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 ∼8nm. 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.