Nanometer-scale displacement measurement using a simple diffraction grating with a quadrature detection technique

A phase-sensitive transparent grating interferometer is proposed to measure small displacements. A transparent grating is inserted between a light source and a reflective mirror. The diffracted light beams of the forward and backward propagation are superposed to form the interference pattern. When two detectors are placed at two different positions of the interference fringe in such a way that the signals have quadrature phase difference, the phase variation can infer the displacement of the reflected mirror. This simple setup can measure the displacement of the mirror at nanometer scale with 98.2% accuracy, high precision with 10 nm in standard deviation, and lowest bound of 0.4 nm resolution.