Decomposition of deformable-mirror shapes based on influence functions of stroke-saturation actuators

Fedoseev, V.N.

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Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Федосеев В.Н. Декомпозиция формы деформируемого зеркала по функциям влияния приводов с ограничениями на диапазон // Оптический журнал. 2021. Т. 88. № 1. С. 32–36. http://doi.org/10.17586/1023-5086-2021-88-01-32-36

Fedoseev V.N. Decomposition of deformable-mirror shapes based on influence functions of stroke-saturation actuators [in Russian] // Opticheskii Zhurnal. 2021. V. 88. № 1. P. 32–36. http://doi.org/10.17586/1023-5086-2021-88-01-32-36

For citation (Journal of Optical Technology):

V. N. Fedoseev, "Decomposition of deformable-mirror shapes based on influence functions of stroke-saturation actuators," Journal of Optical Technology. 88(1), 21-24 (2021). https://doi.org/10.1364/JOT.88.000021

Abstract:

We describe a deformable-mirror control algorithm based on mirror-actuator influence functions. Since these influence functions are nonorthogonal, the voltages transmitted to the actuators are calculated using a least-squares technique. The resulting solution was then optimized to take into account the constraints on maximum permissible actuator voltages. A practical demonstration of this algorithm was performed in MATLAB, using the example of a deformable mirror with 49 actuators. We show that in certain cases, the root-mean-square deviation between the surface and the specified shape can be reduced by as much as 70% through additional optimization.

Keywords:

adaptive optics, deformable mirror, mirror-actuator influence functions, wavefront correction, least-squares technique, range constraints consideration

OCIS codes: 220.1000, 220.1080

References:

1. U. Wittrock, ed., Adaptive Optics for Industry and Medicine: Proceedings of the 4th International Workshop, Münster, Germany, October 19–24, 2003 (Springer, Berlin, 2003).
2. O. I. Shanin, Adaptive Optical Systems in High-Power Pulsed Laser Installations (Tekhnosfera, Moscow, 2012).
3. M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52, 091803 (2013).
4. S. Boyd and L. Vandenberghe, Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares (Cambridge University Press, Cambridge, 2018).
5. Y. Teng, S. Qi, D. Xiao, L. Xu, J. Li, and Y. Kang, “A general solution to least squares problems with box constraints and its applications,” Math. Probl. Eng. 2016, 3934872 (2016).