  Rydberg atom-based electrometry enables traceable electric field measurements
with high sensitivity over a large frequency range, from gigahertz to
terahertz. Such measurements are particularly useful for the calibration of
radio frequency and terahertz devices, as well as other applications like near
field imaging of electric fields. We utilize frequency modulated spectroscopy
with active control of residual amplitude modulation to improve the signal to
noise ratio of the optical readout of Rydberg atom-based radio frequency
electrometry. Matched filtering of the signal is also implemented. Although we
have reached similarly, high sensitivity with other read-out methods, frequency
modulated spectroscopy is advantageous because it is well-suited for building a
compact, portable sensor. In the current experiment, $\sim 3 \mu V
cm^{-1}Hz^{-1/2}$ sensitivity is achieved and is found to be photon shot noise
limited.
