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arXiv · 1806.07938

Fast Iterative Tomographic Wave-front Estimation with Recursive Toeplitz Reconstructor Structure for Large Scale Systems

Yoshito H. Ono·Carlos Correia·Rodolphe Conan·Leonardo Blanco·Benoit Neichel·Thierry Fusco
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Abstract

Tomographic wave-front reconstruction is the main computational bottleneck to realize real-time correction for turbulence-induced wave-front aberrations in future laser-assisted tomographic adaptive-optics (AO) systems for ground-based Giant Segmented Mirror Telescopes (GSMT), because of its unprecedented number of degrees of freedom, $N$, i.e. the number of measurements from wave-front sensors (WFS). In this paper, we provide an efficient implementation of the minimum-mean-square error (MMSE) tomographic wave-front reconstruction mainly useful for some classes of AO systems not requiring a multi-conjugation, such as laser-tomographic AO (LTAO), multi-object AO (MOAO) and ground-layer AO (GLAO) systems, but also applicable to multi-conjugate AO (MCAO) systems. This work expands that by R. Conan [ProcSPIE, 9148, 91480R (2014)] to the multi-wave-front, tomographic case using natural and laser guide stars. The new implementation exploits the Toeplitz structure of covariance matrices used in a MMSE reconstructor, which leads to an overall $O(N\log N)$ real-time complexity compared to $O(N^2)$ of the original implementation using straight vector-matrix multiplication. We show that the Toeplitz-based algorithm leads to 60\,nm rms wave-front error improvement for the European Extremely Large Telescope Laser-Tomography AO system over a well-known sparse-based tomographic reconstruction, but the number of iterations required for suitable performance is still beyond what a real-time system can accommodate to keep up with the time-varying turbulence

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Yoshito H. Ono, Carlos Correia, Rodolphe Conan, Leonardo Blanco, Benoit Neichel, Thierry Fusco. 2018-06-20. Fast Iterative Tomographic Wave-front Estimation with Recursive Toeplitz Reconstructor Structure for Large Scale Systems. https://doi.org/10.1364/josaa.35.001330

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