CEAS Space Journal

, Volume 11, Issue 4, pp 553–559 | Cite as

Misalignment estimation for active telescopes

  • C. Escolle
  • V. MichauEmail author
  • M. Ferrari
  • T. Fusco
  • E. Hugot
Original Paper


The estimation of the misalignment of an active telescope, from aberrations measured in its focal plane, is a tomographic issue. MMSE-based estimation is successfully used in optical tomography issues, like multiconjugate adaptive optics, where the problem is linear, and the phase perturbation spectrum rapidly decreasing. The implementation of MMSE developed in the case of multiconjugate adaptive optics has been applied to the alignment of active telescopes, although the forward problem is not linear, and the aberration spectrum different. Its performance is characterized by numerical modeling in the case of a TMA type large-field imaging space telescope, and compared to the classical Least-Square approach. The MMSE estimation brings a significant gain in terms of robustness and accuracy.


Active optics Telescope MMSE Inverse problem Space 



This work has been performed with the support of a Ph.D. grant from CNES. The authors would like to thank F. Cassaing, J. M. Conan, and L. Mugnier for fruitful discussion.


  1. 1.
    Acton, D.S., Atcheson, P.D., Cermak, M., Kingsbury, L.K., Shi, F., Redding, D.C.: James Webb Space Telescope wavefront sensing and control algorithms. In: Optical, Infrared, and Millimeter Space Telescopes. Glasgow  (2004).
  2. 2.
    Arridge, S.R., Schotland, J.C.: Optical tomography: forward and inverse problems. Inverse Prob. 25(12), 123010 (2009). MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bastaits, R., Rodrigues, G., Mokrani, B., Preumont, A.: Active optics of large segmented mirrors: dynamics and control. J. Guid. Control Dyn. 32(6), 1795–1803 (2009). CrossRefGoogle Scholar
  4. 4.
    Cassar, G., Costes, V., Escarrat, L.: Optical design of a compact telescope for the next generation Earth observation system. In: Armandillo, E., Karafolas, N., Cugny, B. (eds.) International Conference on Space Optics—ICSO 2012. Ajaccio (2017).
  5. 5.
    Dimmler, M., Erm, T., Bauvir, B., Sedghi, B., Bonnet, H., Müller, M., Wallander, A.: E-ELT primary mirror control system. In: Ground-based and Airborne Telescopes II, vol. 70121O. Marseille (2008).
  6. 6.
    Feinberg, L., Cohen, L., Dean, B., Hayden, W., Howard, J., Keski-Kuha, R.: Space telescope design considerations. Opt. Eng. 51(1), 011006 (2012). CrossRefGoogle Scholar
  7. 7.
    Fusco, T., Conan, J.M., Rousset, G., Mugnier, L.M., Michau, V.: Optimal wave-front reconstruction strategies for multiconjugate adaptive optics. J. Opt. Soc. Am. 18(10), 2527–38 (2001)CrossRefGoogle Scholar
  8. 8.
    Gardner, J.P., Mather, J.C., Clampin, M., Doyon, R., Greenhouse, M.A., Hammel, H.B., Hutchings, J.B., Jakobsen, P., Lilly, S.J., Long, K.S., Lunine, J.I., Mccaughrean, M.J., Mountain, M., Nella, J., Rieke, G.H., Rieke, M.J., Rix, H.W., Smith, E.P., Sonneborn, G., Stiavelli, M., Stockman, H.S., Windhorst, R.A., Wright, G.S.: The James Webb Space Telescope. Sp. Sci. Rev. 123(4), 485–606 (2006). CrossRefGoogle Scholar
  9. 9.
    Guisard, S., Noethe, L., Spyromilio, J.: Performance of active optics at the VLT. In: Optical Design, Materials, Fabrication, and Maintenance. Munich (2000).
  10. 10.
    Joseph, D.P., Tou, T.J.: On linear control theory. Trans. Am. Inst. Electr. Eng. Part II Appl. Ind. 80(4), 193–196 (1961)Google Scholar
  11. 11.
    Korsch, D.: Anastigmatic three-mirror telescope. Appl. Opt. 16(8), 2074 (1977). CrossRefGoogle Scholar
  12. 12.
    McLeod, B.A.: Collimation of fast wide-field telescopes. Publ. Astron. Soc. Pac. 108(720), 217 (1996)CrossRefGoogle Scholar
  13. 13.
    Michau, V., Rousset, G., Fontanella, J.: Wavefront sensing from extended sources. In: Real Time and Post Facto Solar Image Correction, pp. 124–128 (1993)Google Scholar
