3DOF displacement sensor based on the self-imaging effect of optical micro-gratings

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 ∼8