Modelling Fourier filtering wavefront sensors for power spectral density-based methods: The AOPERA tool

Abstract

Compensating for atmospheric turbulence through the use of adaptive optics (AO) has now become commonplace for VLT and ELT class telescopes in order to retrieve a resolution close to their diffraction limit. Accompanying this trend is a greater need for simulations that can be used to understand and predict performance when facing different observing conditions, namely the evolution of the atmospheric turbulence or the diversity of the AO guide source. The so-called power spectral density (PSD)-based methods are well adapted to this demand thanks to their simplicity and speed. Moreover, they provide a comprehensive breakdown error budget and impact on the focal plane, which is of especially high interest in the case of extreme AO. The drawback of these methods is the challenge to describe non-linear wavefront sensors (WFSs), such as the pyramid WFS or the Zernike WFS. Thus, there is a need for the development of fast yet accurate methods to describe the behaviour of AO systems including sensitive WFSs. AO systems We have developed a method to compute the AO system response (electromagnetic phase power spectral density and point spread function) based on the accuracy of the convolutive formalism. Our method allows for the inclusion of the non-linear behaviour of the WFS within PSD-based numerical tools. We compared the numerical implementation of the method with end-to-end simulations using the OOPAO tool. Indeed, end-to-end simulations reproduced the response of AO systems with high fidelity, especially regarding WFS sensitivity and non-linearity. Combining mathematical formalism to describe the Fourier-filtering WFS sensitivity with non-linearity management greatly improves the accuracy of the description of AO systems through numerical simulations. fitting error, temporal error, and noise error proves the validity of our method in managing Fourier-filtering WFS sensitivity and non-linearity . It also cross-validates the numerical implementations of our method and OOPAO as a justification for any future use of either tool. The computed with our method are similar to end-to-end simulation in terms of optical path difference, power spectral density and eventually PSF shape. It from mild to severe AO conditions The development of a PSD-based method accurately describing Fourier-filtering WFS and justification of its validity is critical to understanding the behaviour of AO systems during their design or operation phases. The model we present and its numerical implementation have been applied to the PROVIDENCE 2.5 m telescope to be built in France by the end of 2028. could be used for ELT instruments that include a pyramid AO system. Our method