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Imaging exo-Earths is an exciting but challenging task because of the 10^-10contrast ratio between these planets and their host star at separationsnarrower than 100 mas. Large segmented aperture space telescopes enable thesensitivity needed to observe a large number of planets. Combined withcoronagraphs with wavefront control, they present a promising avenue togenerate 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 forlong-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 observingsequence. To calibrate these pointing errors and other critical low-orderaberrations, we propose a wavefront sensing path based on Zernikephase-contrast methods to analyze the starlight that is filtered out by thecoronagraph at the telescope focus. In this work we present the analyticalretrieval of the incoming low order aberrations in the starlight beam that isfiltered out by an Apodized Pupil Lyot Coronagraph, one of the leadingcoronagraph types for starlight suppression. We implement this approachnumerically for the active control of these aberrations and present anapplication with our first experimental results on the High-contrast imager forComplex Aperture Telescopes (HiCAT) testbed, the STScI testbed for Earth-twinobservations with future large space observatories, such as LUVOIR and HabEx,two NASA flagship mission concepts.

Estimating low-order aberrations through a Lyot coronagraph with a Zernike wavefront sensor for exoplanet imaging