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As core elements of photoelectric displacement measurement, installation coaxiality and rotation parallelism are the main factors affecting measurement accuracy. When there is a processing error or an offset in the installation process of structural elements, the plane of the grating disk will be tilted, which seriously affects the accuracy of angular displacement measurements. In this study, error caused by inclination of the grating disk was analyzed and a method to eliminate this error presented. First, an error model was established by analyzing the mechanism of measurement error caused by grating disk tilting, analysis showed that the error caused by grating disk tilt showed a “double cycle” fluctuation in the circle. Then, by using “double cycle” fluctuation, a method for eliminating errors was presented. Finally, the validity of the proposed theory and method was verified by simulation and experimentation. To eliminate errors, angular displacement measurements needed to be made using at least three reading heads to produce a mean. In these experiments, when the grating disk was tilted, the error was perfectly eliminated using three reading head measurements. The experimental results verified the validity of the proposed theory, which provided a theoretical basis for improving the displacement measurement accuracy.

As the feedback link of a numerical control system, the measurement accuracy of absolute angular displacement measurements directly affects the control performance of a numerical control system. In previous research, angular displacement measurements based on dual image sensors can achieve higher measurement performance. However, the elimination of harmonic error by the dual image sensor is still limited. For this reason, this paper proposes an image-type angular displacement measurement method based on self-correction error compensation of three image sensors. First, the mathematical model of harmonic error is established, and the shortcomings of using dual image sensors to compensate the error are analyzed. Then, a high precision angular displacement measurement method based on three image sensors is proposed. Finally, the self-correction error compensation method of three image sensors is applied to the angular displacement measurement system, and the measurement performance is verified. The experimental results show that a measurement accuracy of 1.76^′′ can be achieved on the circular grating with a diameter of 96 mm. In contrast, the dual image sensor can only achieve a measurement accuracy of 2.88^′′. It is concluded that the odd number of image sensors can achieve higher measurement accuracy than the even number. This research lays a foundation for the realization of high precision image angular displacement measurement.