Assessing and mitigating alignment defects of the pyramid wavefront sensor: a translation insensitive control method

The pyramid wavefront sensor (PWFS) is the currently preferred design for adaptive optics (AO) systems for extremely large telescopes, as focal plane wavefront sensing bears potential for a large intrinsic sensitivity gain when compared to Shack-Hartmann (SH) sensors. Yet, obtaining a high quality pyramidal prism and a model-consistent assembly remains a critical design factor. We demonstrate that the traditional gradient sensing controller is extremely sensitive to prism shape defects and assembly misalignments. We show that even optimal registration of quadrants on the detector may be insufficient to prevent misalignment induced performance loss through a theoretical analysis of the impact of detection plane quadrants sampling errors and individual translations, which may be induced by a variety of mechanical defects. These misalignments displace wavefront information to terms not included in the conventional gradient-like slopes maps and high spatial frequencies become invisible to the sole X- and Y- axis differences. We introduce expanded space control (ESC) for quad-cell signal by generalizing output measurements of the PWFS and demonstrate its insensitivity to misalignment-induced information loss, therefore dramatically relaxing machining and alignment constraints for PWFS engineering. This work presents the theoretical developments leading to ESC design, along with validating performance and robustness results, both in end-to-end numerical simulations and on a PWFS demonstrator bench at LESIA.