Fundamental limits of high contrast imaging with continuous WFS&C control in space.

We explore the high contrast capabilities of large segmented telescopes with Active and Adaptive Optics, with particular focus on a system view, which includes use of approaches that are routine for current large ground-based telescopes. These approaches include continuous Wavefront Sensing and control (WFS&C), and proper partitioning of engineering challenges by optimizing the error budget allocations. We present a methodology to compute wavefront stability requirements in the presence of temporal variations of the observatory optical errors at all spatial scales: global low order aberrations, segment to segment misalignments and high spatial frequencies. We start by deriving the sensitivity of the starlight suppression of a coronagraph instrument (e.g. the relationship between contrast and wavefront variance) for each family of spatial modes. We then propagate open loop wavefronts variances, alongside with the actual photons carrying the information associated with these misalignments, through diffractive linear wavefront sensor models. We calculate the Fisher information of measurements using those. That quantity is then used in the context of a Cramer-Rao bound to evaluate closed loop residuals, which are then propagated through coronagraph models to yield contrast fundamental limits. Working under the assumption that such WFS&C systems will be limited by the information content bottleneck due to the finite magnitude of a natural guide star, we use results from these calculations to quantify observatory requirements for a variety of exoplanet imaging missions. We highlight the similarities and differences between monolithic and segmented architectures, and show that the often-cited need for picometer stability is no longer required for the latter across the full aperture, but rather within combinations of segments. We also consider both the case of batch and recursive wavefront estimators (that take into account the entire sensing history) and make the case for significantly less challenging observatory requirements when the latter class of algorithms is implemented.