Quadrature phase detection based on a laser self-mixing interferometer with a wedge for displacement measurement

•Phase shift is generated by the optical path difference of the beam propagating in the wedge.•Quadrature phase shift is detected by shifting the position of the iris diaphragm.•The quadrature phase detection based on the laser self-mixing interferometer with a wedge is unaffected by the inherent phase shift error produced by other optical components in the optical path.•Simplified displacement demodulation process and might be applied in online displacement measurement.•The max error is 182 nm with a relative error of about 0.91 % for a target displacement of 20 μm. We report a novel and simple method to generate a pair of self-mixing signals with quadrature phase difference in He-Ne laser by introducing a wedge into the external cavity. A wedge phase-shift laser self-mixing effect theory is developed to explain the phase-shift phenomenon, and the relationship between the phase difference and the distance from the center of the iris diaphragm to the center of the spot is given. Then a simple and effective wedge-quadrature laser self-mixing interferometer is established for displacement measurement by the quadrature phase detection method. Experimental results show that the max error is 182 nm for a target displacement of 20 μm. This structure provides a useful exploration for phase-shift signal generation and simplifies the self-mixing signal demodulation process with only a single four-quadrant inverse tangent operation, which has potential application in real-time displacement measurement.