  The ability to characterize static and time-dependent electric fields in situ
is an important prerequisite for quantum-optics experiments with atoms close to
surfaces. Especially in experiments which aim at coupling Rydberg atoms to the
near field of superconducting circuits, the identification and subsequent
elimination of sources of stray fields is crucial. We present a technique that
allows the determination of stray-electric-field distributions
$(F^\text{str}_\text{x}(\vec{r}),F^\text{str}_\text{y}(\vec{r}),F^\text{str}_\text{z}(\vec{r}))$
at distances of less than $2~\text{mm}$ from (cryogenic) surfaces using
coherent Rydberg-Stark spectroscopy in a pulsed supersonic beam of metastable
$1\text{s}^12\text{s}^1~{}^{1}S_{0}$ helium atoms. We demonstrate the
capabilities of this technique by characterizing the electric stray field
emanating from a structured superconducting surface. Exploiting coherent
population transfer with microwave radiation from a coplanar waveguide, the
same technique allows the characterization of the microwave-field distribution
above the surface.
