Fast iterative tomographic wavefront estimation with recursive Toeplitz reconstructor structure for large-scale systems

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-objcet 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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Journal of the Optical Society of America. A Optics, Image Science, and Vision, Optical Society of America, 2018, 35 (8), pp.1330-1345. 〈10.1364/JOSAA.35.001330〉
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Yoshito H. Ono, Carlos Correia, Rodolphe Conan, Leonardo Blanco, Benoit Neichel, et al.. Fast iterative tomographic wavefront estimation with recursive Toeplitz reconstructor structure for large-scale systems. Journal of the Optical Society of America. A Optics, Image Science, and Vision, Optical Society of America, 2018, 35 (8), pp.1330-1345. 〈10.1364/JOSAA.35.001330〉. 〈hal-01842351〉

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