A Dual-Interferometer-Based Angular Measurement System With Absolute Angle Recovery Method

A dual-interferometer-based angular measurement system is proposed and studied, obtaining analytical expressions for the measured distance of each interferometric axis. The nonzero convexity of the characteristic curve during a rotation is proven to be an intrinsic characteristic of the setup. An absolute angle recovery method is proposed relying on the use of this characteristic curve as an absolute reference to overcome the limitation of the relative operation of conventional interferometric systems. The recovery method is evaluated by Monte Carlo simulations, studying the effect of the noise and the number of points on the performance of the recovery. Finally, the technique is successfully applied to a high-precision rotational stage, where an independent dual-interferometer system is used to experimentally evaluate the performance of the method. The results show an accuracy of $\pm 1.29 \mu$rad ($3 \sigma$) in the recovery of the angle, which is in agreement with the Monte Carlo simulations.