Adaptive optics or numerical restoration algorithms that restore high resolution imaging through atmospheric turbulence are subject to isoplanatic wave-front errors. Mitigating those errors requires that the wave-front aberrations be estimated within the 3D volume of the atmosphere. Present techniques rely on multiple beacons, either natural stars or laser guide stars, to probe the atmospheric aberration along different lines of sight, followed by tomographic projection of the measurements onto layers at defined ranges. In this paper we show that a three-dimensional estimate of the wave-front aberration can be recovered from measurements by a single guide star in the case where the aberration is stratified, provided that the telescope tracks across the sky with non-uniform angular velocity. This is generally the case for observations of artificial earth-orbiting satellites, and the new method is likely to find application in ground based telescopes used for space situational awareness.

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