Abstract: The x-f-k transform is drawn into the phase demodulation method in frequency domain for quickly realizing the three-dimensional surface measurement. Compared with the traditional method, the x-f-k transform can realize the local analysis and demodulation of signal in horizontal and vertical directions, which accelerates the measurement speed, improves the accuracy of the measurement results and reduces memory requirement. It simply means that taking the S-transform and then taking the Fourier transform in both horizontal and vertical directions respectively obtain the coefficient matrix of the pixel points and the phase information. The shape of three-dimensional objects is reconstructed through the modulation relationship between the phase and the height distribution. The experimental results show that the proposed method can effectively realize the optical three-dimensional surface measurement and provide results in the form of fringe, then the measurement error is less than 0.6%.

Key words: deformed fringe, three-dimensional measurement, frequency domain phase unwrapping, x-f-k transform

摘要： 为了快速实现三维面形测量，提出一种x-f-k变换频域解相方法。相比传统方法，x-f-k变换在水平及垂直方向上分析变形条纹实现条纹相位解调，测量速度快、测量精度高并且内存需求小。该方法分别对变形条纹的行和列先做S变换，再做傅里叶变换，得到像素点的系数矩阵，进而得到相位信息，通过相位与高度分布的调制关系重建三维物体的面形。结果表明，所提方法能够快速实现以条纹形式提供测量结果的光学三维面形测量，测量误差在0.6%以内。

关键词: 变形条纹, 三维测量, 频域解相, x-f-k变换