Atmospheric tomography for artificial satellite observations with a single guide star

Estimation of wavefront errors in three dimensions is required to mitigate isoplanatic errors when using adaptive optics or numerical restoration algorithms to recover high-resolution images from blurred data taken through atmospheric turbulence. 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. In this Letter, we show that a three-dimensional estimate of the wavefront 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 nonuniform 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.