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Discussions of the Unruh effect are often confused by the unrealistic nature of the trajectory (acceleration ad infinitum) and by the invocation of accelerated observers. We present a formalism that allows the calculation of radiation emission from accelerated atoms and mirrors in time-dependent perturbation theory moving along asymptotically inertial trajectories. The description is unambiguously set in terms pertaining to the laboratory frame. In the limit of constant acceleration of infinitedoi:10.1088/1742-6596/161/1/012030 fatcat:mhfxttzzyfaafizm6ojgolfiiy