Skuratovskyi S. Image reconstruction over the series of instantaneous images, obtained through the turbulent atmosphere

The research object: the interfering influence of the Earth's atmosphere on astronomical observations. The purpose of the thesis: searching for a new, more effective methods for forming and post-processing of astronomical images, that allows one to improve resolution closer to diffraction limit of observational instrument. Research methods: theoretical analysis of distorting Fourier-components phase of an image under atmosphere inhomogeneities influence, numerical simulation of observation process and computer experiment for obtaining results of image reconstruction. New theoretical and practical results: the convergence maps for iteration process of reconstruction of an image from its spectra are ascertained to have complex fractal-like structure, so the development of regular algorithm for initial approximation selection is impossible; the new application of iteration algorithm for reconstruction of atmosphere-aperture function from an image of point-like object is proposed; the new technique of total phases accumulation is proposed by the way of improving existing phase accumulation technique for application under variance of atmosphere phase distortions more than 1 radian; the existence of effective application of phase accumulation techniques is ascertained for the firs time in case of observations using traditional telescope; the new image forming technique combining phase accumulation and interferometric scheme is proposed, and the possibility of improving resolution closer to diffraction limit using this technique is shown even for mean-square deviation of atmosphere phase distortions more than 2Pi radian. Application field: astrophysics, radioastronomy, astronomy.