In view of the problem of “jumping points” in the phase unwrapping of the multifrequency heterodyne principle, this paper proposes a novel method to improve the multifrequency heterodyne. By solving the root-mean-square error of the original frequency function, it includes the relationship between the error and the adjacent phase in the condition of constrained phase unwrapping, and it compensates phase of the skip point. To ensure the accuracy of phase unwrapping, the function with a “jump point” after each phase unwrapping and the absolute phase curve of the principal value function are used to establish the threshold judgment model of the least square method, and the initial phase unwrapping of the principal value function with different frequencies is carried out continuously. The simulation analysis of phase compensation with the four-step phase-shifting method shows that the error is reduced to 36% under the set environment. The experimental result of 3D reconstruction by measuring the flatness of the plate shows that the error decreases by 41% after phase compensation compared with before phase compensation. The three-dimensional reconstruction experiment of pitch measurement with a nut shows that the nut after phase compensation is smooth without noise, and the pitch error is 0.033 mm, which verified the method is workable and effective.

中文翻译：

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用于3D重建的多频外差相位误差补偿方法

针对多频外差原理在相位解缠中存在“跳点”的问题，提出了一种改进多频外差的新方法。通过求解原始频率函数的均方根误差，它包含了在约束相位解缠条件下误差与相邻相位之间的关系，并对相位进行了补偿。跳过点。为了确保相位解开的准确性，使用每个相位解开后带有“跳变点”的函数和主值函数的绝对相位曲线来建立最小二乘法的阈值判断模型，以及连续执行不同频率的主值函数。四步相移法对相位补偿的仿真分析表明，在设定的环境下，误差减小到36％。通过测量平板的平面度进行3D重建的实验结果表明，与相位补偿之前相比，相位补偿之后的误差降低了41％。