Modal estimation of high-order wavefront drifts on coronagraphic testbeds for high-contrast direct imaging of exoplanets

Long-term wavefront stability will be critical for the upcoming Habitable Worlds Observatory which aims to directly image exo-Earths. Mechanical and thermal instabilities induce slow, high-order wavefront errors which can degrade the contrast and in turn, the scientific yield of the observatory. Dark zone maintenance (DZM) has been proposed as a high-order wavefront sensing and control strategy to maintain contrast despite wavefront error drifts. This approach uses an Extended Kalman Filter (EKF) to estimate the electric field at each pixel in the dark zone of the science camera. However, relying on individual pixel information to estimate wavefront errors can discard information stored in the underlying wavefront. This is a fundamental limitation on the best achieved contrast compared to the model-based theoretical bounds derived from photon noise. An alternative EKF can incorporate more wholistic information by estimating the drifting wavefront modes present in the system. In this work we analyze the performance of this Modal EKF on the High-contrast Imager for Complex Aperture Telescopes (HiCAT) simulator at the Space Telescope Science Institute. A parameter scan is performed across key variables: deformable mirror (DM) drift, the direct photon rate at the telescope aperture governing the mean number of photons in the dark zone (DZ), and the dither magnitude used to provide phase diversity. While prior studies explored a range of dither magnitudes, this work introduces a covariance-based approach within the Extended Kalman Filter (EKF) framework to optimally determine the probe magnitude required. Results from the modal EKF demonstrate a 15-fold improvement in contrast relative to the single-pixel DZM experiments, reducing the gap to within a factor of two to three of the theoretical bounds.