  We have recently introduced the Vernier-based Direct Frequency Comb
Cavity-Enhanced Spectroscopy technique and we present the corresponding
formalism for quantitative broadband spectroscopy. We achieve high sensitivity
and broadband performance by acquiring spectra covering more than 2000
cm$^{-1}$ around 12600 cm$^{-1}$ (800 nm), resolving the 3$\nu$+$\delta$ band
of water vapor and the entire A-band of oxygen in ambient air. 31 300
independent spectral elements are acquired at the second time scale with an
absorption baseline noise of 2$\times$10$^{-8}$ cm$^{-1}$ providing a merit
figure of 1,1.10$^{-10}$ cm$^{-1}$/$\sqrt{Hz}$ with a cavity finesse of 3000
and a cavity round-trip length around 3,3 m. This state-of-the-art performance
is reached through a continuous Vernier filtering of a Titanium:Saphire
frequency comb with the cavity grid of resonances, obtained when the cavity
free spectral range and the laser repetition rate are slightly mismatched.
Here, we discuss the effect of the Vernier filtering on the measured absorbtion
lineshape and we derive the formalism needed to fit molecular spectra.
