Heterodyne interferometers have been widely used for primary vibration calibration in recent years. Primary vibration calibration performance depends on the precision and real-time nature of vibration measurements, factors determined by the acquisition and demodulation of the heterodyne interferometer signal. This signal is commonly collected using the Nyquist sampling method, requiring devices with high sampling rates and large memories, or a sampling method using a mixer and low-pass filter-analog devices which may create time delays. This study proposes a novel bandpass sampling method that reduces sampling rate and storage capacity without generating time delays. To improve vibration measurement precision, an optimal sampling rate is designed to collect the heterodyne interferometer signal, and the collected signal is demodulated using the phase-unwrapping sine approximation method. The proposed method is compared with existing methods through simulated and experimental data. Experimental results show that the proposed method avoids time delays and high sampling rates, while providing high-precision vibration measurements.