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Tomographic Reconstruction for Single Conjugate Adaptive Optics

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Time-dependent Problems in Imaging and Parameter Identification

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Abstract

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.

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Acknowledgements

The work of the authors was partially supported by the Austrian Science Fund (FWF), project F 6805-N36: SFB Tomography Across the Scales and by the Austrian Ministry of Research (Hochschulraumstrukturmittel) in the project Observation oriented Astrophysics in the ELT era. Both authors would like to thank Roland Wagner and Markus Pöttinger for fruitful discussions.

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Authors and Affiliations

  1. Johann Radon Institute Linz, Linz, Austria

    Jenny Niebsch

  2. Institute of Industrial Mathematics, Johannes Kepler University Linz, Linz, Austria

    Ronny Ramlau

  3. Johann Radon Institute Linz, Linz, Austria

    Ronny Ramlau

Authors
  1. Jenny Niebsch
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  2. Ronny Ramlau
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Correspondence to Ronny Ramlau .

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Editors and Affiliations

  1. Department of Mathematics, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

    Barbara Kaltenbacher

  2. Department of Mathematics, Saarland University, Saarbrücken, Saarland, Germany

    Thomas Schuster

  3. Department of Mathematics, Saarland University, Saarbrücken, Saarland, Germany

    Anne Wald

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Niebsch, J., Ramlau, R. (2021). Tomographic Reconstruction for Single Conjugate Adaptive Optics. In: Kaltenbacher, B., Schuster, T., Wald, A. (eds) Time-dependent Problems in Imaging and Parameter Identification. Springer, Cham. https://doi.org/10.1007/978-3-030-57784-1_11

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