  14. 14.
    Mora, A., Vosteen, A.: Gaia in-orbit realignment: overview and data analysis. In: Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, vol. 84421Q.  Amsterdam (2012).
  15. 15.
    Mugnier, L.M., Robert, C., Conan, J.M., Michau, V., Salem, S.: Myopic deconvolution from wave-front sensing. J. Opt. Soc. Am. A 18(4), 862–872 (2001). CrossRefGoogle Scholar
  16. 16.
    Neichel, B., Rigaut, F., Bec, M., Garcia-Rissmann, A.: Reconstruction strategies for GeMS. In: 1st AO4ELT Conference—Adaptive Optics for Extremely Large Telescopes, p. 02010. EDP Sciences, Paris, France (2010).
  17. 17.
    Noethe, L., Guisard, S.: Analytical expressions for field astigmatism in decentered two mirror telescopes and application to the collimation of the ESO VLT. Astron. Astrophys. Suppl. Ser. 144(1), 157–167 (2000). CrossRefGoogle Scholar
  18. 18.
    Noethe, L., Guisard, S.: Final alignment of the VLT. In: Optical Design, Materials, Fabrication, and Maintenance.  Munich (2000).
  19. 19.
    Noll, R.J.: Zernike polynomials and atmospheric turbulence*. J. Opt. Soc. Am. 66(3), 207 (1976). CrossRefGoogle Scholar
  20. 20.
    Ono, Y.H., Correia, C., Conan, R., Blanco, L., Neichel, B., Fusco, T.: Fast iterative tomographic wavefront estimation with recursive Toeplitz reconstructor structure for large-scale systems. J. Opt. Soc. Am.A 35(8), 1330 (2018). CrossRefGoogle Scholar
  21. 21.
    Piatrou, P., Chanan, G.: Tomographic alignment algorithm for an extremely large three-mirror telescope: invisible modes. Appl. Opt. 49(33), 6395 (2010). CrossRefGoogle Scholar
  22. 22.
    Platt, B.C., Shack, R.: History and principles of Shack-Hartmann wavefront sensing. J. Refract. Surg. 17(5), S573–S577 (2001). CrossRefGoogle Scholar
  23. 23.
    Rousset, G.: Wave-front sensors. In: Roddier, F. (ed.) Adaptive Optics in Astronomy. Cambridge University Press, Cambridge (1999)Google Scholar
  24. 24.
    Schechter, P.L., Burley, G.S., Hull, C.L., Johns, M., Martin, H.M., Schaller, S., Shectman, S.A., West, S.C.: Active optics on the Baade 6.5-m (Magellan I) Telescope. In: Large Ground-based Telescopes, vol. 4837, pp. 619–628. International Society for Optics and Photonics (2003)Google Scholar
  25. 25.
    Schechter, P.L., Levinson, R.S.: Generic misalignment aberration patterns in wide-field telescopes. Publ. Astron. Soc. Pac. 123(905), 812–832 (2011). CrossRefGoogle Scholar
  26. 26.
    Schipani, P., Brescia, M., Marty, L.: The active optics control software for the VST telescope. In: Advanced Software and Control for Astronomy, vol. 627417.  Orlando (2006).
  27. 27.
    Schroeder, D.J.: Astronomical Optics. Elsevier, Oxford (1999)Google Scholar
  28. 28.
    Shack, R.V., Thompson, K.: Influence of alignment errors of a telescope system on its aberration field. In: Optical Alignment I. San Diego (1980).
  29. 29.
    Thompson, K.: Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry. J. Opt. Soc. Am. A 22(7), 1389–1401 (2005). CrossRefGoogle Scholar
  30. 30.
    Upton, R., Cho, M., Rimmele, T.: Force-optimized alignment for optical control of the advanced technology solar telescope. Appl. Opt. 49(31), G105 (2010). CrossRefGoogle Scholar
  31. 31.
    Wallner, E.P.: Optimal wave-front correction using slope measurements. J. Opt. Soc. Am. 73(12), 1771 (1983). CrossRefGoogle Scholar
  32. 32.
    Wilson, R., Franza, F., Noethe, L.: Active optics: I. A system for optimizing the optical quality and reducing the costs of large telescopes. J. Mod. Opt. 34(4), 485–509 (1987). CrossRefGoogle Scholar

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© CEAS 2019

Authors and Affiliations

  1. 1.ONERA/DOTA, Université Paris SaclayChâtillonFrance
  2. 2.LAM, UMR 7326MarseilleFrance

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