Introduction and Preliminaries

  • Zhizheng WuEmail author
  • Azhar Iqbal
  • Foued Ben Amara


In this chapter, an introduction to adaptive optics (AO) systems and to magnetic fluid deformable mirrors is presented. The advantages of magnetic fluid deformable mirrors over the conventional solid mirrors are outlined, and the major contributions of this book are summarized. To help the readers better understand the contents of this book, some mathematical preliminaries are also introduced. These preliminaries cover the basic techniques used in developing the analytic model of magnetic fluid deformable mirrors and also in developing the surface shape control algorithms for these mirrors.


Linear Matrix Inequality Magnetic Fluid Adaptive Optic Linear Quadratic Regulator Adaptive Optic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Babcock HW (1953) The possibility of compensating astronomical seeing. Publ Astron Soc Pac 65:229–236CrossRefGoogle Scholar
  2. Basmadjian D, Farnood R (2007) The art of modeling in science and engineering with mathematica. Chapman and Hall/CRC, Boca RatonzbMATHGoogle Scholar
  3. Bennett TJ, Barry CJ (2009) Ophthalmic imaging today: an ophthalmic photographers viewpoint a review. Clin Experiment Ophthalmol 37:2–13CrossRefGoogle Scholar
  4. Borra EF (2009) Liquid mirrors in engineering, Optics & Photonics News, pp 14–17, September 2009Google Scholar
  5. Borra EF, Brousseau D, Vincent A (2006) Large magnetic liquid mirrors. Astron Astrophys 446(1):389–393CrossRefGoogle Scholar
  6. Borra EF, Brousseau D, Cliche M, Parent J (2008) Aberration correction with a magnetic liquid active mirror. Mon Not R Astron Soc 391(4):1925–1930CrossRefGoogle Scholar
  7. Boyd S, Barratt C (1991) Linear controller design: limits of performance. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  8. Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiazbMATHCrossRefGoogle Scholar
  9. Brousseau D, Borra EF, Ruel HJ, Parent J (2006) A magnetic liquid deformable mirror for high stroke and low order axially symmetrical aberrations. Opt Express 14:11486–11493CrossRefGoogle Scholar
  10. Brousseau D, Borra EF, Thibault S (2007) Wavefront correction with a 37–actuator ferrofluid deformable mirror. Opt Express 15:18190–18199CrossRefGoogle Scholar
  11. Brousseau D, Borra EF, Rochette M, Landry DB (2010) Linearization of the response of a 91-actuator magnetic liquid deformable mirror. Opt Express 18(8):8239–8250CrossRefGoogle Scholar
  12. Brousseau D, Drapeau J, Piché M, Borra EF (2011) Generation of Bessel beams using a magnetic liquid deformable mirror. Appl Opt 50:4005–4010CrossRefGoogle Scholar
  13. Chen T, Francis B (1996) Optimal sampled data control systems. Springer, LondonzbMATHGoogle Scholar
  14. Doble N, Miller DT (2006) Wavefront correctors for vision science. In: Porter J, Queener H, Lin J, Thorn K, Awwal A (eds) Adaptive optics for vision science: principles, practices, design and applications. Wiley, HobokenGoogle Scholar
  15. Doble N, Williams DR (2004) The applications of MEMS technology for AO in vision science. IEEE J Sel Top Quantum Electron 10(3):629–635CrossRefGoogle Scholar
  16. Dorf RC, Bishop RH (2008) Modern control systems. Prentice Hall, Englewood CliffsGoogle Scholar
  17. Godara P, Dubis AM, Roorda A, Duncan JL, Carroll J (2010) Adaptive optics retinal imaging: emerging clinical applications. Optom Vis Sci 87(12):930–941CrossRefGoogle Scholar
  18. Hardy JW (1998) Adaptive optics for astronomical telescopes. Oxford University Press, New YorkGoogle Scholar
  19. Hart M (2010) Recent advances in astronomical adaptive optics. Appl Opt 49(16):D17–D29CrossRefGoogle Scholar
