The proposed algorithm and interferometric system can effectively detect the microvibration of the gas-solid interface excited via acoustic radiation. The improved PGC-DCM algorithm can accurately calculate the phase-modulation depth and carrier phase delay. Additionally, the orthogonal interference signal components can be completely normalized, thereby considerably reducing the nonlinear errors caused by the fluctuation of the phase-modulation depth and change in the carrier phase delay. The improved PGC-DCM algorithm eliminates the influence of interference signal visibility on the demodulation results. Furthermore, it realizes the complete normalization of orthogonal interference signal components of the sinusoidal phase modulating interferometer and improves the stability of the PGC-demodulation algorithm. The proposed method can detect the microvibration information of the solid surface. In the frequency range of 3 kHz, the average signal-to-noise distortion ratio of phase demodulation is 33.0956 dB and the dynamic range is 22.75 dB.