Statistical framework for the utilization of simultaneous pupil plane and focal plane telemetry for exoplanet imaging I Accounting for aberrations in multiple planes

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.

Empirical Green's function approach for utilizing millisecond focal and pupil plane telemetry in exoplanet imaging

“…Assume that the AO system is using the only the star at the center of the putative solar system under investigation to track the turbulence. As per the discussion in [3], the star at the center of the putative planetary system gives rise to an electromagnetic disturbance impinging on the telescope entrance pupil that can be represented as:…”

“…where Υ D,0 is a propagation operator that relates the field at the telescope entrance (plane 0) to the field at the DM (plane D), and r D is the coordinate on the DM surface. Under the operator notation established in [3], the Υ D,0 (r D , r 0 ) operator includes 2D integration over the entrance pupil coordinate r 0 . In keeping with notational conventions established in [3], the operator Υ B,A , which propagates the field from plane B to plane A, includes interaction with the optical surface A, but does not include interaction with optical surface B.…”

“…where the field u C is a 2 × 1 Jones vector, Υ k C,w is now a 2 × 2 matrix, andȗ w is the 2 × 1 polarization state vector of the light impinging on the WFS. 4 When treating polarization effects, one must consider the 4 × 1 coherency vector (which differs from the better-known Stokes vector by a linear transformation), instead of the simple scalar intensity. The coherency vector of the starlight impinging on the SC detector is J C (r C , t) = u C (r C , t) ⊗ u * C (r C , t), 3 where ⊗ denotes the Kronecker product, and the science camera field, u C , is given by Eq.…”

“…The information required to successfully perform the estimation is provided by the variability of the residual phase (so it is closely related to other phase diversity methods), although multi-wavelength and diurnal rotation constraints could be employed as well. In [3,4], the author extended this approach to include non-pupil plane NCPA, which requires summing the contributions from unknown aberrations in various optical planes. The resulting expression is very complicated and computationally demanding because it requires propagation operators between the various optical planes.…”

Recurrence quantification analysis as a post-processing technique in adaptive optics high contrast imaging

“…However, even if these techniques make good use of the high acquisition rate, the temporal information in the data sequence is not fully exploited. Many authors have proposed alternative approaches to the techniques based on PSF subtraction: these alternative approaches rely on the statistical discrimination of the planet signal with respect to speckle statistics (see for instance Labeyrie 1995;Cagigal & Canales 2001;Aime & Soummer 2004;Fitzgerald & Graham 2006;Gladysz et al 2010;Frazin 2016, to mention a few). More in particular, it was shown ) that the probability density function (PDF) of intensity fluctuations in AO corrected images can be modeled as a Rician distribution: this evolves from an exponential to a Gaussian as one moves from the halo of speckles towards the core of the PSF.…”