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This paper presents the optical design of a multi-spectral piston sensorsuitable to co-phasing giant segmented mirrors equipping the Future ExtremelyLarge Telescopes (ELTs). The general theory of the sensor is described indetail and numerical simulations have been carried out, demonstrating thatdirect piston and tip-tilt measurements are feasible within accuraciesrespectively close to 20 nm and 10 nano-radians. Those values are compatiblewith the co-phasing requirements, although the method seems to be perturbed byuncorrected atmospheric seeing

Multi-spectral piston sensor for co-phasing giant segmented mirrors and multi-aperture interferometric arrays