Sequential phase diversity for wavefront correction using a deformable mirror with modeling errors

The phase diversity (PD) method is effective for scene-based wavefront sensing and control (WFSC) in spaceborne high-resolution imagers for Earth observation. The simplest way of performing the PD WFSC is offering a diversity wavefront by directly actuating a corrective device, such as a deformable mirror. However, this strategy faces a challenge in constructing a numerical model of the provided diversity wavefront because some corrective actuators' properties prevent us from precisely determining their deflection behaviors. To avoid this modeling issue, we propose the sequential PD (SPD) method to compensate for static aberration using a corrective device with modeling errors. The SPD WFSC repeats the PD WFSC to gradually correct the aberration, where the estimated corrective wavefront is regarded as the known diversity in the subsequent PD WFSC. The numerical simulation validated that the proposed idea improved the correction performance when a corrective device had a linear modeling error. Additionally, a demonstration experiment succeeded in aberration removal using a face-sheet deformable mirror with inter-actuator coupling and non-linear responses. An additional simulation demonstrated that the proposed method effectively corrected the discontinuous wavefront aberration in multi-aperture imaging systems. The SPD WFSC can potentially bring us optical remote sensing systems with unprecedentedly high resolution.