Influence of irregular gaps between primary mirror segments on telescope image quality

We study the effect of gaps between the segments on image quality of the extremely large ground-based telescope. We show that if the width of the gap changes arbitrarily from one intersegment boundary to another, the regular diffraction pattern is distorted and speckles appear. Two mechanisms producing irregularity in the gaps' distribution are considered: a random shift of the segment's center and an error in the segment's shape. The analytical approach allows an estimation of ensemble averaged characteristics of the point-spread function, such as a halo and high-order diffraction peaks. We deliver simple formulas for the quantitative estimation of the position and the intensity of the halo as well as the intensity of the diffraction peaks.