The optical design of laser guide star relays for extremely large telescopes

Three Extremely Laser Telescope ELT) projects are currently in construction phases. These telescopes all rely on Adaptive Optics to meet their high-spatial resolution imaging requirements. Laser Guide Star Adaptive Optics (LGSAO) systems require an optical relay to produce images of both the telescope focal surface, and of laser guide stars. Laser guide stars produced in the mesosphere layer of the atmosphere lie at object conjugate distances of between 80 km and 200 km, and these are imaged by the telescope to lie at a range of axial distances from the telescope focal surface. Further, such relays are required to produce sharp metapupils and exit pupil. "Absolute Instruments" provide an image of the entire 3-dimensional object-space of the system that is free of distortion, curvature and point-blurring aberrations. Such systems are well-matched to the requirements of LGSAO systems. In this paper it will be shown that such systems can provide excellent image quality for the science field as well as for any practical range of LGS objects. Further, by splitting the correcting plate that transforms an ordinary relay into an absolute instrument, simultaneous near-perfect correction of metapupils and exit pupil can be achieved with no compromise to the relays' imaging properties.