  In this paper, we consider the atmospheric tomography operator, which
describes the effect of turbulent atmospheric layers on incoming planar
wavefronts. Given wavefronts from different guide stars, measured at a
telescope, the inverse problem consists in the reconstruction of the turbulence
above the telescope. We show that the available data is not sufficient to
reconstruct the atmosphere uniquely. Additionally, we show that classical
regularization methods as Tikhonov regularization or Landweber iteration will
always fail to reconstruct a physically meaningful turbulence distribution.
