Abstract
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.
Highlights
The pyramid wavefront sensor (PyWFS) is an optical device used to perform wavefront sensing, which was first proposed in 1996 (Ragazzoni 1996)
It is possible to describe the PyWFS as a convolutional system that can be fully characterised by the knowledge of its impulse response, as is widely done for many physical systems
When we tried to compensate the non-common path aberrations (NCPA) by applying reference intensities on the PyWFS without compensating for the optical gains (OG), we observed a degradation of performance (Fig. 13)
Summary
The pyramid wavefront sensor (PyWFS) is an optical device used to perform wavefront sensing, which was first proposed in 1996 (Ragazzoni 1996). Inspired by the Foucault knife test, the PyWFS is a pupil plane wavefront sensor (WFS) performing optical Fourier filtering thanks to a glass pyramid located in the focal plane (see Fig. 1) This pyramid splits the electromagnetic (EM) field into four beams, each producing four different filtered images of the entrance pupil. It is possible to describe the PyWFS as a convolutional system that can be fully characterised by the knowledge of its impulse response, as is widely done for many physical systems The advantages of such a convolutional description are numerous: it allows for a fast numerical computation of the response of a sensor to a given input phase and gives the frequency-dependent sensitivity through the transfer. Definition of optical gains and application to PyWFS in presence of residual phases
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