Volume 48, pp. 286-309, 2018.

Model reduction in atmospheric tomography by optimal grouping of turbulent layers

Günter Auzinger


In wide-field applications of adaptive optics systems, the problem of atmospheric tomography has to be solved. Commonly used methods for this purpose operate on a set of two-dimensional reconstruction layers. Due to run-time restrictions and demands on stability, in general the usable number of such reconstruction layers is less than the number of atmospheric turbulence layers. Hence, model reduction has to be applied to the profile of atmosphere layers in order to achieve a smaller number of the most relevant reconstruction layers. In continuation of earlier published and purely heuristic experiments, we concentrate on the question how the choice of the heights of these reconstruction layers influences the performance of the tomographic solver, aiming for a more rigorous analysis. We derive a function representing an approximate expected value for the best-case residual error, i.e., a limitation (in a statistical sense) for what any tomographic solver is able to reach. We provide a method for the minimization of this function, which consequently yields an algorithm for the (approximately) optimal choice of the reconstruction layer heights for a given input atmosphere model, i.e., given the turbulence strength depending on the altitude. Our implementation of the optimization algorithm has acceptable run-time, and first tests of the resulting layer profiles show that the obtained quality is significantly better than for other choices of the reconstruction layer profiles.

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Key words

model reduction, adaptive optics, atmospheric tomography, layer compression, optimization

AMS subject classifications

78M34, 78A10, 85-08

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