Improved atmospheric turbulence tilt-estimation and its effect on astronomical imaging

Two new methods for estimating the atmospherically-induced optical tilt are described and utilized to improve image recovery from short-exposure Rayleigh-sampled astronomical data. The primary tilt-estimation method involves the introduction of a new model describing the temporal transitions of atmospherically-induced optical tilt. The proposed temporal tilt-transition model is derived from a general atmospheric turbulence model and contains many features of a Gauss-Markov process. The tilt model provides additional statistical information that can be used to improve tilt-estimation algorithms. The new model is then used in a Bayesian-based tilt-estimation algorithm that weighs the a priori tilt-transition information with the measured data in computing estimates of the frame-to-frame optical tilt parameters. The second method for improving tilt-estimation relies on transforming each image in the sequence of short-exposure frames into two vector projections formed by accumulating pixel values along the rows and columns of the image. The vector projections corresponding to successive frames are in turn used to estimate the individual horizontal and vertical components of the tilt by means of a one-dimensional cross-correlation-based estimator.; Improved tilt estimates will in turn improve the quality of images extracted from temporal sequences of Rayleigh-sampled astronomical data. It is shown that the effect of spatial under-sampling produced by the Rayleigh-sampling operation, serves to introduce noise into the measured images via aliasing. The general method of phase diversity is considered in this thesis as a means of overcoming aliasing in Rayleigh-sampled images. It will be shown how the changes in optical tilt, as well as other types of aberrations, can be used to improve the effective sample rate and thereby yield improved image resolution. The new tilt-estimation methods are then used in a Bayesian-based image reconstruction algorithm designed to improve the sampling rate of the system and remove the effects of the point-spread function. This set of registration and reconstruction algorithms are tested using both simulated and measured data. Images are estimated from the short-exposure data showing how the improved registration parameters yield improved image estimates.