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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An image-based wavefront sensing and control algorithm for the James Webb Space Telescope (JWST) is presented. The algorithm heritage is discussed in addition to implications for algorithm performance dictated by NASA's Technology Readiness Level (TRL) 6. The algorithm uses feedback through an adaptive diversity function to avoid the need for phase-unwrapping post-processing steps. Algorithm results are demonstrated using JWST Testbed Telescope (TBT) commissioning data and the accuracy is assessed by comparison with interferometer results on a multi-wave phase aberration. Strategies for minimizing aliasing artifacts in the recovered phase are presented and orthogonal basis functions are implemented for representing wavefronts in irregular hexagonal apertures. Algorithm implementation on a parallel cluster of high-speed digital signal processors (DSPs) is also discussed.

Wavefront-sensing performance is assessed for focus-diverse phase retrieval as the aberration spatial frequency and the diversity defocus are varied. The analysis includes analytical predictions for optimal diversity values corresponding to the recovery of a dominant spatial-frequency component in the pupil. The calculation is shown to be consistent with the Cramér-Rao lower bound by considering a sensitivity analysis of the point-spread function to the spatial frequency being estimated. A maximum value of diversity defocus is also calculated, beyond which wavefront-sensing performance decreases as diversity defocus is increased. The results are shown to be consistent with the Talbot imaging phenomena, explaining multiple periodic regions of maximum and minimum contrast as a function of aberration spatial frequency and defocus. Wavefront-sensing performance for an iterative-transform phase-retrieval algorithm is also considered as diversity defocus and aberration spatial frequency are varied.