Reconstruction of the High Resolution Phase in a Closed Loop Adaptive Optics System

Adaptive optics is a commonly used technique to correct the phase distortions caused by the Earth's atmosphere to improve the image quality of the ground-based imaging systems. However, the observed images still suffer from the blur caused by the adaptive optics residual wavefront. In this paper, we propose a model for reconstructing the residual phase in high resolution from a sequence of deformable mirror data. Our model is based on the turbulence statistics and the Taylor frozen flow hypothesis with knowledge of the wind velocities in atmospheric turbulence layers. A tomography problem for the phase distortions from different altitudes is solved in order to get a high quality phase reconstruction. We also consider inexact tomography operators resulting from the uncertainty in the wind velocities. The wind velocities are estimated from the deformable mirror data and, additionally, by including them as unknowns in the objective function. We provide a theoretical analysis on the existence of a minimizer of the objective function. To solve the associated joint optimization problem, we use an alternating minimization method which results in a high resolution reconstruction algorithm with adaptive wind velocities. Numerical simulations are carried out to show the effectiveness of our approach.