Extended linearity in the high-order wavefront sensor for the Roman Coronagraph

Context . The aim of the Coronagraphic Instrument (CGI) on board the Roman Space Telescope is to achieve unprecedented levels of contrast for the direct imaging of exoplanets, which will serve as a critical technology demonstrator for future missions such as the Habitable Worlds Observatory (HWO). Achieving these goals requires advanced wavefront sensing and control (WFS&C) strategies, including the use of pair-wise (PW) probing to estimate the electric field in the focal plane. The optimization of PW probe designs is vital in order to enhance performance and reduce operational overhead. Aims . In this study we investigate the performance of different PW probe designs in the context of Roman CGI. Specifically, we compared the classic sinc-sinc-sine probes, previously introduced single-actuator probes, and newly proposed sharp sinc probes in terms of their effectiveness in focal-plane modulation, resilience to nonlinearities at high probe amplitudes, and overall impact on the convergence and contrast levels achieved in laboratory demonstrations. Methods . We conducted experiments on the THD2 testbed, configured to simulate Roman CGI with a custom-made Hybrid Lyot Coronagraph (HLC). We evaluated the three probe designs through closed-loop WFS&C experiments using PW probing for electric field estimation and electric field conjugation (EFC) for wavefront correction. Simulations and hardware tests assessed the contrast convergence and the impact of nonlinear terms at varying probe amplitudes. We also explored low-flux scenarios to demonstrate the effectiveness of high-amplitude probes in reducing exposure times or closing the loop on faint targets. Results . Single-actuator probes emerged as the most effective design, offering faster convergence and reduced susceptibility to nonlinear effects at high amplitudes compared to sinc-sinc-sine probes. Sharp sinc probes perform moderately well, but are less robust than single-actuator probes. High-amplitude single-actuator probes demonstrate advantages in DH digging under low-flux conditions, achieving faster iterations without significant degradation in contrast performance. The THD2 testbed, operating in a contrast regime analogous to Roman CGI, validated these results and underscored its role as a critical platform for advancing WFS&C techniques.