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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 11 — Apr. 10, 2013
  • pp: 2363–2373

Iterative learning control of a membrane deformable mirror for optimal wavefront correction

Aleksandar Haber, Alessandro Polo, Carlas S. Smith, Silvania F. Pereira, Paul Urbach, and Michel Verhaegen  »View Author Affiliations

Applied Optics, Vol. 52, Issue 11, pp. 2363-2373 (2013)

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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

OCIS Codes
(090.1000) Holography : Aberration compensation
(230.3990) Optical devices : Micro-optical devices
(150.5495) Machine vision : Process monitoring and control
(110.1080) Imaging systems : Active or adaptive optics

ToC Category:
Imaging Systems

Original Manuscript: January 23, 2013
Manuscript Accepted: February 21, 2013
Published: April 10, 2013

Virtual Issues
Vol. 8, Iss. 5 Virtual Journal for Biomedical Optics

Aleksandar Haber, Alessandro Polo, Carlas S. Smith, Silvania F. Pereira, Paul Urbach, and Michel Verhaegen, "Iterative learning control of a membrane deformable mirror for optimal wavefront correction," Appl. Opt. 52, 2363-2373 (2013)

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  1. F. Roddier, Adaptive Optics in Astronomy. (Cambridge, 1999).
  2. R. K. Tyson, Principles of Adaptive Optics, 3rd ed., Series in Optics and Optoelectronics. (CRC, 2010).
  3. M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007). [CrossRef]
  4. 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]
  5. 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]
  6. R. Zawadzki, S. Jones, S. Olivier, M. Zhao, B. Bower, J. Izatt, S. Choi, S. Laut, and J. Werner, “Adaptive-optics optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express 13, 8532–8546 (2005). [CrossRef]
  7. S.-W. Bahk, E. Fess, B. E. Kruschwitz, and J. D. Zuegel, “A high-resolution, adaptive beam-shaping system for high-power lasers,” Opt. Express 18, 9151–9163 (2010). [CrossRef]
  8. 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).
  9. 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]
  10. S. K. Ravensbergen, “Adaptive Optics for Extreme Ultraviolet Lithography, Actuator Design and Validation for Deformable Mirror Concepts,” PhD thesis, Technische Universiteit Eindhoven, 2012.
  11. 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).
  12. L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999). [CrossRef]
  13. S. Bonora and L. Poletto, “Push-pull membrane mirrors for adaptive optics,” Opt. Express 14, 11935–11944 (2006). [CrossRef]
  14. E. Fernandez and P. Artal, “Membrane deformable mirror for adaptive optics, performance limits in visual optics,” Opt. Express 11, 1056–1069 (2003). [CrossRef]
  15. 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]
  16. Adaptica Srl. Saturn user manual. http://www.adaptica.com/site/en/pages/saturn .
  17. G. Vdovin and P. M. Sarro, “Flexible mirror micromachined in silicon,” Appl. Opt. 34, 2968–2972 (1995). [CrossRef]
  18. D. Malacara, Optical Shop Testing, volume 59, (Wiley, 2007).
  19. A. Haber, R. Fraanje, and M. Verhaegen, “Linear computational complexity robust ilc for lifted systems,” Automatica 48, 1102–1110 (2012). [CrossRef]
  20. D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” Control Systems (IEEE, 2006) 26, 96–114.
  21. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996).
  22. A. Haber, P. R. Fraanje, and M. Verhaegen, “Fast and robust iterative learning control for lifted systems,” World Congress 18, 3617–3622 (2011).
  23. M. Verhaegen and V. Verdult, Filtering and System Identification, A Least Squares Approach (Cambridge, 2007).

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