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.