Strategy for sensing petal mode in presence of AO residual turbulence with pyramid wavefront sensor

With the Extremely Large Telescope-generation telescopes come new challenges. The complexity of these telescopes' pupil creates new problems for Adaptive Optics. In particular, the large spiders necessary to support the massive optics of these telescopes create discontinuities in the wavefront measurement. These discontinuities appear as a new phase error dubbed the `petal mode'. This error is described as a differential piston between the fragment of the pupil separated by the spiders and is responsible for reducing the European Extremely Large Telescope's (ELT) resolution to a 15m telescope resolution. The aim of this paper is to study the measurement of the petal mode by adaptive optics sensors. We want to understand why the Pyramid Wavefront Sensor (PyWFS) cannot measure this petal mode under normal conditions and how to allow this measurement by adapting the Adaptive optics control scheme and the PyWFS. To facilitate our study, we consider a simplified version of the petal mode, featuring a simpler pupil than the ELT. We studied specifically how a system that separates the atmospheric turbulence from the petal measurement would behave. The unmodulated PyWFS (uPyWFS) but the uPyWFS does not make accurate measurements in the presence of atmospheric residuals. Studying the petal mode's power spectral density, we propose a filtering step, consisting of a pinhole around the pyramid tip. This reduces the first path residuals seen by the uPyWFS and restores its accuracy. Finally, we demonstrate our proposed system with end-to-end simulations.To address the petal problem, a two-path adaptive optics with a sensor dedicated to the measurement of the petal mode seems necessary. Through this paper, we demonstrate that an uPyWFS can confuse the petal mode with the residuals from the first path. However, adding a spatial filter on top of said uPyWFS makes it a good petalometer candidate.