Focal-plane wavefront estimation and control using the extended Kalman filter

This paper addresses the problem of disturbance rejection for faint Poisson point-like measurements. The aberration function is approximated with a finite Zernike based expansion. We use nonlinear observers to estimate the aberrations and a linear quadratic regulator to reject the aberrations. Kalman filtering is compared with the phase diversity maximum aposteriori estimation. The approach presented here is beneficial for instance for 2-photon observations, single molecule observations or natural/laser guide star observations in astronomy.