Information-theoretical Limits of Recursive Estimation and Closed-loop Control in High-contrast Imaging

TL;DR

This paper establishes fundamental limits on wavefront error estimation and control in high-contrast imaging, providing analytical tools and models to improve coronagraph performance and stability in space telescopes.

Contribution

It introduces a theoretical framework for the limits of recursive wavefront estimation and control, applicable to space-based coronagraphs with combined wavefront sensing methods.

Findings

Recursive estimation benefits from short exposure times.

Contrast scaling laws generalize adaptive optics results.

Model suggests WFE drift can be actively rejected in space telescopes.

Abstract

A lower bound on unbiased estimates of wavefront errors (WFE) is presented for the linear regime of small perturbation and active control of a high-contrast region (dark hole). Analytical approximations and algorithms for computing the closed-loop covariance of the WFE modes are provided for discrete- and continuous-time linear WFE dynamics. Our analysis applies to both image-plane and non-common-path wavefront sensing (WFS) with Poisson-distributed measurements and noise sources (i.e., photon-counting mode). Under this assumption, we show that recursive estimation benefits from infinitesimally short exposure times, is more accurate than batch estimation and, for high-order WFE drift dynamical processes, scales better than batch estimation with amplitude and star brightness. These newly-derived contrast scaling laws are a generalization of previously known theoretical and numerical results for turbulence-driven Adaptive Optics. For space-based coronagraphs, we propose a scheme for combining models of WFE drift, low-order non-common-path WFS (LOWFS) and high-order image-plane WFS (HOWFS) into closed-loop contrast estimates. We also analyze the impact of residual low-order WFE, sensor noise, and other sources incoherent with the star, on closed-loop dark-hole maintenance and the resulting contrast. As an application example, our model suggests that the Roman Space Telescope might operate in a regime that is dominated by incoherent sources rather than WFE drift, where the WFE drift can be actively rejected throughout the observations with residuals significantly dimmer than the incoherent sources. The models proposed in this paper make possible the assessment of the closed-loop contrast of coronagraphs with combined LOWFS and HOWFS capabilities, and thus help estimate WFE stability requirements of future instruments.