  When internal states of atoms are manipulated using coherent optical or
radio-frequency (RF) radiation, it is essential to know the polarization of the
radiation with respect to the quantization axis of the atom. We first present a
measurement of the two-dimensional spatial distribution of the electric-field
amplitude of a linearly-polarized pulsed RF electric field at $\sim 25.6\,$GHz
and its angle with respect to a static electric field. The measurements exploit
coherent population transfer between the $35$s and $35$p Rydberg states of
helium atoms in a pulsed supersonic beam. Based on this experimental result, we
develop a general framework in the form of a set of equations relating the five
independent polarization parameters of a coherently oscillating field in a
fixed laboratory frame to Rabi rates of transitions between a ground and three
excited states of an atom with arbitrary quantization axis. We then explain how
these equations can be used to fully characterize the polarization in a minimum
of five Rabi rate measurements by rotation of an external bias-field, or,
knowing the polarization of the driving field, to determine the orientation of
the static field using two measurements. The presented technique is not limited
to Rydberg atoms and RF fields but can also be applied to characterize optical
fields. The technique has potential for sensing the spatiotemporal properties
of electromagnetic fields, e.g., in metrology devices or in hybrid experiments
involving atoms close to surfaces.
