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.
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