Real-time adaptive optics with pyramid wavefront sensors: part II. Accurate wavefront reconstruction using iterative methods

Abstract

In this paper, we address the inverse problem of fast, stable, and high-quality wavefront reconstruction from pyramid wavefront sensor data for Adaptive Optics systems on Extremely Large Telescopes. For solving the indicated problem we apply well-known iterative mathematical algorithms, namely conjugate gradient, steepest descent, Landweber, Landweber-Kaczmarz and steepest descent-Kaczmarz iteration based on theoretical studies of the pyramid wavefront sensor. We compare the performance (in terms of correction quality and speed) of these algorithms in end-to-end numerical simulations of a closed adaptive loop. The comparison is performed in the context of a high-order SCAO system for METIS, one of the first-light instruments currently under design for the Extremely Large Telescope. We show that, though being iterative, the analyzed algorithms, when applied in the studied context, can be implemented in a very efficient manner, which reduces the related computational effort significantly. We demonstrate that the suggested analytically developed approaches involving iterative algorithms provide comparable quality to standard matrix-vector-multiplication methods while being computationally cheaper.

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

“…Moreover, for the considered operators we derived the corresponding adjoint operators. These are used in the upcoming second part of the paper [39] which will be devoted to the application of iterative algorithms to the problem of wavefront reconstruction from pyramid wavefront sensor data. An extension of the analysis (linearization and calculation of adjoints) to the full pyramid sensor operator as well as the adaption of the aperture mask to segmented pupils on ELTs [17,40,55,66,67] is dedicated to future work.…”

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

“…Table 2 provides an overview of the simulation parameters. The parameters are chosen such that they conform to those chosen in [30] for reasons of a direct comparison of the in this paper proposed non-linear methods to linear Landweber and Landweber-Kaczmarz iteration introduced therein. That is as well the reason for the choice of the observing wavelength which is, according to the METIS specifications, not in the science range but useful for our analysis purposes.…”

“…For the modulated sensor, we recommend employing linear reconstruction algorithms at least as long as it is guaranteed that the residual phases being sensed by the wavefront sensor are small, e.g., in closed loop AO without significant non-common path errors of the system. Concerning the computational complexity, the numerical effort of the proposed algorithm is comparable to the complexity of their linear versions being roughly O N 3/2 a as derived in [30]. Nevertheless, the amount of possible precomputations is larger in case of the linear versions of the algorithms which leads to a preference for linear methods with respect to the computational costs of online calculations.…”

“…There even exist reconstruction methods that reduce the full pyramid sensor model to a one-term assumption meaning that the pyramid sensor model is approximated as the finite Hilbert transform of the incoming phase [32]. The high reconstruction performance delivered by these algorithms (even though they are based on simplifications) is confirmed in, e.g., [28,30,32,63,66,65].…”

Review on methods for wavefront reconstruction from pyramid wavefront sensor data

“…80 Among the earliest are the interaction-matrix-based matrix vector multiplication (MVM) approaches. 70,[81][82][83][84][85][86][87] Later, the development of fast model-based linear reconstructors 60,63,78,79,[88][89][90][91][92][93][94][95][96] began and experiments with nonlinear algorithms, including applications of learning approaches, were reported. 4,60,77,97,98 The algorithms reviewed in this section are split into several groups according to the common underlying model they invert or the common idea they employ for the reconstruction.…”