Modelling Fourier filtering wavefront sensors for PSD-based methods: the AOPERA tool

Abstract

Compensation of the atmospheric turbulence thanks to adaptive optics (AO) has now become commonly used for VLT or ELT class telescopes in order to retrieve a resolution close to their diffraction limit. Following the increasing trend of AO system, there is also a stronger necessity for simulations in order to understand and predict their performance facing different observing conditions, that are the evolution of the atmospheric turbulence or the diversity of AO guide source. The so-called PSD based methods are well adapted to the demand thanks to their simplicity and speed. Moreover, they provide a comprehensive breakdown error budget and impact on focal plane, that is of high interest especially in the case of extreme adaptive optics. Their drawback is the challenge to describe non-linear wavefront sensors (WFS) such as the pyramid WFS or the Zernike WFS. There is a necessity to develop fast yet accurate methods to describe the behaviour of AO systems including sensitive WFS. We thus develop a method to compute the AO system response (electromagnetic phase power spectral density, and point spread function) including the non-linear behaviour of the wavefront sensor within PSD-based numerical tools. Mathematical formalism to describe the FF-WFS sensitivity combined to non-linearity management greatly improve the accuracy of description of AO systems through numerical simulations. After a mathematical description of the method, its numerical implementation is compared with end-to-end simulations using the OOPAO tool. Indeed end-to-end simulations are reproducing the response of AO systems with high fidelity, especially regarding WFS sensitivity and non-linearity. Similarity of results for the fitting error, temporal error and noise error proves the validity of our method in managing Fourier filtering WFS sensitivity and non-linearity.