为了修正精密转台中由圆光栅安装偏心、倾斜等引起的角分度误差，提出一种基于稀疏分解的角分度误差补偿方法。首先，分析了圆光栅安装偏心、倾斜等对精密转台角分度误差的影响。然后，根据圆光栅测角误差中不同阶次误差项的特性，结合稀疏分解思想与谐波分析建立了角分度误差补偿模型，对转台的角分度误差进行补偿。最后，搭建试验平台，采用提出的角分度误差补偿模型对精密转台角分度误差进行修正，验证该方法的有效性。试验结果表明: 该方法能够将角分度精度提高2个数量级，对角分度误差最大值为90.85"的转台进行误差补偿后，能够使角定位误差的最大值减小到0.64"。采用该方法进行误差补偿后，能够显著提高角度定位精度，结果满足精密转台角位移的高精度测试要求。

A compensation method for angular indexing error was introduced based on sparse decomposition to correct the angular indexing error caused by the eccentric and tilt of circular gratings installment in a precision turntable. First, the effect of circular grating installed eccentric and tilt on the angular indexing error was analyzed. Next, according to the characteristics of different orders of error in measuring error of circular grating angle, a compensation model of angular indexing error was built based on the sparse decomposition theory and the harmonic analysis to compensate the angular indexing error of the turntable. Finally, a test platform was established, and the effectiveness of the proposed method was verified to compensate the angular indexing error of a precision turntable. The experimental results show that the proposed method can increase 2 orders of magnitude of the angular indexing accuracy. The maximum value of angular indexing error can be reduced to 0.64" from 90.85" through proposed error compensation method. After error compensation with the method, the accuracy of angle positioning can be remarkably improved, meeting the high-accuracy testing requirements of angular displacement of a precision turntable.