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Fourier transform spectroscopy (FTS) based on optical frequency combs is an excellent spectroscopic tool as it provides broadband molecular spectra with high spectral resolution and an absolutely calibrated frequency scale. Moreover, the equidistant comb mode structure enables efficient coupling of the comb to enhancement cavities, yielding high detection sensitivity. This thesis focuses on further advances in comb-based FTS to improve its performance and extend its capabilities for broadband precision spectroscopy, particularly in terms of i) spectral resolution, ii) accuracy and precision of molecular parameters as well as concentrations retrieved from fitting models to spectra, and iii) species selectivity.

To improve the spectral resolution we developed a new methodology to acquire and analyze comb-based FTS signals that yields spectra with a resolution limited by the comb linewidth rather than the optical path difference of the FTS, referred to as the sub-nominal resolution method. This method enables measurements of narrow features, e.g. low-pressure absorption spectra and modes of enhancement cavities, with frequency scale accuracy and precision provided by the comb. Using the technique we measured low-pressure spectra of the entire 3ν₁+ν₃ carbon dioxide (CO₂) band at 1575 nm with sufficient signal-to-noise ratio and precision to observe collision narrowing of the absorption lineshape, which was for the first time with a comb-based spectroscopic technique. This allowed retrieval of spectral line parameters for this CO₂ band using the speed-dependent Voigt profile.

Using the sub-nominal resolution method, we measured the transmission modes of a Fabry-Perot cavity over 15 THz of bandwidth with kHz resolution and characterized the cavity modes in terms of their center frequency, linewidth, and amplitude. From the mode center frequencies, we retrieved the group delay dispersion of cavity mirror coatings and intracavity gas with an unprecedented combination of spectral bandwidth and resolution. By measuring both the mode broadening and frequency shift simultaneously we performed broadband cavity-enhanced complex refractive index spectroscopy (CE-CRIS), which allows for simultaneous and calibration-free assessment of the absorption and dispersion spectra of intracavity gas. In this first demonstration we measured the absorption and dispersion spectra of three combination bands of CO₂ in the 1525 to 1620 nm range.

Another comb-based FTS technique is noise-immune cavity-enhanced optical frequency comb spectroscopy (NICE-OFCS), which combines phase modulation and cavity-enhancement to obtain broadband and highly sensitive absorption spectra. In this thesis we improved the NICE-OFCS technique in terms of stability, sensitivity and modeling of the NICE-OFCS signal. We implemented a model of the NICE-OFCS signal with multiline fitting for assessment of gas concentration. We also identified the optimum operating conditions of the NICE-OFCS systems for accurate gas concentration assessment.

Finally, to improve the species selectivity we combined comb-based FTS with the Faraday rotation spectroscopy (FRS) technique. In this first demonstration of optical frequency comb Faraday rotation spectroscopy (OFC-FRS), we measured background and interference-free spectra of the entire Q- and R-branches of the fundamental vibrational band of nitric oxide at 5.3 μm showing good agreement with the theoretical model.