International audienceContext. Direct imaging of Earth-like planets from space requires dedicated observatories, combining large segmented apertures with instruments and techniques such as coronagraphs, wavefront sensors, and wavefront control in order to reach the high contrast of 1010 that is required. The complexity of these systems would be increased by the segmentation of the primary mirror, which allows for the larger diameters necessary to image Earth-like planets but also introduces specific patterns in the image due to the pupil shape and segmentation and making high-contrast imaging more challenging. Among these defects, the phasing errors of the primary mirror are a strong limitation to the performance.Aims. In this paper, we foc...