  We demonstrate that it is possible, with sub-micron precision, to locate the
absolute center of a Fabry-P\'erot resonator oriented along the rf-field-free
axis of a linear Paul trap through the application of two simultaneously
resonating optical fields. In particular, we apply a probe field, which is
near-resonant with an electronic transition of trapped ions, simultaneously
with an off-resonant strong field acting as a periodic AC Stark-shifting
potential. Through the resulting spatially modulated fluorescence signal we can
find the cavity center of an 11.7 mm-long symmetric Fabry- P\'erot cavity with
a precision of $\pm$135 nm, which is smaller than the periodicity of the
individual standing wave fields. This can e.g. be used to position the minimum
of the axial trap potential with respect to the center of the cavity at any
location along the cavity mode.
