Improved Digital Arctangent Demodulation Method With Doppler Signal at Special Sampling Rate for Laser Heterodyne Interferometer

The importance of vibration monitoring in the Internet of Things (IoT) is reflected in many aspects, especially in the fields of industry, infrastructure, health monitoring, etc. Laser heterodyne interferometer has been widely used in the measurement of vibration displacement and velocity. The phase demodulation method of the Doppler signal is crucial to realizing the real-time and high-precision measurement with wide bandwidth. To reduce the requirements for the data acquisition system and the resource consumption, the improved digital arctangent (ATAN) demodulation method is proposed, which is more suitable to run on the digital signal processor. Utilizing the symmetry of the Doppler signal spectrum, the Doppler signal can be acquired by special Nyquist or bandpass sampling rates. Then, the pair of orthogonal signals are generated by specific delays of the digitized Doppler signals. With the sine approximation method (SAM), the vibration displacement or velocity can be obtained from the unwrapped phase after the ATAN calculation. Compared with the classical ATAN demodulation method and the commercial decoder of the laser Doppler vibrometer (LDV), experiments are designed to demonstrate the feasibility and performance of the proposed method with the vibration frequency from 500 Hz to 1 MHz and the peak amplitude of the vibration velocity from $31.63~\mu $ m/s to 3.16 m/s. Additionally, simulation experiments further explore its applicability in demodulating Doppler signals with asymmetric spectrum. The improved digital ATAN demodulation method offers significant potential for developing Doppler signal demodulation systems for laser heterodyne interferometers, particularly in real-time, efficient, and high-precision vibration monitoring applications.