Singular value-based atmospheric tomography with Fourier domain regularization

Atmospheric tomography, the problem of reconstructing atmospheric turbulence profiles from wavefront sensor measurements, is an integral part of many adaptive optics systems. To solve this problem, a singular-value decomposition (SVD) based approach has been proposed before. Here, we focus on the numerical implementation of the SVD-based Atmospheric Tomography with Fourier Domain Regularization Algorithm (SAFR) and its performance for 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.