Phase measurement profilometry plays an important role in industrial applications. Traditional fringe projection profilometry (FPP) requires a stable reference plane to record the reference phase for the 3D reconstruction, which makes it sensitive to the motion-induced error caused by the reference plane. Thus, it is challenging for the traditional FPP to implement a robust measurement in industrial scenarios though it exhibits high accuracy. To solve this problem, a phase reconstruction method is proposed where the reference phase is denoised and reconstructed from the background of the modulated phase by minimizing the total variation (TV) via the theory of Sylvester equation. Since this strategy achieves synchronous extraction of the reference phase and the object one, it can correct the reference phase in real-time and reduce the measurement error caused by deviation of the reference plane. The proposed method has been applied to measure the step-shape workpiece with different deviations of the reference plane and the gear workpieces on conveyer. The experimental results show competitive performance with traditional FPP in accuracy and more robustness in complex industrial scenes.

相位测量轮廓测量法在工业应用中发挥着重要作用。传统的条纹投影轮廓仪 (FPP) 需要一个稳定的参考平面来记录 3D 重建的参考相位，这使得它对由参考平面引起的运动引起的误差很敏感。因此，尽管传统 FPP 具有很高的精度，但它在工业场景中实现稳健的测量是具有挑战性的。为了解决这个问题，提出了一种相位重构方法，通过西尔维斯特方程理论，通过最小化总变化（TV），从调制相位的背景中对参考相位进行去噪和重构。由于该策略实现了参考相位和目标相位的同步提取，可实时修正参考相位，减少参考平面偏差造成的测量误差。所提出的方法已应用于测量具有不同参考平面偏差的阶梯形工件和传送带上的齿轮工件。实验结果表明，在复杂的工业场景中，在准确性和鲁棒性上与传统 FPP 具有竞争力。