All coronagraphic instruments for exoplanet high-contrast imaging need
wavefront correction systems to reject optical aberrations and create
sufficiently dark holes. Since the most efficient wavefront correction
algorithms (controllers and estimators) are usually model-based, the modeling
accuracy of the system influences the ultimate wavefront correction
performance. Currently, wavefront correction systems are typically approximated
as linear systems using Fourier optics. However, the Fourier optics model is
usually biased due to inaccuracies in the layout measurements, the imperfect
diagnoses of inherent optical aberrations, and a lack of knowledge of the
deformable mirrors (actuator gains and influence functions). Moreover, the
telescope optical system varies over time because of instrument instabilities
and environmental effects. In this paper, we present an
expectation-maximization (E-M) approach for identifying and real-time adapting
the linear telescope model from data. By iterating between the E-step (a Kalman
filter and a Rauch smoother) and the M-step (analytical or gradient-based
optimization), the algorithm is able to recover the system even if the model
depends on the electric fields, which are unmeasurable hidden variables.
Simulations and experiments in Princeton's High Contrast Imaging Lab
demonstrate that this algorithm improves the model accuracy and increases the
efficiency and speed of the wavefront correction
