  We present a simple, continuous, cavity-enhanced optical absorption
measurement technique based on high-bandwidth Pound-Drever-Hall (PDH) sideband
locking. The technique provides a resonant amplitude quadrature readout that
can be mapped onto the cavity's internal loss rate, and is naturally compatible
with weak probe beams. With a proof-of-concept 5-cm-long Fabry-Perot cavity, we
measure an absorption sensitivity of $6.6 \times 10^{-11}
~\text{cm}^{-1}/\sqrt{\text{Hz}}$ at 100 kHz (roughly the cavity bandwidth) and
$\sim 10^{-10}~\text{cm}^{-1}/\sqrt{\text{Hz}}$ from 30 kHz to 1 MHz, with
$38~\mu$W collected from the cavity's circulating power.
