Development of a coplanar grating interferometer for displacement and angle measurements

In this study, we propose a grating-based interferometer designed with a coplanar type and double-diffraction configurations to enhance the sensitivity while still simultaneously maintaining nanometric resolution of displacement and angle. According to our proposed method, two heterodyne beams with orthogonally polarized directions are propagated to a transmission grating with a symmetrical angle, and then diffracted. Since the two beams incident to different positions of the grating surface, two detection points are formed for establishing "coplanar type" optical configuration (detection configurations A and B). Each detection configuration has the same optical arrangement. Moreover, through the optical configuration design of "double-diffraction", fours corresponding diffraction beams will pass through the transmission grating again along the original paths, which could induce double phase variations in each beam. This means the sensitivity and resolution of the proposed interferometer will be enhanced double. When the grating moves along the in-plane direction, changes in the two interference phases in detection configurations A and B are the same, and can be observed from the two detectors. Moreover, the rotation angle of θz can be obtained by comparing the measurement results of in-plane displacement measured by detection configurations A and B. To verify the feasibility and performance of the proposed interferometer, a series of experiments were conducted, with the measurement results obtained from the proposed interferometer compared with the built-in capacitive sensor and linear encoder of two different commercial positioning stages. As can be seen from the results, the displacement and angle resolution of the system was found to be 1.5 nm and 50 nrad while the values of repeatability was found to be 2 nm and 80 nrad together with a long-term stability of about 8 nm and 200 nrad for 10 minutes. Experimental results also demonstrate that the proposed interferometer has the ability to perform precision displacement and angle information simultaneously without changing its optical configuration.