A new generation of telescopes with mirror diameters of 20 m or more, called extremely large telescopes (ELTs), has the potential to provide unprecedented imaging and spectroscopy of exoplanetary systems, if the difficulties in achieving the extremely high dynamic range required to differentiate the planetary signal from the star can be overcome to a sufficient degree. Fully utilizing the potential of ELTs for exoplanet imaging will likely require simultaneous and self-consistent determination of both the planetary image and the unknown aberrations in multiple planes of the optical system, using statistical inference based on the wavefront sensor and science camera data streams. This approach promises to overcome the most important systematic errors inherent in the various schemes based on differential imaging, such as angular differential imaging and spectral differential imaging. This paper is the first in a series on this subject, in which a formalism is established for the exoplanet imaging problem, setting the stage for the statistical inference methods to follow in the future. Every effort has been made to be rigorous and complete, so that validity of approximations to be made later can be assessed. Here, the polarimetric image is expressed in terms of aberrations in the various planes of a polarizing telescope with an adaptive optics system. Further, it is shown that current methods that utilize focal plane sensing to correct the speckle field, e.g., electric field conjugation, rely on the tacit assumption that aberrations on multiple optical surfaces can be represented as aberration on a single optical surface, ultimately limiting their potential effectiveness for ground-based astronomy.
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