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Demonstrating the sub-nanometer sensitivity of a pyramid WaveFrontSensor for active space telescopes

In order to deliver high contrast, high resolution images, a keypoint in future space telescopes is to implement a correction chain, composed by a WaveFront Sensor (WFS) and an active/deformable mirror (DM) running in closed loop. While the current baseline for WFS is mostly focused on PSF sensing, no or little attention has been paid to a crucial element: after an initial startup phase, a space telescope will be operating in quasi diffraction-limited regime, so that a WFS shall be able to stably measure nanometer-level aberrations. In this scenario, the aberration signal in the PSF is overwhelmed by the bright core and to get rid of the photon noise a long time integration is required, which is converted into a more stringent stability requirement for the DM. We propose the implementation of the pyramid WFS (PWFS), which has been already demonstrated on-sky for high contrast at large ground based observatories. In this paper we present numerical simulations of a PWFS controlling an active primary in space. We will show the signal measured by the pyramid when a offset is applied on the mirror and the closed loop performances. The results indicate that the PWFS is able to detect nanometer-level low spatial scale aberrations and drive the active mirror with an optical stability consistent with typical requirements.