Imaging exo-Earths is an exciting but challenging task because of the 10^-10 contrast ratio between these planets and their host star at separations narrower than 100 mas. Large segmented aperture space telescopes enable the sensitivity needed to observe a large number of planets. Combined with coronagraphs with wavefront control, they present a promising avenue to generate a high-contrast region in the image of an observed star. Another key aspect is the required stability in telescope pointing, focusing, and co-phasing of the segments of the telescope primary mirror for long-exposure observations of rocky planets for several hours to a few days. These wavefront errors should be stable down to a few tens of picometers RMS, requiring a permanent active correction of these errors during the observing sequence. To calibrate these pointing errors and other critical low-order aberrations, we propose a wavefront sensing path based on Zernike phase-contrast methods to analyze the starlight that is filtered out by the coronagraph at the telescope focus. In this work we present the analytical retrieval of the incoming low order aberrations in the starlight beam that is filtered out by an Apodized Pupil Lyot Coronagraph, one of the leading coronagraph types for starlight suppression. We implement this approach numerically for the active control of these aberrations and present an application with our first experimental results on the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed, the STScI testbed for Earth-twin observations with future large space observatories, such as LUVOIR and HabEx, two NASA flagship mission concepts.
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