Spectral broadening caused by dynamic speckle in self-mixing velocimetry sensors

Self-mixing laser sensors require few components and can be used to measure velocity. The self-mixing laser sensor consists of a laser emitting a beam focused onto a rough target that scatters the beam with some of the emission re-entering the laser cavity. This 'self-mixing' causes measurable interferometric modulation of the laser output power that leads to a periodic Doppler signal spectrum with a peak at a frequency proportional to the velocity of the target. Scattering of the laser emission from a rough surface also leads to a speckle effect that modulates the Doppler signal causing broadening of the signal spectrum adding uncertainty to the velocity measurement. This article analyzes the speckle effect to provide an analytic equation to predict the spectral broadening of an acquired self-mixing signal and compares the predicted broadening to experimental results. To the best of our knowledge, the model proposed in this article is the first model that has successfully predicted speckle broadening in a self-mixing velocimetry sensor in a quantitative manner. It was found that the beam spot size on the target and the target speed affect the resulting spectral broadening caused by speckle. It was also found that the broadening is only weakly dependent on target angle. The experimental broadening was consistently greater than the theoretical speckle broadening due to other effects that also contribute to the total broadening.