The modal-decomposition method in active-mirror control theory

Klebanov, Y.M., Akhmetov, R.N., Polyakov, K.A., Adeyanov, I.E., Simakov, A.I.

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Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Клебанов Я.М., Ахметов Р.Н., Поляков К.А., Адеянов И.Е., Симаков А.И. Метод модального разложения в теории управления активным зеркалом // Оптический журнал. 2018. Т. 85. № 5. С. 26–33. http://doi.org/10.17586/1023-5086-2018-85-05-26-33

Klebanov Ya.M., Akhmetov R.N., Polyakov K.A., Adeyanov I.E., Simakov A.I. The modal-decomposition method in active-mirror control theory [in Russian] // Opticheskii Zhurnal. 2018. V. 85. № 5. P. 26–33. http://doi.org/10.17586/1023-5086-2018-85-05-26-33

For citation (Journal of Optical Technology):

Ya. M. Klebanov, R. N. Akhmetov, K. A. Polyakov, I. E. Adeyanov, and A. I. Simakov, "The modal-decomposition method in active-mirror control theory," Journal of Optical Technology. 85(5), 275-280 (2018). https://doi.org/10.1364/JOT.85.000275

Abstract:

This paper analyzes the efficiency of the mode shapes used to describe the displacements of the reflective surface of controllable mirrors in active optical systems. A new method is proposed for determining the orthogonal eigenshapes of the quasi-steady-state deformation of an active mirror with local-force control. This method is used to carry out modal analysis of a mirror simulator that has the same geometrical shape and the same elastic properties as the controllable mirror but possesses zero density, except for concentrated unit masses attached at the sites where the actuators act and taken into account only in the direction of application of the forces or displacements that deform the mirror. It is shown that the use of the eigenshapes obtained by means of a mirror simulator requires less energy and consequently smaller forces by the actuators than when the shapes obtained by singular decomposition are used.

Keywords:

deformable mirror, actuator, aberration, finite-element method, eigenshape, Zernike polynomials

Acknowledgements:

The research was supported by the Russian Foundation for Basic Research and the Government of Samara region, project No. 16-41-630542.

OCIS codes: 220.1080

References:

1. A. M. Savitskiı˘, “How the thermal regime affects the structural characteristics of a space telescope,” J. Opt. Technol. 76(10), 662–665 (2009) [Opt. Zh. 76(10), 89–93 (2009)].
2. E. Hecht, Optics (Addison-Wesley Pub. Co., Boston, 1987).
3. J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66(6), 651–697 (1978).
4. P. Hallibert and A. Z. Marchi, “Developments in active optics for space instruments: an ESA perspective,” Proc. SPIE 9912, 99121H (2016).
5. E. Pearson, L. Stepp, and J. Fox, “Active optics correction of thermal distortion of a 1.8-meter mirror,” Opt. Eng. 27(2), 115–122 (1988).
6. K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis (SPIE Press, Bellingham, Wash., 2012).
7. G. R. Lemaitre, Astronomical Optics and Elasticity Theory (Springer, Berlin, 2009).
8. Ya. M. Klebanov, L. N. Kirdina, K. A. Polyakov, and A. N. Davydov, “Transformation of the results of the finite-element analysis of optical-surface displacements for use in optical-analysis packages,” J. Opt. Technol. 81(7), 388–391 (2014) [Opt. Zh. 81(7), 34–38 (2014)].
9. A. N. Tikhonov and A. Ya. Arsenin, Methods of Solving Ill-Posed Problems (Nauka, Moscow, 1986).
10. M. K. Cho, “Active optics performance study of the primary mirror of the Gemini Telescopes Project,” Proc. SPIE 2871, 272–290 (1997).
11. C. Paterson, I. Munro, and J. C. Dainty, “A low-cost adaptive optics system using a membrane mirror,” Opt. Express 6(9), 175–185 (2000).
12. J. S. Gibson, C.-C. Chang, and N. Chen, “Adaptive optics with a new modal decomposition of actuator and sensor spaces,” in Proceedings of the American Control Conference, Arlington, VA, June 25–27, 2001.
13. Ya. M. Klebanov, R. N. Akhmetov, and K. A. Polyakov, “Method of compensating optical aberrations using a deformable mirror,” Russian Patent No. 2,623,661 (2017).
14. I. Klebanov, R. Akhmetov, and K. Polyakov, “Method for compensating optical aberrations with a deformable mirror,” U.S. Patent No. 980-4388 (2017).
15. V. P. Lukin and B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Izd. SO RAN, Novosibirsk, 1999).
16. L. N. Lavrinova and V. P. Lukin, Adaptive Correction of Thermal and Turbulent Distortions of Laser Radiation by a Deformed Mirror (Izd. Inst. Optiki Atmos. SO RAN, Tomsk, 2008).
17. M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).