We report the theoretical analysis of a quasi-distributed sensor system for absorption measurements based on the frequency- modulated continuous wave (FMCW) technique combined with frequency modulation spectroscopy (FMS). The laser diode injection current is sawtooth modulated to provide a linear scan of the output over a certain frequency/wavelength range and the output is also externally modulated at radio frequencies. The sensor units consist of a series of open-path micro-optic cells constructed from graded index (GRIN) lenses, each with a unique beat frequency. By arranging for only one sideband of the modulation to be attenuated by the absorption feature, a new signal, proportional to the absorbance, appears in the output spectrum at a frequency corresponding to the difference between the rf- modulation frequency and the beat frequency of a cell. The method is highly sensitive and applicable to a variety of chemical species with narrow absorption lines, such as in trace gas analysis. We present the mathematical analysis of the proposed method for single and multiple cell systems, using methane detection as an example.