1D Phase Unwrapping Based on the Quasi-Gramian Matrix and Deep Learning for Interferometric Optical Fiber Sensing Applications

Phase unwrapping is one of the key problems in interferometric fiber sensors, which usually acts as the system performance bottleneck. Compared with the two-dimensional phase unwrapping, the one-dimensional phase unwrapping suffers more seriously from noise. Because modern phase unwrapping algorithms need to make the best use of all the adjacent phase points when evaluating the true phase at a given point. But the available adjacent points in one-dimensional phase unwrapping are very limited. A two-step one-dimensional phase unwrapping algorithm is proposed in this work to combat the above problems. In the first step, the one-dimensional phase is encoded into two-dimensional array based on the quasi-Gramian matrix, and in the second step the deep convolutional neural network (DCNN) is adopted for phase unwrapping. Both simulation and actual experiment results show that the unwrapped phase quality by using our method obviously outperforms the traditional methods with the signal-to-noise ratio (SNR) of lower than 4 dB, and it can still work stably even for negative SNR.