Fourier transform spectroscopy based on incoherent light sources is a well-established tool in research fields from molecular spectroscopy and atmospheric monitoring to material science and biophysics. It provides broadband molecular spectra and info
rmation about the molecular structure and composition of absorptive media. However, the spectral resolution is fundamentally limited by the maximum delay range ({Delta}$_{max}$) of the interferometer, so acquisition of high-resolution spectra implies long measurement times and large instrument size. We overcome this limit by combining the Fourier transform spectrometer with an optical frequency comb and measuring the intensities of individual comb lines by precisely matching the {Delta}$_{max}$ to the comb line spacing. This allows measurements of absorption lines narrower than the nominal (optical path-limited) resolution without ringing effects from the instrumental lineshape and reduces the acquisition time and interferometer length by orders of magnitude.
Noise-immune cavity-enhanced optical frequency comb spectroscopy (NICE-OFCS) is a recently developed technique that utilizes phase modulation to obtain immunity to frequency-to-amplitude noise conversion by the cavity modes and yields high absorption
sensitivity over a broad spectral range. We describe the principles of the technique and discuss possible comb-cavity matching solutions. We present a theoretical description of NICE-OFCS signals detected with a Fourier transform spectrometer (FTS), and validate the model by comparing it to experimental CO2 spectra around 1575 nm. Our system is based on an Er:fiber femtosecond laser locked to a cavity and phase-modulated at a frequency equal to a multiple of the cavity free spectral range (FSR). The NICE-OFCS signal is detected by a fast-scanning FTS equipped with a high-bandwidth commercial detector. We demonstrate a simple method of passive locking of the modulation frequency to the cavity FSR that significantly improves the long term stability of the system, allowing averaging times on the order of minutes. Using a cavity with a finesse of ~9000 we obtain absorption sensitivity of 6.4 x 10^{-11} cm^{-1} Hz^{-1/2} per spectral element, and concentration detection limit for CO2 of 450 ppb Hz^{-1/2}, determined by multiline fitting.
