Fast estimation method of feedback factor based on the derivative of the self-mixing signal

The self-mixing (SM) technique has been a promising optical measurement technique for a few decades. The estimation of the optical feedback factor C is the key to SM displacement measurement with a better resolution than half a wavelength. But this estimation is extremely complex and tricky, and thus leads to its time-consuming nature, which is one of the important causes that increases the cost and labor for the development of a self-mixing sensor. There have been many methods reported for the C estimation, but they are very time consuming, very sensitive to noise, or can only work in a certain feedback regime. This paper presents a novel approach to the C estimation, which is straightforward and can work for all feedback regimes including weak, moderate, and strong. The estimation precision of the proposed method is not only comparable to that of the data fitting technique but also much simpler.