A Demodulation Model of Dynamic Low-Finesse Fabry-Perot Cavity Based on the Instantaneous Frequency

If the measurand changes during the spectrum acquisition process, it easily leads to the failure of the classic demodulation algorithms of low-finesse optical fiber Fabry-Perot (FP) sensors. To address this problem, a novel demodulation model is proposed based on the definition of the instantaneous frequency. The proposed model establishes the relationship between the optical path length (OPL) of the FP cavity and the instantaneous frequency distribution of the FP interference spectrum. The link between the classic FFT algorithm and this model is discussed, and it is found that this model can be viewed as a generalized form of the FFT algorithm. Based on this model, the Doppler-induced demodulation error is analyzed. The analysis uncovers that the average frequency of the FP interference spectrum should be used for the evaluation of the error, and the error is proportional to the variation of OPL during the spectrum acquisition period. Further, numerical simulation and an experiment were carried out to verify the proposed model, and results show that the proposed model is effective for the dynamic low-finesse FP cavity. It is the first time that the idea of instantaneous frequency is introduced for the FP demodulation, and this model provides us a new way to cope with the FP sensing signal.