  20. Herrmann G, Matthew C, Turner MC, Postlethwaite I (2007) Linear matrix inequalities in control. In: Mathematical methods for robust and nonlinear control, vol 367, LNCIS. Springer, Berlin, pp 123–142CrossRefGoogle Scholar
  21. Iqbal A, Ben Amara F (2007) Modeling of a magnetic fluid deformable mirror for retinal imaging adaptive optics systems. Int J Optomechatron 1(2):180–208CrossRefGoogle Scholar
  22. Iqbal A, Ben Amara F (2008) Modeling and experimental evaluation of a circular magnetic-fluid deformable mirror. Int J Optomechatron 2(2):126–143CrossRefGoogle Scholar
  23. Iqbal A, Wu Z, Ben Amara F (2009) Closed-loop control of magnetic fluid deformable mirrors. Opt Express 17(21):18957–18970CrossRefGoogle Scholar
  24. Iqbal A, Wu Z, Ben Amara F (2010a) A decentralized robust PID controller design for the shape control of a magnetic fluid deformable mirror. Int J Optomechatron 4(3):246–268CrossRefGoogle Scholar
  25. Iqbal A, Wu Z, Ben Amara F (2010b) Mixed sensitivity H control of magnetic fluid deformable mirrors. IEEE/ASME Trans Mechatron 15(4):548–556CrossRefGoogle Scholar
  26. Laird P, Bergamasco R, Berube V, Borra EF, Ritcey AM, Rioux M, Robitaille N, Thibault S, Lande Vieira da Silva Jr., Yockell-Lelivre H (2003) Ferrofluid-based deformable mirrors: a new approach to AO using liquid mirrors. In: Wizinowich PL, Bonaccini D (eds) Proceedings of the SPIE volume 4839, Adaptive Optical System Technologies II, SPIE – The International Society of Optical EngineeringGoogle Scholar
  27. Laird P, Caron N, Rioux M, Borra EF, Ritcey AM (2006) Ferrofluid adaptive mirrors. Appl Opt 45(15):3495–3500CrossRefGoogle Scholar
  28. Parent J, Borra EF, Brousseau D, Ritcey AM, Dery JP, Thibault S (2009) Dynamic response of ferrofluidic deformable mirrors. Appl Opt 48(1):1–6CrossRefGoogle Scholar
  29. Rosensweig RE (1997) Ferrohydrodynamics. Dover Publications, MineolaGoogle Scholar
  30. Scherer C, Weiland S (2004) Linear matrix inequalities in control. Delft University of Technology, DelftGoogle Scholar
  31. Seaman A, Macpherson JB, Borra EF, Ritcey AM, Asselin D, Jerominek H, Thibault S, Campbell MC (2007) Hartmann-Shack measurements of ferrofluidic mirror dynamics. In: Photonics North 2007, Proceedings of the SPIE 6796, no.679603Google Scholar
  32. Skogestad S, Postlethwaite I (2005) Multivariable feedback control: analysis and design. Wiley, ChichesterGoogle Scholar
  33. Thibault S, Brousseau D, Rioux M, Senkow S, Dery JP, Borra EF, A Ritcey AM (2006) Nanoengineered ferrofluid deformable mirror: a progress report. In: Ellerbroek BL, Domenico BC (eds) Advances in adaptive optics II, Proceedings of SPIE 6272, no.627231Google Scholar
  34. Tyson RK (2011) Principles of adaptive optics. CRC Press, Boca RatonGoogle Scholar
  35. Wu Z, Azhar I, Ben Amara F (2010a) LMI-based decentralized PID controller design with application to the shape control of magnetic fluid deformable mirror. ASME international mechanical engineering congress and exposition, Vancouver, British Columbia, Canada, 12–18 Nov 2010Google Scholar
  36. Wu Z, Azhar I, Ben Amara F (2010b) Magnetic fluid deformable mirror shape control with a multivariable PID controller. IEEE American control conference, Baltimore, Maryland, USA, June 30–July 2 2010Google Scholar
  37. Wu Z, Azhar I, Ben Amara F (2011) LMI-based multivariable PID controller design and its application to the control of the surface shape of magnetic fluid deformable mirrors. IEEE Trans Control Syst Technol 19(4):717–729CrossRefGoogle Scholar
  38. Zhou K, Doyle J, Golver K (1995) Robust and optimal control. Prentice Hall, Upper Saddle RiverGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Shanghai UniversityShanghaiChina, People’s Republic
  2. 2.University of TorontoTorontoCanada

Personalised recommendations