Extended Linearity in the High-Order Wavefront Sensor for the Roman Coronagraph

Context. The Coronagraphic Instrument (CGI) on the Roman Space Telescope aims for unprecedented contrast for direct imaging of exoplanets, serving as a critical tech demo for future missions like the Habitable Worlds Observatory. This requires advanced wavefront sensing and control (WFS&C), including pair-wise (PW) probing for electric field estimation in the focal plane. Optimizing PW probe designs is vital to enhance performance and reduce overheads. Aims. We investigate different probe designs for PW probing in the context of Roman CGI. We compare classic sinc-sinc-sine probes, previously introduced single-actuator probes, and newly proposed sharp sinc probes in terms of effectiveness in focal-plane modulation, resilience to non-linearities, and overall impact on convergence and contrast. Methods. We conducted experiments on the THD2 testbed, configured to emulate Roman CGI with a custom Hybrid Lyot Coronagraph. We evaluated the three probe designs through WFS&C experiments using PW probing for estimation and electric field conjugation for wavefront correction. Simulations and hardware tests assessed contrast convergence and the impact of non-linear terms at varying probe amplitudes. We also explored low-flux scenarios to demonstrate the use of high-amplitude probes in reducing exposure times or closing the loop on faint targets. Results. Single-actuator probes emerged as the most effective, with faster convergence and reduced non-linear effects at high amplitudes. Sharp sinc probes performed moderately well but were less robust than single actuators. High-amplitude single-actuator probes showed advantages in dark-hole digging under low-flux, through faster iterations without significant degradation in contrast. The THD2 testbed, operating at contrasts analogous to Roman CGI, validated our results and underscored its role as a critical platform for advancing WFS&C techniques.