基于奇异值分解与傅里叶域正则化的大气层析成像方法（SAFR） (Singular Value-based Atmospheric Tomography with Fourier Domain Regularization (SAFR))

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.

翻译：大气层析成像是根据波前传感器测量数据重建大气湍流剖面的问题，它是许多自适应光学系统的核心组成部分。该方法被用于提升地基望远镜的成像质量，例如应用于极大望远镜（ELT）上的多共轭自适应光学中继观测仪器（MORFEO）。为解决该问题，先前已有研究提出了基于奇异值分解（SVD）的方法。本文聚焦于基于奇异值分解的大气层析成像傅里叶域正则化算法（SAFR）的数值实现及其在多共轭自适应光学（MCAO）系统中的性能表现。SAFR算法的关键特征在于快速傅里叶变换（FFT）的运用以及计算密集型模块的预计算处理。这些设计使得该算法在保持快速运算的同时，其内存需求低于常用的矩阵向量乘法（MVM）类方法。我们利用仿真环境COMPASS开展数值实验，评估了SAFR在重建质量与计算开销方面的性能。实验中采用的MCAO配置模拟了ELT望远镜MORFEO仪器的实际物理参数。