Combined Displacement and Angle Sensor with Ultra-High Compactness Based on Self-Imaging Effect of Optical Microgratings

In this paper, an ultracompact combined sensor for displacement and angle-synchronous measurement is proposed based on the self-imaging effect of optical microgratings. Using a two-grating structure, linear and angular displacement can be measured by detecting the change of phase and amplitude of the optical transmission, respectively, within one single structure in the meantime. The optically transmitted properties of the two-grating structure are investigated in both theory and simulation. Simulated results indicate that optical transmission changes in a sinusoidal relationship to the input linear displacement. Meanwhile, the amplitude of the curve decreases with an input pitch angle, indicating the ability for synchronous measurement within one single compact structure. The synchronous measurement of the linear displacement and the angle is also demonstrated experimentally. The results show a resolution down to 4 nm for linear displacement measurement and a maximum sensitivity of 0.26 mV/arcsec within a range of ±1° for angle measurement. Benefiting from a simple common-path structure without using optical components, including reflectors and polarizers, the sensor shows ultra-high compactness for multiple-degrees-of-freedom measuring, indicating the great potential for this sensor in fields such as integrated mechanical positioning and semiconductor fabrication.