Nonlinear wavefront reconstruction methods for pyramid sensors using Landweber and Landweber-Kaczmarz iterations

Accurate and robust wavefront reconstruction methods for pyramid wavefront sensors are in high demand, as these sensors are planned to be part of many instruments currently under development for ground-based telescopes. The pyramid sensor relates the incoming wavefront and its measurements in a nonlinear way. Nevertheless, almost all existing reconstruction algorithms are based on a linearization of the model. The assumption of a linear pyramid sensor response is justifiable in closed-loop adaptive optics (AO) when the measured phase information is small, but, depending on the system, may not be feasible due to unpreventable errors such as non-common path aberrations. In order to solve the nonlinear inverse problem of wavefront reconstruction from pyramid sensor data, we introduce two new methods based on the nonlinear Landweber and Landweber-Kaczmarz iterations. Using these algorithms, we experience high-quality wavefront estimation, especially for the non-modulated sensor, by still keeping the numerical effort feasible for large-scale AO systems.