Tomographic Reconstruction for Single Conjugate Adaptive Optics

Single Conjugate Adaptive Optic systems use the light of one bright guide star and a deformable mirror to correct for the loss of image quality of earthbound astronomical telescopes caused by turbulences in the atmosphere. The system achieves best correction in guide star direction. The imaging quality of the scientific object, which is usually separated from the guide star, can further be improved if the turbulence distribution is known. We propose to use wavefront sensor measurements from the past to recover the turbulence in the atmosphere. Mathematically, a limited angle tomography problem has to be solved. We present a model for the related tomography equations and discuss solvability and uniqueness of the solutions. Based on our analysis we develop an algorithm for the inversion and obtain a first numerical reconstruction.