]

A. Haber, R. Fraanje, and M. Verhaegen, “Linear computational complexity robust ilc for lifted systems,” Automatica 48, 1102–1110 (2012).
[CrossRef]

J. Antonello, M. Verhaegen, R. Fraanje, T. van Werkhoven, H. C. Gerritsen, and C. U. Keller, “Semidefinite programming for model-based sensorless adaptive optics,” J Opt. Soc. Am. A 29, 2428–2438 (2012).
[CrossRef]

A. Haber, P. R. Fraanje, and M. Verhaegen, “Fast and robust iterative learning control for lifted systems,” World Congress 18, 3617–3622 (2011).

M. Verhaegen and V. Verdult, Filtering and System Identification, A Least Squares Approach (Cambridge, 2007).

Vorontsov, M. A.

T. Weyrauch, M. A. Vorontsov, J. Gowens, and T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” Proc. SPIE 4489, 177–184 (2002).

Werner, J.

Weyrauch, T.

T. Weyrauch, M. A. Vorontsov, J. Gowens, and T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” Proc. SPIE 4489, 177–184 (2002).

Zawadzki, R.

Zhao, M.

Zhu, L.

Zuegel, J. D.

Appl. Opt. (2)

Automatica (1)

A. Haber, R. Fraanje, and M. Verhaegen, “Linear computational complexity robust ilc for lifted systems,” Automatica 48, 1102–1110 (2012).
[CrossRef]

J Opt. Soc. Am. A (1)

J. Antonello, M. Verhaegen, R. Fraanje, T. van Werkhoven, H. C. Gerritsen, and C. U. Keller, “Semidefinite programming for model-based sensorless adaptive optics,” J Opt. Soc. Am. A 29, 2428–2438 (2012).
[CrossRef]

Opt. Express (7)

Phil. Trans. R. Soc. A (1)

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

Precision Engineering (1)

S. K. Ravensbergen, P. C. J. N. Rosielle, and M. Steinbuch, “Deformable mirrors with thermo-mechanical actuators for extreme ultraviolet lithography, design, realization and validation,” Precision Engineering 37, 353–363 (2013).
[CrossRef]

Proc. SPIE (1)

T. Weyrauch, M. A. Vorontsov, J. Gowens, and T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” Proc. SPIE 4489, 177–184 (2002).

World Congress (1)

A. Haber, P. R. Fraanje, and M. Verhaegen, “Fast and robust iterative learning control for lifted systems,” World Congress 18, 3617–3622 (2011).

Other (8)

M. Verhaegen and V. Verdult, Filtering and System Identification, A Least Squares Approach (Cambridge, 2007).

D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” Control Systems (IEEE, 2006) 26, 96–114.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996).

F. Roddier, Adaptive Optics in Astronomy. (Cambridge, 1999).

R. K. Tyson, Principles of Adaptive Optics, 3rd ed., Series in Optics and Optoelectronics. (CRC, 2010).

S. K. Ravensbergen, “Adaptive Optics for Extreme Ultraviolet Lithography, Actuator Design and Validation for Deformable Mirror Concepts,” PhD thesis, Technische Universiteit Eindhoven, 2012.

Adaptica Srl. Saturn user manual. http://www.adaptica.com/site/en/pages/saturn .

D. Malacara, Optical Shop Testing, volume 59, (Wiley, 2007).

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