  Optical cavities provide high sensitivity to dispersion since their resonance
frequencies depend on the index of refraction. We present a direct, broadband,
and accurate measurement of the modes of a high finesse cavity using an optical
frequency comb and a mechanical Fourier transform spectrometer with a kHz-level
resolution. We characterize 16000 cavity modes spanning 16 THz of bandwidth in
terms of center frequency, linewidth, and amplitude. We retrieve the group
delay dispersion of the cavity mirror coatings and pure N${_2}$ with 0.1
fs${^2}$ precision and 1 fs${^2}$ accuracy, as well as the refractivity of the
3{\nu}1+{\nu}3 absorption band of CO${_2}$ with 5 x 10${^{-12}}$ precision.
This opens up for broadband refractive index metrology and calibration-free
spectroscopy of entire molecular bands.
