A Singular-Value-Type Decomposition for the Atmospheric Tomography Operator

The new generation of extremely large telescopes currently under construction relies on adaptive optics techniques for the correction of image degradation due to atmospheric turbulences. A crucial part of the correction is related to atmospheric tomography, which will be analyzed in this paper. In particular, we derive a singular value type decomposition for the related operator. Despite being a limited angle problem, we show that atmospheric tomography is, in general, not ill-posed, although ill-conditioned.