为了减小由投影仪-摄像机γ非线性引起的红蓝棋盘格标定板相位误差, 分析了非线性相位误差的产生原因和表现特征, 建立了非线性相位误差和相位主值之间的数学模型, 由该模型得到相位误差补偿矩阵并修正展开相位;同时采用MATLAB仿真并结合相关试验对该算法进行了验证。结果表明, 误差补偿后棋盘格平面展开相位的均方根误差从0.0836rad下降到0.0218rad; 由γ非线性引起的棋盘格角点在标靶图像中像素坐标的最大误差值约从补偿前的0.3pixel降低到0.1pixel。该方法有效减小了由投影仪-摄像机γ非线性引起相位误差, 提高了标靶图像的角点坐标精度。

In order to overcome the phase error caused by γ nonlinearity of projector-camera pair about red/blue checkerboard in the projector calibration processing, the reason and the characteristics of nonlinear phase error were studied and the mathematical model between the nonlinear phase error and the wrapped phase was established. Based on the mathematical model, the phase error compensation matrix was obtained to correct the unwrapped phase. The experimental results show that the root mean square of the unwrapped phase after compensation is decreased from 0.0836rad to 0.0218rad. The maximum pixel error of grid corner caused by γ nonlinearity of the projector-camera pair at digital micro-mirror device (DMD) image is approximately reduced from 0.3pixel to 0.1pixel after phase compensation. The proposed method is useful to decrease the periodic phase error caused by γ nonlinear of the projector-camera paird and obtain higher accuracy coordinates of the red/blue checkerboard grid corner at DMD images.