Context. With the Extremely Large Telescope (ELT) generation of telescopes come new challenges. The complexity of these telescopes’ pupils creates new problems for adaptive optics (AO) that prevent the telescopes from reaching the theoretical resolutions that their size allows. 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 a strong degradation in the imaging quality, reducing the European ELT’s resolution to that of a 15m telescope. Aims. The aim of this paper is to study the measurement of the petal mode by AO sensors. In particular, we want to understand why the pyramid wavefront sensor (PyWFS), the first-light wavefront sensor of any ELT-generation telescope, cannot measure this petal mode under normal conditions, and how to enable this measurement by adapting the AO control scheme and the PyWFS. Methods. To facilitate our study, we considered a simplified version of the petal mode, featuring a simpler pupil than the ELT. This allowed us to quickly simulate the properties of the petal mode and its measurement by the PyWFS. We studied specifically how a system that separates the atmospheric turbulence from the petal measurement would behave. Studying the petal mode’s power spectral density, we proposed using a spatial filter to reduce the contribution of AO residuals to the benefit of petal mode contribution, eventually enabling it to be measured. Finally, we demonstrated our proposed system with end-to-end simulations. Results. A solution proposed to measure the petal mode is to use an unmodulated PyWFS (uPyWFS), but the uPyWFS does not make accurate measurements in the presence of atmospheric residuals. A spatial filtering step, consisting of a pinhole around the pyramid tip, reduces the first path residuals seen by the uPyWFS and restores its accuracy. This system was able to measure and control the petal mode during the end-to-end simulation. Conclusions. To address the petal problem, a two-path AO with a sensor dedicated to the measurement of the petal mode seems necessary. The question remains as to what could be used as the second path petalometer. 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. This spatial filtering step makes the uPyWFS less sensitive to the first path residuals while retaining its ability to measure the petal mode.
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