A novel approach for measuring fast oscillations of an absolute value of interferometer optical path difference (OPD) has been developed. The principles of frequency-scanning interferometry are utilized for registration of the interferometer spectral function, from which the OPD is calculated. The proposed approach enables one to capture the absolute baseline variations at frequencies much higher than the spectral acquisition rate. Despite the conventional approaches, associating a single baseline indication to the registered spectrum, in the proposed method a specially developed demodulation procedure is applied to the spectrum. This provides an ability to capture the baseline variations which took place during the spectrum acquisition. An analytical model describing the limitations on the parameters of the possibly registered baseline variations are formulated. The experimental verification of the proposed approach and the developed model has been performed.