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Restoration of interferometric images - IV. An algorithm for super-resolution of stellar systems
B. Anconelli, M. Bertero, P. Boccacci, and M. Carbillet
A&AS - 431, 747-756 (2005)
In the framework of the methods we introduced for the restoration of images of Fizeau interferometers such as the Large Binocular Telescope, we propose an algorithm which is able to super-resolve compact stellar objects such as a binary system with an angular separation smaller than the angular resolution of the telescope. The method, which works also in the case of a monolithic mirror, is based on a simple modification of the Richardson-Lucy (RL) method or of the Ordered Subsets - Expectation Maximization (OS-EM) method for image deconvolution. In general, it consists of three steps: the first one requires a large number of RL-iterations, which are used to identify and estimate the domain of the unresolved object; the second one is a RL-restoration initialized with the mask of the domain. These two steps can provide a super-resolved image of the stellar system but the photometry of the stars may not be correct. Therefore their positions are derived from the result of the first two steps while their magnitudes are estimated in a third step by solving a simple least-squares problem. In order to show that the method can work in practice, we use (simulated) adaptive-optics-corrected point spread functions (PSF), both in the case of a monolithic and in the case of a binocular telescope, and we investigate mainly the case of binary systems. We analyze the limitations of the method in evaluating the angular separation and the relative magnitude of the two stars. The results we obtain are quite promising.