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Calculating diffraction-limited point spread functions for large segmented telescopes

We present techniques for Fourier analysis of the diffraction-limited optical performance of large-aperture astronomical telescopes. We use combinations of Fast Fourier Transform, Discrete Fourier Transform, and Fourier interpolation algorithms as well as the symmetry properties of the segmented mirrors to achieve full calculation of the diffraction pattern in a computationally-efficient manner. We discuss the implementation and results of these techniques in the context of a 15-meter segmented-mirror telescope design for the Large Atacama Telescope.