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The Use of The Principal Components of Transverse Wavefront Aberrations in Model-Based Control Algorithms for Adaptive Optics
Russian version
Yagnyatinskiy D. A. 1, Kuznetsov A.P. 2
1V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences,Tomsk, Russia
2National Research Nuclear University MEPhI, Moscow, Russia
Email: lambsky@yandex.ru, apkuznetsov@mephi.ru
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For model-based adaptive optics control algorithms based on measuring the rms focal spot radius with an intensity sensor, we propose to use the principal components of transverse wavefront aberrations as control modes. These components are the Karhunen-Loeve-Lukosz functions corresponding to the given phase-distortion statistics. The approach is demonstrated for the Kolmogorov turbulence model of the optical medium. By means of numerical simulation, we compared the performance of algorithms for two bases of control modes: Lukosz polynomials and Karhunen-Loeve-Lukosz functions. The use of Karhunen-Loeve-Lukosz modes instead of Lukosz modes was shown to statistically reduce the wavefront RMS error and improve the focusing of the laser beam. It was found that Karhunen-Loeve-Lukosz modes are also preferable to Lukosz modes in that they allow for a more precise measurement of mode coefficients by aperture probing. The simulations were performed for an ideal corrector and for the optimized models of a stacked-array piezoelectric deformable mirror. Keywords: adaptive optics, control algorithms, rms focal spot radius, aberrations, Kolmogorov turbulence model, Lukosz polynomials, Karhunen-Loeve-Lukosz functions, deformable mirror.
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