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Active Control of Large Telescopes: Adaptive Optics

  • André Preumont
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 246)

Abstract

This chapter begins with a brief description of the requirements for image quality, the measurement of the wavefront aberration with a Shack–Hartmann (SH) sensor and its decomposition in a set of orthogonal functions named the Zernike modes. Next, the Kolmogorov turbulence model is used, together with the assumption of frozen turbulence shape transported by the wind to evaluate the RMS value of the phase error, the image quality, and the power spectral density of the various Zernike modes. The next section discusses the main features of deformable mirrors for adaptive optics, with a special attention to the bimorph piezoelectric mirrors in various actuator configurations (keystone and honeycomb). The following section is devoted to the feedback control using a frequency-shaped singular value decomposition (SVD) controller and assuming a quasi-static response of the deformable mirror; the closed-loop response of the various Zernike modes and the RMS phase error is evaluated as a function of the control bandwidth. Next, a dynamical model of the mirror is used and the control-structure interaction is analyzed, leading to spillover; the importance of the structural damping of the vibration modes is pointed out. The damping augmentation via passive piezo shunt and active damping using modal filtering is then analyzed. The chapter concludes with some remarks on manufacturing and a list of references.

Keywords

Adaptive optics (AO) Deformable mirror Wavefront control Shack–Hartmann sensor Zernike modes Kolmogorov turbulence Piezoelectric mirror Bimorph Stoney formula SVD controller Control–structure interaction Spillover 

References

  1. 1.
    Alaluf D (2016) Piezoelectric mirrors for adaptive optics in space telescopes. Ph.D. thesis, Université Libre de Bruxelles, Active Structures LaboratoryGoogle Scholar
  2. 2.
    Bastaits R, Alaluf D, Belloni E, Rodrigues G, Preumont A (2014) Segmented bimorph mirrors for adaptive optics: morphing strategy. Appl Opt 53(22):4825–4832CrossRefGoogle Scholar
  3. 3.
    Bastaits R, Alaluf D, Horodinca M, Romanescu I, Burda I, Martic G, Rodrigues G, Preumont A (2014) Segmented bimorph mirrors for adaptive optics: segment design and experiment. Appl Opt 53(29):6635–6642CrossRefGoogle Scholar
  4. 4.
    Bely PY (2003) The design and construction of large optical telescopes. Springer, BerlinGoogle Scholar
  5. 5.
    Blevins RD (1979) Formulas for natural frequencies and mode shapes, Van Nostrand ReinholdGoogle Scholar
  6. 6.
    Conan JM, Rousset G, Madec PY (1995) Wave-front temporal spectra in high-resolution imaging through turbulence. J Opt Soc Am A 12(7):1559–1570CrossRefGoogle Scholar
  7. 7.
    Dainty JC (2010) Optical effects of atmospheric turbulence. Laser guide star adaptive optics for astronomy. Springer, BerlinGoogle Scholar
  8. 8.
    Enard D, Marechal A, Espiard J (1996) Progress in ground-based optical telescopes. Rep Prog Phys 59:601–656CrossRefGoogle Scholar
  9. 9.
    Feng X, Huang Y, Jiang H, Ngo D, Rosakis AJ (2006) The effect of thinfilm/substrate radii on the Stoney formula for thin film/substrate subject to nonuniform axisymmetric misfit strain and temperature. J Mech Mater Struct 1(6):1041–1053CrossRefGoogle Scholar
  10. 10.
    Freund LB, Suresh S (2003) Thin film materials. Stress, defect formation and surface evolution. Cambridge University Press, CambridgeGoogle Scholar
  11. 11.
    Greenwood DP (1977) Bandwidth specification for adaptive optics systems. JOSA 67:390–393CrossRefGoogle Scholar
  12. 12.
    Hardy JW (1998) Adaptive optics for astronomical telescopes. Oxford University Press, OxfordGoogle Scholar
  13. 13.
    Madec PY (2012) Overview of deformable mirror technologies for adaptive optics and astronomy. In: SPIE astronomical telescopes+ instrumentationGoogle Scholar
  14. 14.
    Meirovitch L, Baruh H (1985) The implementation of modal filters for control of structures. AIAA J Guid Control Dyn 8(6):707–716CrossRefzbMATHGoogle Scholar
  15. 15.
    Noll RJ (1976) Zernike polynomials and atmospheric turbulence. J Opt Soc Am A 66:207–211, MarchGoogle Scholar
  16. 16.
    Preumont A, Bastaits R, Rodrigues G (2009) Scale effects in active optics of large segmented mirrors. Mechatronics 19(8):1286–1293CrossRefGoogle Scholar
  17. 17.
    Roddier F (1999) Adaptive optics in astronomy. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  18. 18.
    Rodrigues G (2010) Adaptive optics with segmented deformable bimorph mirrors. Ph.D. thesis, Université Libre de Bruxelles, Active Structures LaboratoryGoogle Scholar
  19. 19.
    Rodrigues G, Bastaits R, Roose S, Stockman Y, Gebhardt S, Schoenecker A, Villon P, Preumont A (2009) Modular bimorph mirrors for adaptive optics. Opt Eng 38(3):034001CrossRefGoogle Scholar
  20. 20.
    Tyson RK (2000) Introduction to adaptive optics. SPIE Press, WashingtonCrossRefGoogle Scholar
  21. 21.
    Wang K, Alaluf D, Mokrani B, Preumont A (2017) Dynamic control of deformable mirrors for adaptive optics. In: ECCOMAS thematic conference on smart structures and materials, MadridGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Active Structures LaboratoryUniversité Libre de BruxellesBrusselsBelgium

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