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A new method based on fractal theory is proposed to analyze velocity sensing. The waveform of a self-mixing speckle signal is processed as a pattern of a fractal. Fractal boxes are defined as a set of grids used to divide the fractal pattern, and box-counting (BC) is introduced to characterize the statistical property of a speckle signal. A group of simulated speckle signals are analyzed by calculating the BCs corresponding to different velocities of the object. A linear dependence between the BCs of speckle signals and velocities is obtained, the result of which is validated by the analysis of a group of signals obtained from experiments. The performance of the fractal analysis is compared with those of the previous analysis methods. Better linearity and higher measurement sensitivity of the fractal analysis are indicated. The experimental result shows that the fractal method can be used as a valid analysis tool for the self-mixing speckle signal in velocity sensing.

The experiment observation of self-mixing interference in distributed feedback (DFB) laser has been illuminated in this paper. The influences on self-mixing interference have been discussed in both simulation and experiment through changing the conditions of external cavity. The experiment results show a good agreement with the simulation results, and validate the feasibility of DFB lasers for self-mixing interference application. Combining the self-mixing interference technique and DFB laser, we can obtain the compact structure and high-accuracy self-mixing interference sensors.

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