改进的双频几何约束条纹投影三维测量方法

双频条纹投影已经广泛应用于三维形貌测量，然而其相位展开的准确性受噪声影响较大。文中提出了一种改进的双频几何约束条纹，通过提高低频相位的频率，有效地提升了相位展开的鲁棒性。在三维测量过程中，首先，利用五步相移算法计算出双频条纹的高频相位和低频相位。然后，利用几何约束方法展开低频相位。最后，采用双频算法展开高频相位，进而重建出物体的三维形貌。仿真和实验结果均表明，相对于传统双频条纹，改进的双频条纹具有更高的鲁棒性和适用性。

Modified dual-frequency geometric constraint fringe projection for 3D shape measurement

Dual-frequency fringe projection methods have been widely used in three-dimensional (3D) shape measurement, but the phase unwrapping is very sensitive to random noises. A modified dual-frequency geometric constraint fringe was presented. The robustness of phase unwrapping can be effectively enhanced by improving the frequency of low-frequency phase. During the 3D shape measurement, firstly, the five-step phase-shifting algorithm was used to extract two wrapped phases. Secondly, the low-frequency phase was unwrapped based on the geometric constraint method. Finally, the dual-frequency algorithm was used to unwrap the high-frequency phase, and then the 3D shape could be reconstructed. Both simulations and experiments demonstrate that the modified dual-frequency fringe is more robust and applicable than the traditional one.