On some analytic properties of the atmospheric tomography operator: Non-Uniqueness and reconstructability issues
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910413336084480 |
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| author | Ramlau, Ronny Stadler, Bernadett |
| author_facet | Ramlau, Ronny Stadler, Bernadett |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some analytic properties of the atmospheric tomography operator: Non-Uniqueness and reconstructability issues Ramlau, Ronny Stadler, Bernadett Numerical Analysis 78A10, 47A52 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. |
| title | On some analytic properties of the atmospheric tomography operator: Non-Uniqueness and reconstructability issues |
| topic | Numerical Analysis 78A10, 47A52 |
| url | https://arxiv.org/abs/2404.11126 |