Weighted nonnegative tensor factorization for atmospheric tomography reconstruction

¹ Universidad de La Laguna, Facultad de Física, Departamento de Ingeniería Industrial, Av. Astrofísico Sánchez, San Cristóbal de La Laguna 38206, Spain
e-mail: dcarmona@ull.edu.es
² Wooptix S.L., Av. Trinidad-Torre Agustín Arévalo, San Cristóbal de La Laguna 38205, Spain

Received: 5 January 2018
Accepted: 19 February 2018

Abstract

Context. Increasing the area on the sky over which atmospheric turbulences can be corrected is a matter of wide interest in astrophysics, especially when a new generation of extremely large telescopes (ELT) is to come in the near future.

Aims. In this study we tested if a method for visual representation in three-dimensional displays, the weighted nonnegative tensor factorization (WNTF), is able to improve the quality of the atmospheric tomography (AT) reconstruction as compared to a more standardized method like a randomized Kaczmarz algorithm.

Methods. A total of 1000 different atmospheres were simulated and recovered by both methods. Recovering was computed for two and three layers and for four different constellations of laser guiding stars (LGS). The goodness of both methods was tested by means of the radial average of the Strehl ratio across the field of view of a telescope of 8m diameter with a sky coverage of 97.8 arcsec.

Results. The proposed method significantly outperformed the Kaczmarz in all tested cases (p ≤ 0.05). In WNTF, three-layers configuration provided better outcomes, but there was no clear relation between different LGS constellations and the quality of Strehl ratio maps.

Conclusions. The WNTF method is a novel technique in astronomy and its use to recover atmospheric turbulence profiles was proposed and tested. It showed better quality of reconstruction than a conventional Kaczmarz algorithm independently of the number and height of recovered atmospheric layers and of the constellation of laser guide star used. The WNTF method was shown to be a useful tool in highly ill-posed AT problems, where the difficulty of classical algorithms produce high Strehl value maps.