Singular Value-based Atmospheric Tomography with Fourier Domain Regularization (SAFR)

TL;DR

This paper introduces SAFR, a fast, memory-efficient Fourier domain regularization algorithm for atmospheric tomography in adaptive optics, improving reconstruction speed and quality for ELT-scale systems.

Contribution

It presents a novel implementation of SVD-based atmospheric tomography using FFT and pre-computation, enhancing efficiency for MCAO systems.

Findings

SAFR achieves faster reconstruction times than traditional MVM approaches.

SAFR requires less memory due to FFT-based implementation.

Numerical experiments show SAFR maintains high reconstruction quality.

Abstract

Atmospheric tomography, the problem of reconstructing atmospheric turbulence profiles from wavefront sensor measurements, is an integral part of many adaptive optics systems. It is used to enhance the image quality of ground-based telescopes, such as for the Multiconjugate Adaptive Optics Relay For ELT Observations (MORFEO) instrument on the Extremely Large Telescope (ELT). To solve this problem, a singular-value decomposition (SVD) based approach has been proposed before. In this paper, we focus on the numerical implementation of the SVD-based Atmospheric Tomography with Fourier Domain Regularization Algorithm (SAFR) and its performance for Multi-Conjugate Adaptive Optics (MCAO) systems. The key features of the SAFR algorithm are the utilization of the FFT and the pre-computation of computationally demanding parts. Together, this yields a fast algorithm with less memory requirements than commonly used Matrix Vector Multiplication (MVM) approaches. We evaluate the performance of SAFR regarding reconstruction quality and computational expense in numerical experiments using the simulation environment COMPASS, in which we use an MCAO setup resembling the physical parameters of the MORFEO instrument of the ELT.