Laser self-mixing interferometer with scalable fringe precision based on phase multiplication algorithm

In this paper, we present a phase multiplication algorithm (PMA) to obtain scalable fringe precision in laser self-mixing interferometer under a weak feedback regime. Merely by applying the double angle formula on the self-mixing signal multiple times, the continuously improved fringe precision will be obtained. Theoretical analysis shows that the precision of the fringe could be improved to λ /2 n +1 The validity of the proposed method is demonstrated by means of simulated SMI signals and confirmed by experiments under different amplitudes. A fringe precision of λ /128 at a sampling rate of 500 kS/s has been achieved after doing 6th the PMA. Finally, an amplitude of 50 nm has been proved to be measurable and the absolute error is 3.07 nm, which is within the theoretical error range. The proposed method for vibration measurement has the advantage of high accuracy and reliable without adding any additional optical elements in the optical path, thus it will play an important role in nanoscale measurement field.