Tradeoff between segment density and IWA for high-contrast imaging of exoplanets with a large segmented space mission
Imaging Earth-like exoplanets with coronagraphs on future large segmented space telescopes such as the Habitable Worlds Observatory requires contrasts down to $10^{-10}$ at separations below 100 mas, imposing segment phasing control down to a few picometers. We evaluate how this constraint can be relaxed by optimizing telescope and instrument design, quantifying the impact on performance stability under segment phasing aberrations. We propose a system-level approach, adjusting the primary mirror segmentation and the focal-plane mask size (inner working angle). We compare the passive robustness to segment phasing errors across systems, and the ability of a Zernike low-order wavefront sensor to reconstruct aberrations and recover target performance. Increasing the focal-plane mask radius or decreasing segment count improves both passive robustness and sensor reconstruction: Increasing the mask radius from 3.5 to 6.5λ/D relaxes phasing constraints by up to a factor 4 near the IWA, and reducing the segment count from 85 (5 rings) to 7 (1 ring) relaxes them by up to a factor 2; The same mask radius increase also doubles, on average, the sensor's sensitivity to photon noise across segment piston, tip, and tilt modes. To conclude, jointly optimizing the segmentation scheme and mask size, so the low-order PSD envelope is blocked by the mask, can significantly relax phasing requirements, complementing active correction, with direct implications for HWO.