This paper characterizes the actual science performance of the James Webb Space Telescope (JWST), as determined from the six month commissioning period. We summarize the performance of the spacecraft, telescope, science instruments, and ground system, with an emphasis on differences from pre-launch expectations. Commissioning has made clear that JWST is fully capable of achieving the discoveries for which it was built. Moreover, almost across the board, the science performance of JWST is better than expected; in most cases, JWST will go deeper faster than expected. The telescope and instrument suite have demonstrated the sensitivity, stability, image quality, and spectral range that are necessary to transform our understanding of the cosmos through observations spanning from near-earth asteroids to the most distant galaxies.

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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.

The James Webb Space Telescope (JWST) is a large, infrared space telescope that has recently started its science program which will enable breakthroughs in astrophysics and planetary science. Notably, JWST will provide the very first observations of the earliest luminous objects in the universe and start a new era of exoplanet atmospheric characterization. This transformative science is enabled by a 6.6 m telescope that is passively cooled with a 5 layer sunshield. The primary mirror is comprised of 18 controllable, low areal density hexagonal segments, that were aligned and phased relative to each other in orbit using innovative image-based wave front sensing and control algorithms. This revolutionary telescope took more than two decades to develop with a widely distributed team across engineering disciplines. We present an overview of the telescope requirements, architecture, development, superb on-orbit performance, and lessons learned. JWST successfully demonstrates a segmented aperture space telescope and establishes a path to building even larger space telescopes.

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