  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) 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.
