How to train your Jacobian: least-squares system identification for space-based coronagraphy

Stellar coronagraphs use closed-loop focal-plane wavefront sensing and control algorithms to create high-contrast dark zones suitable for imaging exoplanets and exozodiacal dust clouds around nearby stars. Model-based algorithms are susceptible to model mismatch, wherein a departure of the coronagraph’s true optical characteristics from the assumed model causes reduced control loop performance. We describe a simple technique for empirically tuning the wavefront control Jacobian matrix using applied deformable mirror commands and observed images. This mitigates model mismatch and recovers near-optimal control loop performance, and additionally provides a simple means for verifying model quality on-orbit or in a laboratory setting. We demonstrate the proposed least-squares system identification method experimentally using the High-contrast Imager for Complex Aperture Telescopes (HiCAT) testbed, as well as via simulations with a Habitable Worlds Observatory–like system configuration.