Abstract

In recent years, there has been an increasing demand for a multiple degrees of freedom (DOF) measurement system with high performance and high integration. Here, we report a 3DOF displacement sensor based on the self-imaging effect of optical micro-gratings. The optical field distribution behind a micro-grating with a period of 3 µm is analyzed theoretically. The transmission properties of a double-grating structure are investigated in theory. In the experiment, 3DOF displacement measurement within a range of 1 mm is demonstrated. Using an interpolation circuit with a subdividing factor of 1000, displacement measurement with a theoretical resolution of 3 nm is realized. The experimental resolution is ${\sim}{8}\;{\rm nm}$. An error within 2 µm is obtained experimentally within a range of 1 mm for 3DOF measurement. With a few optical components such as a beam splitter prism and beam expanders, the sensor shows potential in developing ultra-compact multi-DOF displacement measuring systems. Together with a nanometric resolution, the 3DOF displacement sensor has shown great potential in applications such as high-precision mechanical engineering and semiconductor processing.

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