A novel method nicknamed ELASTIC is proposed for the alignment of multiple-aperture telescopes, in particular segmented telescopes. It only needs the acquisition of two diversity images of an unresolved source, and is based on the computation of a modified, frequency-shifted, cross-spectrum. It provides a polychromatic large range tip/tilt estimation with the existing hardware and an inexpensive noniterative unsupervised algorithm. Its performance is studied and optimized by means of simulations. They show that with 5000 photo-electrons/sub-aperture/frame and 1024x1024 pixel images, residues are within the capture range of interferometric phasing algorithms such as phase diversity. The closed-loop alignment of a 6 sub-aperture mirror provides an experimental demonstration of the effectiveness of the method. Author accepted version. Final version is Copyright 2017 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.
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