基于光束法平差的相位测量偏折术镜面面形测量

Specular Shape Measurement with Phase Measuring Deflectometry Based on Bundle Adjustment

为了简化相位测量偏折术的系统标定,并减少系统标定和图像噪声对测量精度的影响,提出在相位测量偏折术中引入自由参考系,并在自由参考系内对测量结果进行光束法平差。由于基于梯度恢复面形的相位测量偏折术缺少绝对高度信息,因而不能直接进行光束法平差,自由参考系使入射光线和反射光线处于同一个坐标系内,通过光线三角交会计算自由参考系下的待测点三维坐标。根据待测点与其对应入射光线共线的几何约束,采用约束光束法平差对摄像机内外参数和面形三维坐标同时进行优化,使重投影误差最小。数值模拟和实验结果表明,光束法平差可以提高相位测量偏折术的测量精度。

In order to simplify the system calibration and reduce the influence of the error of system calibration and image noise on measurement accuracy by phase measuring deflectometry （PMD）, free frame of axes is introduced in PMD, and bundle adjustment in free frame of axes is performed to improve the measurement accuracy. Commonly, the specular shape is measured by PMD with gradient information. However, bundle adjustment can not be directly performed since there is no absolute height information. The introduction of free frame unifies the incident and reflected ray in the same frame, and the absolute coordinate of tested points can be obtained by intersection of incidence and reflected ray. According to the geometrical constraint that, the 3D points must be located on the corresponding incident ray, constraint bundle adjustment is performed to refine the intrinsic, extrinsic parameters and 3D coordinates of shape simultaneously to minimize the reprojection error. Numerical simulation and experimental results demonstrate that bundle adjustment can indeed improve the measurement accuracy in PMD.