Phase Unwrapping of Self-mixing Signals Observed in Optical Feedback Interferometry for Displacement Measurement

With an Optical feedback interferometry (OFI), a self-mixing signal (SMS) can be observed and employed to determine parameters of the semiconductor laser and metrological quantities of an object. In the cases of the measurement of the movement trace of an external target, phase unwrapping of the SMS must be performed, which remains a challenging issue. We report a technique for achieving phase unwrapping of the SMS signals as follows. Firstly, the behaviour of the phase equation of the OFI is studied, based on which general laws for laser phase change with respect to external target movement is extracted. Secondly, the correlation between the laser phase change and SMS signal is studied. Finally phase unwrapping algorithm is developed based on the relationship. In order to make sure that the proposed approach works well in the cases of noisy SMS data, pre-processing algorithms are also discussed. The proposed techniques have been tested by both computer simulation and experimental data which show that excellent agreement can be achieved and the movement trace of the external target can be retrieved.