Abstract

Adaptive Optics systems are frequently used to improve the imaging quality of optical systems, in particular in astronomy, ophthalmology and microscopy. To achieve this goal, the incoming wavefronts from the science object are corrected based on measurements with a suitable wavefront sensor. Unfortunately, the wavefronts cannot be measured directly but have to be obtained by solving an ill-posed inverse problem. We in particular consider the Pyramid sensor which has superior optical properties. Mathematically, the sensor can be modelled by a nonlinear operator equation. In our talk, we will present the mathematical model as well as its analysis, and provide simulation and reconstruction results. As a reconstruction scheme suitabale in particular when the reconstruction process has to be done frequently, we introduce and analyze regularized recycling techniques. Finally, we present applications from astronomy and ophthalmology.