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

Yoshito H. Ono (1, 2) , Carlos Correia (2) , Rodolphe Conan (3) , Leonardo Blanco (4) , Benoit Neichel (2) , Thierry Fusco (2, 4)

1 Subaru Telescope
2 LAM - Laboratoire d'Astrophysique de Marseille
3 Giant Magellan Telescope Corporation
4 DOTA, ONERA, Université Paris Saclay (COmUE) [Palaiseau]

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.

Mots clés: ACTIVE OR ADAPTIVE OPTICS; INVERSE PROBLEMS

Mots clés: OPTIQUE ADAPTATIVE; TURBULENCE; PROBLEME INVERSE

Domaines: Optique / photonique

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, 2018, 35 (8), pp.1330-1345. ⟨10.1364/JOSAA.35.001330⟩. ⟨hal-01842351⟩