针对条纹投影三维形貌测量涉及的相位提取, 提出了一种基于变分模态分解的单幅条纹投影相位提取方法。通过建立变分模态分解模型和极小化变分模态分解将单幅投影条纹图分解成背景部分、条纹部分和噪声部分。然后对得到条纹部分进行Hilbert变换和反正切变换得到包裹相位; 对其进行质量导向相位解包裹和Zernike多项式去载频得到解包裹相位。将该方法与Fourier变换、连续小波变换进行了对比, 结果显示: 本文提出的相位提取方法相位误差为3.14×10-4, 小于Fourier变换和连续小波变换方法对应的误差3.30×10-4和6.52×10-4。模拟和实验结果表明: 本文提出的方法在处理具有边缘信息投影条纹图时具有优势, 能够提取出更准确的相位信息, 可有效地用于含边缘不连续和突起的三维物体测量。

For the phase retrieval in fringe projection 3D shape measurements, a new fringe projection phase retrieval method based on variational mode decomposition was proposed. Firstly, the projection fringe pattern was decomposed into a background part, a fringe part and a noise part by the development of variational mode decomposition model and the minimization of the model. Then, the fringe part was processed by Hilbert and arc tangent transform to obtain a wrapping phase, and by quality guided phase unwrapping and Zernike carrier removal to acquire the final absolute phase. Simulation and experimental results show that the phase error by the proposed method is 3.14×10-4, smaller than the errors 3.30×10-4 and 6.52×10-4 that respectively obtained by Fourier transform method and continuous wavelet transform method. The proposed method is superior to the Fourier transform method and continuous wavelet transform method in the process of projection fringes with edge information, providing more accurate results, and is more effective for the application of the three dimensional measurement of objects with discontinuous and abrupt changes.