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 exo-planetary 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 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 paper is the first in a series on this subject, in which a formalism is established for the exoplanet imaging problem in a polarizing optical system that has optical aberrations in multiple planes. Every effort has been made to be rigorous and complete, so that that validity of approximations to be made later can be assessed. It is shown that current methods that utilize focal plane sensing to correct the speckle field, i.e., as electric field conjugation and dark hole methods, 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. Generalizing these methods to correct for aberrations in multiple planes would lessen their reliance on this assumption, potentially making them more effective.
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