Angle measurement error and compensation for pitched rotation of circular grating

As circular grating is not vertical to the shaft,the angle measurement error of the circular grating is　analyzed.Based on the moire fringe equations in pitched condition,the mathematic model of the angle measurement error is derived.The paper comes to the conclusion that the nonorthogonal angle between the circular grating and the shaft leads to the second harmonic error of the angle measurement,and the correctness of the result 　is proved by the experimental data.The method of the error compensation is presented,and the angle measurement accuracy of the circular grating is improved by the error compensation.