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Continuous Vernier filtering of an optical frequency comb for broadband cavity-enhanced molecular spectroscopy

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$ν$+$δ$ 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.