A Numerical Investigation into the Influence of Langevin Noise on Vibration Measurement Using Self-Mixing Laser Diode

Abstract

We report on the influence of intrinsic noise on the self-mixing signal associated with a vibrating target. The signal intensity of a semiconductor laser is investigated using a numerical simulation based on the rate equations incorporating Langevin noise forces. The photon density (signal intensity) as a function of the target displacement was calculated for the spontaneous emission factor beta=10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> ~10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> . The reconstructed displacement waveform was obtained from the sawtooth signal caused by the self-mixing effect between the backscattered light from the target and the light in the laser diode. The influence of the noise on the displacement waveform of the vibrating target as a function of the feedback amplitude reflectivity r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ext </sub> and the spontaneous emission factor beta was shown. While the Langevin noise is greatly affect by beta and the photon density was found to be more stable when beta is less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , we found that the amplitudes of the reconstructed waveform with different p values are close to the true value of the target displacement amplitude (7.8mum peak to peak) when r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ext</sub> =0.5%~1.2%. The variation coefficient in the case of r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ext</sub> =0.5%~1.2% remained below 7%. These results are potentially useful for precise displacement measurement