Atmospheric turbulence profiling with unknown power spectral density
For astronomers using ground-based telescopes, this work addresses the practical limitation of assuming Kolmogorov turbulence, offering improved atmospheric profiling when the ground-layer spectrum is unknown.
The paper extends the SLODAR method for atmospheric turbulence profiling in adaptive optics by modeling a non-Kolmogorov ground layer with unknown power spectral density, proving the problem is ill-posed, and proposing three numerical reconstruction methods that improve profile reconstruction and accurately locate local spectral perturbations.
Adaptive optics (AO) is a technology in modern ground-based optical telescopes to compensate the wavefront distortions caused by atmospheric turbulence. One method that allows to retrieve information about the atmosphere from telescope data is so-called SLODAR, where the atmospheric turbulence profile is estimated based on correlation data of Shack--Hartmann wavefront measurements. This approach relies on a layered Kolmogorov turbulence model. In this article, we propose a novel extension of the SLODAR concept by including a general non-Kolmogorov turbulence layer close to the ground with an unknown power spectral density. We prove that the joint estimation problem of the turbulence profile above ground simultaneously with the unknown power spectral density at the ground is ill-posed and propose three numerical reconstruction methods. We demonstrate by numerical simulations that our methods lead to substantial improvements in the turbulence profile reconstruction, compared to standard SLODAR-type approach. Also, our methods can accurately locate local perturbations in non-Kolmogorov power spectral densities.