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ISSN: 1023-5086


ISSN: 1023-5086

Scientific and technical

Opticheskii Zhurnal

A full-text English translation of the journal is published by Optica Publishing Group under the title “Journal of Optical Technology”

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DOI: 10.17586/1023-5086-2018-85-05-26-33

УДК: 535.313

The modal-decomposition method in active-mirror control theory

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.


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.  

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).


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.


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


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


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