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

Abstract

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 non-linear 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 AO when the measured phase information is small but may not be reasonable in reality due to unpreventable errors depending on the system such as non common path aberrations. In order to solve the non-linear inverse problem of wavefront reconstruction from pyramid sensor data we introduce two new methods based on the non-linear Landweber and Landweber-Kaczmarz iteration. 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.the Subaru Telescope (SCexAO), the Magellan Telescope (MagAO), the Mont Megantic Telescope (INO Demonstrator), and the Calar Alto Telescope (PYRAMIR).

Nonlinear wavefront reconstruction with convolutional neural networks for Fourier-based wavefront sensors

“…Here I ± is the pupil intensity of the corresponding transmission mask T ± , k is the linear optical gain of the WFS [8] and P is WFS response from the step function due to a wavefront abberation φ. The measurement from a step filter is complicated and is a mixture of the wavefront gradient and the wavefront itself [12,21]. The response from a step filter is very similar to the PWFS response.…”

“…The response from a step filter is very similar to the PWFS response. Some works even model the response of a PWFS by two step functions, because the step response is so similar in behaviour to the unmodulated PWFS [21]. The g-ODWFS has been demonstrated in the lab and recently at the telescope as a wavefront sensor that can be used for astronomical adaptive optics [22].…”

“…Instead of using a model based approach to nonlinear wavefront reconstruction, such as done by [20,21], it is also possible to use a data-driven approach. The advantages of a data-driven approach is that it is not necessary to know the exact details of the optical system and its environment.…”

“…The advantages of a data-driven approach is that it is not necessary to know the exact details of the optical system and its environment. Model based methods are very sensitive to any model errors, which can even dominate the reconstruction error [21]. Deep learning is a promising approach to data-driven learning of complicated nonlinear relations between input-ouput sets.…”

Real-time adaptive optics with pyramid wavefront sensors: part I. A theoretical analysis of the pyramid sensor model

“…The main goal of this paper is to provide an extensive mathematical analysis of the PWFS operators in order to develop suitable wavefront reconstruction methods. So far, the existing algorithms are (with a small number of exceptions as, e.g., [11,14,28,29,37,46,47,48,83]) based on a linear assumption of the pyramid sensor model [36,41]. Nevertheless, the simplifications of the non-linear pyramid operator allow for acceptable wavefront reconstruction quality.…”