Towards analytical model optimization in atmospheric tomography

TL;DR

This paper introduces a Bayesian framework for atmospheric turbulence modeling in adaptive optics, enabling simultaneous estimation and model optimization of atmospheric layers using wavefront data.

Contribution

It presents two novel algorithms for maximum a posteriori estimation, integrating model optimization and sparsity enforcement in atmospheric tomography.

Findings

Effective turbulence strength profile estimation demonstrated

Automated model reduction achieved via regularization parameter

Algorithms integrate with existing atmospheric tomography methods

Abstract

Modern ground-based telescopes rely on a technology called adaptive optics (AO) in order to compensate for the loss of image quality caused by atmospheric turbulence. Next-generation AO systems designed for a wide field of view require a stable and high-resolution reconstruction of the refractive index fluctuations in the atmosphere. By introducing a novel Bayesian method, we address the problem of estimating an atmospheric turbulence strength profile and reconstructing the refractive index fluctuations simultaneously, where we only use wavefront measurements of incoming light from guide stars. Most importantly, we demonstrate how this method can be used for model optimization as well. We propose two different algorithms for solving the maximum a posteriori estimate: the first approach is based on alternating minimization and has the advantage of integrability into existing atmospheric tomography methods. In the second approach, we formulate a convex non-differentiable optimization problem, which is solved by an iterative thresholding method. This approach clearly illustrates the underlying sparsity-enforcing mechanism for the strength profile. By introducing a tuning/regularization parameter, an automated model reduction of the layer structure of the atmosphere is achieved. Using numerical simulations, we demonstrate the performance of our method in practice.