Full-link optical differential piston-sensing strategy towards extremely large segmented telescopes

Context . Explorations of Earth-like exoplanets mostly rely on the large segmented telescopes, which allow a larger primary-mirror diameter. Such segmentation requires a piston-monitoring procedure with successive steps from coarse-phasing to fine-phasing control in order to provide the high-resolution scientific image for stringent science operations. In this context, focal-plane piston sensing represents a promising option for such a calibration. However, confronted with the future observation demands for stitching hundreds of segments, existing focal-plane techniques are consistently unable to provide both large-scale and high-precision piston-sensing capabilities. Aims . We propose a novel focal-plane piston-sensing theory that simultaneously combines the capabilities of accommodating hundreds of segments and enabling large-scale measurements with high precision levels and then generate a full-link piston-monitoring procedure that is independent of segmented arrangement. This should pave the way for the deployment of future extremely large segmented telescopes. Methods . Our approach initially extracted the electric field features that respond to the pistons of each non-reference segment through both continuous piston modulation and differential operation under broadband illumination. Then, the Gaussian fitting and phase-transfer function (PTF) were used to jointly identify the optimal response, and the piston inversion can be finally realised without any prior information. We verified the effectiveness of the proposed method through simulations and close-loop experiments. Results . The proposed strategy not only significantly mitigates the intrinsic constraint of piston characterisation caused by redundant baselines, it also makes up for the detection range shortfall of former optical differential models in segmented co-phasing, namely 2 π ambiguity, making it more suitable for future extremely large segmented telescopes. To systematically evaluate its piston-sensing performance, we conducted further numerical simulations to investigate its robustness under different noise levels, tip-tilt residuals, and phase variations, and then analysed its applicability boundaries in real-world scenarios. Notably, as the most critical limiting factor, phase variations must be kept within 20 nm to ensure the effective implementation of this approach.