A heterodyne grating-based interferometer for three-degree-of-freedom (3-DOF) displacement measurement is proposed. This technique has the merits of both heterodyne interferometry and grating interferometry. A heterodyne light beam is obtained using an electro-optic modulating technique for amplitude modulation. While the heterodyne light beam is normally incident into a transmission-type 2D grating, two detection parts for in-plane and out-of-plane displacement measurements will be obtained. The heterodyne light beam is utilized to carry the optical phase variation that results from grating displacement in three directions. The experimental results demonstrate that the proposed interferometer is capable of sensing the displacement of a motion stage in 3-DOF. The resolution and range of the measurement can achieve up to nanometric and millimetric levels.
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