Autocorrelation of self-mixing speckle in an EDFR laser and velocity measurement

Autocorrelation analysis for a velocity measurement based self-mixing speckle in an erbium-doped fiber ring (EDFR) laser is presented. The expression for the velocity measurement is deduced. Theoretical analysis reveals that the velocity of a random surface is inversely proportional to the autocorrelation time of the self-mixing signal produced in the EDFR laser. In experiments, a linear fit between the velocity and the reciprocal of autocorrelation time (autocorrelation frequency) is obtained for velocity measurement. In a range of velocities from 100 mm/s to 350 mm/s, the measurement errors are evaluated to be less than 5%. The signal length, the measurement distance, and the pump power are experimentally studied for gaining knowledge of the influence on the velocity measurement.