  In this paper we deal with several issues regarding the localization
properties of the Unruh-DeWitt (UdW) detector model. Since its original
formulation as a pointlike detector, the UdW model has been used to study
extensively the physics of quantum fields in presence of accelerations or
curved backgrounds. Natural extensions of it have tried to take into account
the spatial profile of such detectors, but all of them have met a series of
problems in their spectral response which render them useless to study some of
the most interesting physical scenarios. In this paper we provide a derivation
of the smeared UdW interaction from QED first principles, then we analyze the
spectral response of spatially smeared UdW detectors, and discuss the kind of
spatial profiles which are useful for the study of relevant cases.
