A Novel Self-Calibration Method for Ultrahigh-Precision Angular Displacement Measurement

This article proposes a new self-calibration method for ultrahigh-precision angular displacement measurement, called the association constrained relative rotation self-calibration method. The combined sensor applied in this method consists of two independent sensors, one serves as a reference benchmark and the other performs association constrained relative rotation. The method is achieved by controlling two sensors with a double-bearing turntable for multiple interlocking rotations and relative rotations. Two sensors are concentric and coaxial, and the axis center will not be inconsistent due to the shaft rotation in the operation condition. The reading heads have a round, uniformly distributed design on the rotor substrate, satisfy the circular closure principle, and without accumulated error. All reading heads can be processed and formed at one time on the substrate face by manufacturing methods. Thus, the consistency and the position accuracy of the reading heads can be guaranteed by manufacturing processes. The average effect of the whole circumference closed ring sampling scheme can improve the sensor performance and can reduce the influence of axial and radial runout errors of the rotation shaft system on the measurement results. The measurement accuracy after self-calibration is about $\pm 0.03''$ , which is much better than the sensor measurement accuracy before self-calibration. From the comparative experiments with the polygon mirror and an autocollimator, it can be seen that the association constrained relative rotation self-calibration method is effective, and the combined sensor will also be used in the development of angle benchmarks in the future.