A frame decomposition of the atmospheric tomography operator
A frame decomposition of the atmospheric tomography operator
复制标题
大气层析成像算子的框架分解
作者：
Simon Hubmer;R. Ramlau
我们考虑大气层层析成像的问题，因为它出现在例如自适应光学系统的超大望远镜。我们得到一个框架分解，即，基础大气层析成像算子的框架分解，通过允许自然和激光引导星的混合以及任意孔径形状，扩展了Neubauer和Ramlau（2017 SIAM J. Appl. Math. 77 838-853）的奇异值类型分解结果。基于这两个分析的考虑，以及数值说明，我们提供了深入了解的派生框架分解和它的积木的属性。
We consider the problem of atmospheric tomography, as it appears for example in adaptive optics systems for extremely large telescopes. We derive a frame decomposition, i.e., a decomposition in terms of a frame, of the underlying atmospheric tomography operator, extending the singular-value-type decomposition results of Neubauer and Ramlau (2017 SIAM J. Appl. Math. 77 838–853) by allowing a mixture of both natural and laser guide stars, as well as arbitrary aperture shapes. Based on both analytical considerations as well as numerical illustrations, we provide insight into the properties of the derived frame decomposition and its building blocks.