High resolution astronomical imaging through the turbulent atmosphere

This research is principally concerned with the digital reconstruction of star images observed with large ground-based telescopes, although the techniques developed here will have application to a broad class of reconstruction problems. Since the work of Labeyrie, the difficulty in producing accurate and detailed reconstructions of stars has stemmed primarily from the extreme degradation of the phase spectrum caused by the atmospheric turbulence, and secondarily from the low-pass filter characteristic of the telescope itself. In this research, we describe solutions to both problems. Our phase estimator is based on the Knox-Thompson phase difference estimator, which we have extended and modified to produce more accurate estimates. The performance of this estimator is evaluated by simulation at various signal-to-noise ratios. We also describe a new non-linear super-resolution algorithm which appears to exhibit the best accuracy and convergence characteristics of any such algorithm proposed to date. It is also evaluated empirically. These two techniques were then used to restore images of the stars Betelgeuse and Capella. In the latter restoration resolution is realized well beyond the diffraction-limit of the telescope. Both reconstructions are consistent with known astrophysical facts, and both appear to be of high quality.