With the rapid development of numerical control technology in the industrial field, the accuracy of angular displacement measurement technology has become more demanding.

In the traditional displacement measurement technology, in order to achieve higher measurement accuracy, it needs to go through "cumbersome debugging" or "later correction". The dependence on "signal ideal degree" limits the development of traditional angular displacement measurement technology to higher measurement accuracy.

 In a study published in Applied Optics, Prof. YU Hai from Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP) of the Chinese Academy of Sciences (CAS) proposed an image-type angular displacement measurement technology based on linear-scan image recognition method. It does not depend on "signal ideal degree", making it easier to realize high-precision angular displacement measurements.

After analysis, researchers proposed that when there are p image sensors distributed in the circumference of the circular grating, the harmonic error of integer multiple order of p cannot be eliminated. Generally speaking, the circular grating used for angular displacement measurement contains 2^N coding lines, and most of the harmonic errors contained in the measurement error are "even harmonics". Therefore, the odd number of image sensors can achieve higher measurement accuracy than the even number of image sensors.

In this study, three linear-scan image sensors were uniformly distributed in the circumference of the circular grating. The measurement accuracy (standard deviation) of 1.76" was achieved on the circular grating with a diameter of 96 mm.

The error self correction algorithm of three image sensors provides a theoretical and technical basis for improving the accuracy of angular displacement measurement.