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.
© 2003 Optical Society of America
(050.0050) Diffraction and gratings : Diffraction and gratings
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(110.1220) Imaging systems : Apertures
(110.3000) Imaging systems : Image quality assessment
(110.6770) Imaging systems : Telescopes
Natalia Yaitskova, Kjetil Dohlen, and Philippe Dierickx, "Analytical study of diffraction effects in extremely large segmented telescopes," J. Opt. Soc. Am. A 20, 1563-1575 (2003)