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The optical output power of a laser diode is modulated by the self-mixing effect when the optical beam is back-reflected or back-scattered into the laser cavity by a target. The optical feedback factor <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> is the most important one that defines the feature of the self-mixing signals (SMSs). And the estimation of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> is indispensable for the displacement reconstruction by the phase unwrapping method because it is impossible to reconstruct the displacement with sub-wavelength resolution, provided the exact value of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> is unknown. Unfortunately, <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> is subject to constant change during the measurement and, what is worse; its estimation is usually very time-consuming. This paper studies the feature of a high and low fringe of SMSs in moderate and strong feedback regime and the effect of the feedback factor and the linewidth enhancement factor on the fringes and presents a simple approach to the estimation of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> when <inline-formula> <tex-math notation="LaTeX">$C>1.5$ </tex-math></inline-formula> based on the behavioral model proposed by Plantier <italic>et al.</italic> In particular, the novel approach enables fast direct estimation of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> because it is based on analytic relations between <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> and the amplitudes of the high and low peak in SMSs.

Effect of Linewidth Enhancement Factor on Fringe in a Self-Mixing Signal and Improved Estimation of Feedback Factor in Laser Diode