A grating-based interferometer for 6-DOF displacement and angle measurement is proposed in this study. The proposed interferometer is composed of three identical detection parts sharing the same light source. Each detection part utilizes three techniques: heterodyne, grating shearing, and Michelson interferometries. Displacement information in the three perpendicular directions (X, Y, Z) can be sensed simultaneously by each detection part. Furthermore, angle information (θX, θY, θZ) can be obtained by comparing the displacement measurement results between two corresponding detection parts. The feasibility and performance of the proposed grating-based interferometer are evaluated in displacement and angle measurement experiments. In comparison with the internal capacitance sensor built into the commercial piezo-stage, the measurement resolutions of the displacement and angle of our proposed interferometer are about 2 nm and 0.05 μrad.

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.

In this research, a novel heterodyne laser encoder for 6-DOF displacement and angle measurements is proposed. The technique combines the advantages of heterodyne interferometry, grating shearing interferometry, and Michelson interferometry. When a heterodyne light beam with two orthogonally polarized directions is used to focus on a semitransmission grating, two detection configurations for in-plane and out-of-plane will be obtained. By means of measuring the phase variations of the interfering signals from the moving grating, the in-plane displacement can be acquired. Besides, the out-of-plane displacement can be obtained by detecting the optical path difference between the reference beam and the reflection beam. Furthermore, 6-DOF displacement and angle information can be measured simultaneously by using the beam dividing method. According to the experimental results, the measurement resolution is about 2 nm. The experimental results show that our proposed method has the ability to measure 6-DOF displacement and angle information with high system stability. Comparing with other commercial measurement instructions, this laser encoder has the advantages of high resolution, high stability, and high flexibility.

This paper presented a heterodyne speckle interferometer (HSI) for the measurement of two-dimensional in-plane displacement. A diffraction grating is used to split the light source into four beams, which are then reflected into a non-mirror measurement surface at symmetrical incident angles, before being scattered to form an interference pattern. In accordance with the Doppler Effect, in-plane displacement of the surface causes phase variations in speckle interference patterns, from which displacement information can be obtained. Several experiments were performed to evaluate the feasibility of the proposed HSI. Experiment results demonstrate that the proposed system is capable of accurately measuring in-plane displacement with a resolution of approximately 1.5 nm.

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