The circular grating angular displacement measurement technology, with advantages such as arc-second-level precision and full-cycle large measurement range, has become a core sensing technology in the field of industrial automation and is widely applied in high-end CNC machine tools, industrial robots, and other fields. This study analyzes the principles, error categories, compensation technologies, current limitations, and future prospects of this technology.

The measurement principle involves converting angular displacement into optical signals through the interference effect between absolute grating code disc and index grating, followed by photoelectric conversion and signal processing to achieve high-precision analysis. Measurement errors can be decomposed into long-period harmonic errors, random variation errors, and fixed offset errors. The first two are the main factors affecting precision, caused by issues such as code disc eccentricity and tilt, and environmental interference, respectively.

In terms of error compensation technologies, long-period error compensation is relatively mature. For eccentricity errors, methods such as the three-center model and eccentricity self-detection are available. For tilt errors, technologies such as the rotation angle prediction model and three-reading-head average compensation are adopted. Additionally, metal cylindrical circular gratings can promote device miniaturization, but some methods have problems such as time-consuming calibration and complex algorithms. Short-period error compensation focuses on nonuniform grating ruling and interpolation subdivision errors, such as angular velocity quantification ruling errors and parallel coordinate rotation calculation methods. Although these approaches can improve precision, they face limitations such as poor real-time performance and constrained dynamic response. Random variation error compensation addresses interferences like contamination, temperature, and vibration using methods such as pattern normalization and nonlinear fitting models. However, these compensation models have poor universality and are prone to signal loss.

Current technologies have multiple shortcomings. Long-period compensation ignores inherent defects of code discs. Short-period compensation struggles to quantify harmonic components in real time. Random error compensation fails to consider the coupling of environmental factors, and increasing code disc engraved line density brings new problems.

Future technological development can be promoted from four aspects: introducing intelligent control systems for long-period error compensation, adopting enhanced circuits and algorithms for short-period error compensation, integrating random variation compensation with environmental adaptation technologies, and leveraging the structural advantages of metal cylindrical circular gratings to enhance system performance. Through systematic compensation technologies, circular grating measurement systems can achieve higher-precision angular displacement measurement in various complex scenarios.