The estimation of self-mixing interferometry (SMI) parameters such as optical feedback factor C and linewidth enhancement factor α is essential to self-mixing (SM) displacement sensors with sub-wavelength resolution. We propose a new method, which is a very simple and fast method to estimate C and α when C > 1 based on an analysis of self-mixing signals (SMSs) in a laser diode. The proposed method is extremely simple, because it takes advantage of analytic relations which enable one to obtain C and α from the simple algebraic operations of the data from SMSs. The simplicity of the method is a great help to developing a compact and low-cost self-mixing (SM) displacement sensor with sub-wavelength resolution which cannot ensure complex operation such as optimization. And the proposed method is highly effective in developing real-time and fast algorithm for the C estimation. This method is applicable when the sensor operates under a moderate or strong feedback regime. The estimation accuracy of C and α are comparable to the results of Yu et al 2004 IEEE Photon. Technol. Lett. 16 990-2; Zabit 2010 PhD Thesis Toulouse; and Fan 2011 MS Thesis University of Wollongong, respectively, and the estimation time of the C parameter is over 30 times faster than Zabit and Fan.

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