Wavelet methods in multi-conjugate adaptive optics

TL;DR

This paper presents a novel wavelet-based reconstruction method for atmospheric tomography in multi-conjugate adaptive optics, improving stability and efficiency in solving the ill-posed inverse problem for next-generation telescopes.

Contribution

It introduces a new wavelet-based Bayesian MAP estimator with accelerated algorithms for atmospheric tomography in MCAO systems, demonstrating enhanced performance and flexibility.

Findings

Effective reconstruction demonstrated on ESO's OCTOPUS simulation tool

Accelerated algorithm with preconditioning improves computational efficiency

Wavelet locality properties enhance stability in ill-posed problems

Abstract

The next generation ground-based telescopes rely heavily on adaptive optics for overcoming the limitation of atmospheric turbulence. In the future adaptive optics modalities, like multi-conjugate adaptive optics (MCAO), atmospheric tomography is the major mathematical and computational challenge. In this severely ill-posed problem a fast and stable reconstruction algorithm is needed that can take into account many real-life phenomena of telescope imaging. We introduce a novel reconstruction method for the atmospheric tomography problem and demonstrate its performance and flexibility in the context of MCAO. Our method is based on using locality properties of compactly supported wavelets, both in the spatial and frequency domain. The reconstruction in the atmospheric tomography problem is obtained by solving the Bayesian MAP estimator with a conjugate gradient based algorithm. An accelerated algorithm with preconditioning is also introduced. Numerical performance is demonstrated on the official end-to-end simulation tool OCTOPUS of European Southern Observatory.