Coadding Techniques for Image-based Wavefront Sensing for Segmented-mirror Telescopes

Image-based wavefront sensing algorithms are being used to characterize optical performance for a variety of current and planned astronomical telescopes. Phase retrieval recovers the optical wavefront that correlates to a series of diversity-defocused point-spread functions (PSFs), where multiple frames can be acquired at each defocus setting. Multiple frames of data can be coadded in different ways; two extremes are in "image-plane space," to average the frames for each defocused PSF and use phase retrieval once on the averaged images, or in "pupil-plane space," to use phase retrieval on every set of PSFs individually and average the resulting wavefronts. The choice of coadd methodology is particularly noteworthy for segmented-mirror telescopes that are subject to noise that causes uncorrelated motions between groups of segments. Using data collected on and simulations of the James Webb Space Telescope Testbed Telescope (TBT) commissioned at Ball Aerospace, we show how different sources of noise (uncorrelated segment jitter, turbulence, and common-mode noise) and different parts of the optical wavefront, segment and global aberrations, contribute to choosing the coadd method. Of particular interest, segment piston is more accurately recovered in "image-plane space" coadding, while segment tip/tilt is recovered in "pupil-plane space" coadding.