This paper introduces an analytical method to calculate segment-level wavefront error (WFE) tolerances to enable the detection of faint extra-solar planets using segmentedaperture telescopes in space. This study provides a full treatment of the case of spatially uncorrelated segment phasing errors for segmented telescope coronagraphy, which has so far only been approached using ad-hoc Monte Carlo (MC) simulations. Instead of describing the wavefront tolerance globally for all segments, our method produces spatially dependent requirement maps. We relate the statistical mean contrast in the coronagraph dark hole to the standard deviation of the WFE of each individual segment on the primary mirror. This statistical framework for segment-level tolerancing extends the Pair-based Analytical model for Segmented Telescope Imaging from Space (PASTIS), which is based uniquely on a matrix multiplication for the optical propagation. We confirm our analytical results with MC simulations of end-to-end optical propagations through a coronagraph. Comparing our results for the Apodized Pupil Lyot Coronagraph designs for the Large Ultraviolet Optical Infrared telescope to previous studies, we show general agreement but we provide a relaxation of the requirements for a significant subset of segments in the pupil. These requirement maps are unique to any given telescope geometry and coronagraph design. The spatially uncorrelated segment tolerances we calculate are a key element of a complete error budget that will also need to include allocations for correlated segment contributions. We discuss how the PASTIS formalism can be extended to the spatially correlated case by deriving the statistical mean contrast and its variance for a nondiagonal aberration covariance matrix. The PASTIS tolerancing framework therefore brings a new capability that is necessary for the global tolerancing of future segmented space observatories.

Aims. We describe the design and first light observations from the β Pictoris b Ring ("bRing") project. The primary goal is to detect photometric variability from the young star β Pictoris due to circumplanetary material surrounding the directly imaged young extrasolar gas giant planet β Pictoris b. Methods. Over a nine month period centred on September 2017, the Hill sphere of the planet will cross in front of the star, providing a unique opportunity to directly probe the circumplanetary environment of a directly imaged planet through photometric and spectroscopic variations. We have built and installed the first of two bRing monitoring stations (one in South Africa and the other in Australia) that will measure the flux of β Pictoris, with a photometric precision of 0.5% over 5 min. Each station uses two wide field cameras to cover the declination of the star at all elevations. Detection of photometric fluctuations will trigger spectroscopic observations with large aperture telescopes in order to determine the gas and dust composition in a system at the end of the planet-forming era. Results. The first three months of operation demonstrate that bRing can obtain better than 0.5% photometry on β Pictoris in five minutes and is sensitive to nightly trends enabling the detection of any transiting material within the Hill sphere of the exoplanet.

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Context. The detection and characterization of Earth-like exoplanets (exoEarths) from space requires exquisite wavefront stability at contrast levels of 10−10. On segmented telescopes in particular, aberrations induced by co-phasing errors lead to a light leakage through the coronagraph, deteriorating the imaging performance. These need to be limited in order to facilitate the direct imaging of exoEarths. Aims. We perform a laboratory validation of an analytical tolerancing model that allows us to determine wavefront error requirements in the 10−6 − 10−8 contrast regime for a segmented pupil with a classical Lyot coronagraph. We intend to compare the results to simulations, and we aim to establish an error budget for the segmented mirror on the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed. Methods. We use the Pair-based Analytical model for Segmented Telescope Imaging from Space to measure a contrast influence matrix of a real high-contrast instrument, and use an analytical model inversion to calculate per-segment wavefront error tolerances. We validate these tolerances on the HiCAT testbed by measuring the contrast response of segmented mirror states that follow these requirements. Results. The experimental optical influence matrix is successfully measured on the HiCAT testbed, and we derive individual segment tolerances from it that correctly yield the targeted contrast levels. Further, the analytical expressions that predict a contrast mean and variance from a given segment covariance matrix are confirmed experimentally.

Direct imaging of exo-Earths and search for life is one of the most exciting and challenging objectives for future space observatories. Segmented apertures in space will be required to reach the needed large diameters beyond the capabilities of current or planned launch vehicles. These apertures present additional challenges for high-contrast coronagraphy, not only in terms of static phasing but also in terms of their stability. The Pair-based Analytical model for Segmented Telescope Imaging from Space (PASTIS) was developed to model the effects of segmentlevel optical aberrations on the final image contrast. In this paper, we extend the original PASTIS propagation model from a purely analytical to a semi-analytical method, in which we substitute the use of analytical images with numerically simulated images. The inversion of this model yields a set of orthonormal modes that can be used to determine segment-level wavefront tolerances. We present results in the case of segment-level piston error applied to the baseline coronagraph design of LUVOIR A, with minimum and maximum wavefront error constraint between 56 pm and 290 pm per segment. The analysis is readily generalizable to other segment-level aberrations modes, and can also be expanded to establish stability tolerances for these missions.where c is the mean contrast in the dark-hole, c 0 the coronagraph floor (i.e. the average contrast in the dark-hole in the absence of aberrations), M is the PASTIS matrix with elements m ij , a is the aberration vector of the local Zernike coefficients on all n seg segments and a T its transpose.The PASTIS matrix M can be calculated using either the analytical approach [8, Eq. 20], or directly using an end-to-end simulation in the semi-analytical approach introduced in the next section. Once the PASTIS

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We discuss the use of parametric phase-diverse phase retrieval as an in-situ high-fidelity wavefront measurement method to characterize and optimize the transmitted wavefront of a high-contrast coronagraphic instrument. We apply our method to correct the transmitted wavefront of the HiCAT (High contrast imager for Complex Aperture Telescopes) coronagraphic testbed. This correction requires a series of calibration steps, which we describe. The correction improves the system wavefront from 16 nm RMS to 3.0 nm RMS.