Analytical study of diffraction effects in extremely large segmented telescopes.
We present an analysis of the diffraction effects from a segmented aperture with a very large number of segments-prototype of the next generation of extremely large telescopes. This analysis is based on the point-spread-function analytical calculation for Keck-type hexagonal segmentation geometry. We concentrate on the effects that lead to the appearance of speckles and/or a regular pattern of diffraction peaks. These effects are related to random piston and tip-tilt errors on each segment, gaps between segments, and segment edge distortion. We deliver formulas and the typical numerical values for the Strehl ratio, the relative intensity of higher-order diffraction peaks, and the averaged intensity of speckles associated with each particular case of segmentation error.