We study the optimization of the Apodized Pupil Lyot Coronagraph (APLC) in the context of exoplanet imaging with ground-based telescopes. The APLC combines an apodization in the pupil plane with a small Lyot mask in the focal plane of the instrument. It has been intensively studied in the literature from a theoretical point of view, and prototypes are currently being manufactured for several projects. This analysis is focused on the case of Extremely Large Telescopes, but is also relevant for other telescope designs. We define a criterion to optimize the APLC with respect to telescope characteristics like central obscuration, pupil shape, low order segment aberrations and reflectivity as function of the APLC apodizer function and mask diameter. Specifically, the method was applied to two possible designs of the future European-Extremely Large Telescope (E-ELT). Optimum configurations of the APLC were derived for different telescope characteristics. We show that the optimum configuration is a stronger function of central obscuration size than of other telescope parameters. We also show that APLC performance is quite insensitive to the central obscuration ratio when the APLC is operated in its optimum configuration, and demonstrate that APLC optimization based on throughput alone is not appropriate.
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