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Context. Upcoming giant segmented mirror telescopes will use laser guide stars (LGS) for their adaptive optics (AO) systems. Two options of wavefront sensors (WFSs) are the Shack-Hartmann wavefront sensor (SHWFS) and the pyramid wavefront sensor (PWFS). Aims. In this paper, we compare the noise performance of the PWFS and the SHWFS. We aim to identify which of the two is best to use in the context of a single or tomographic configuration. Methods. To compute the noise performance, we extended a noise model developed for the PWFS to be used with the SHWFS. To do this, we expressed the centroiding algorithm of the SHWFS as a matrix-vector multiplication, which allowed us to use the statistics of noise to compute its propagation through the AO loop. We validated the noise model with end-to-end simulations for telescopes of 8 and 16 m in diameter. Results. For an AO system with only one WFS, we found that given the same number of subapertures, the PWFS outperforms the SHWFS. For a 40 m telescope, the limiting magnitude of the PWFS is around one magnitude higher than the SHWFS. When using multiple WFS and a generalized least-squares estimator to combine the signal, our model predicts that in a tomographic system, the SHWFS performs better than the PWFS (with a limiting magnitude that is higher by a 0.3 magnitude. When using sub-electron RON detectors for the PWFS, the performance quality is almost identical for the two WFSs. Conclusions. We find that when using a single WFS with LGS, PWFS is a better alternative than the SH. For a tomographic system, both sensors would give roughly the same performance. [ABSTRACT FROM AUTHOR]

Context. Extremely large telescopes are overwhelmingly equipped with pyramid wavefront sensors (PyWFS) over the more widely used Shack–Hartmann wavefront sensor to perform their single-conjugate adaptive optics (SCAO) mode. The PyWFS, a sensor based on Fourier filtering, has proven to be highly successful in many astronomy applications. However, this sensor exhibits non-linear behaviours that lead to a reduction of the sensitivity of the instrument when working with non-zero residual wavefronts. This so-called optical gains (OG) effect, degrades the closed-loop performance of SCAO systems and prevents accurate correction of non-common path aberrations (NCPA). Aims. In this paper, we aim to compute the OG using a fast and agile strategy to control PyWFS measurements in adaptive optics closed-loop systems. Methods. Using a novel theoretical description of PyWFS, which is based on a convolutional model, we are able to analytically predict the behaviour of the PyWFS in closed-loop operation. This model enables us to explore the impact of residual wavefront errors on particular aspects such as sensitivity and associated OG. The proposed method relies on the knowledge of the residual wavefront statistics and enables automatic estimation of the current OG. End-to-end numerical simulations are used to validate our predictions and test the relevance of our approach. Results. We demonstrate, using on non-invasive strategy, that our method provides an accurate estimation of the OG. The model itself only requires adaptive optics telemetry data to derive statistical information on atmospheric turbulence. Furthermore, we show that by only using an estimation of the current Fried parameter r0 and the basic system-level characteristics, OGs can be estimated with an accuracy of less than 10%. Finally, we highlight the importance of OG estimation in the case of NCPA compensation. The proposed method is applied to the PyWFS. However, it remains valid for any wavefront sensor based on Fourier filtering subject from OG variations. [ABSTRACT FROM AUTHOR]