  We characterize a high-finesse Fabry-Perot resonator for coupling with single
neutral atoms. Our cavity consists of two mirrors with different
reflectivities: One has minimal optical loss, and the other high transmission
loss where more than 90% of the intracavity photons would be emitted. Cavity
finesse, birefringent effects, and mechanical resonances are measured using the
lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters,
we drive the adjacent longitudinal or transverse modes with two lasers
simultaneously, and measure those frequencies using a precision wavelength
meter (WLM). A major novelty of this method is that the parameters' uncertainty
is solely determined by the resolution of the WLM, eliminating all of the
temporal environment fluctuations. Moreover, the technique with two lasers
consists of a vital approach for determining geometric parameters of a short
cavity, with a free spectral range on the order of THz. Our system operates in
the strong atom-cavity coupling regime that allows us to explore fundamental
quantum optics and implement quantum network protocols.
