A Statistical Framework for the Utilization of Simultaneous Pupil Plane and Focal Plane Telemetry for Exoplanet Imaging, Part I: Accounting for Aberrations in Multiple Planes

TL;DR

This paper develops a formal statistical framework for exoplanet imaging with extremely large telescopes, accounting for aberrations in multiple optical planes to improve image accuracy and overcome systematic errors.

Contribution

It introduces a comprehensive formalism for modeling aberrations across multiple optical planes, enabling more accurate simultaneous estimation of planetary images and system aberrations.

Findings

Formalism for aberrations in multiple planes established

Current focal plane sensing methods assume single-surface aberrations

Framework sets stage for advanced statistical inference methods

Abstract

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 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 ADI and SDI. 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.