An undersampling phase unwrapping algorithm based on Kalman motion estimation for heterodyne interferometer

When heterodyne interferometers employ the traditional successive phase unwrapping algorithm (SPUA) for implementing online low-frequency vibration measurements, challenges posed by extensive data volume and time-consuming data processing typically arise. To address these challenges, this paper introduces an undersampling phase unwrapping algorithm (UPUA) based on Kalman motion estimation for heterodyne interferometers. Specifically, the UPUA utilizes the six preceding phases to estimate the phase jerk at the next sampling moment. Furthermore, the sampling frequency for the next sampling moment, denoted as fs, is determined utilizing the peak jerk of the phase. Subsequently, the three preceding phases and fs are employed to derive the estimated phase at the next sampling moment. Following this, the SPUA is further utilized to determine the measurement phase at the next sampling moment after setting the sampling frequency to fs. Ultimately, the actual phase is determined by combining the measured phase with the estimated phase, thus achieving online undersampling phase unwrapping. Simulation and experimental results demonstrate that UPUA adaptively adjusts the sampling frequency and significantly reduces the data volume compared with SPUA in the case of low-frequency vibration measurements.