Abstract: In order to solve the problem of the deformation phase extraction from a single fringe pattern, two kinds of improved methods are proposed, which are based on the spectrum-shift approach and the phase-shift approach by using Hilbert transform respectively, and a comparative analysis of their performance is given. In the spectrum-shift method, the dilating Gabor transform is used to optimize the accuracy of the fundamental frequency. In the phase-shift method, the Hibert transform is used to achieve the physical phase shift prosess, combined with the average slope of the phase method to remove the carrier phase component effectively. Common advantages of both methods are only single fringe image being phtographed, simple operation, no complex calculations and conducive to rapid measurment with good prospects.

Key words: spectrum shift, phase shift, dilating Gabor transform, Hilbert transform

摘要： 针对单幅变形条纹图的调制相位提取问题，提出了两种分别基于频移法和基于希尔伯特变换的相移法从变形条纹图中提取面形相位的改进方法，并对它们的性能进行比较分析。在频移法中，通过使用伸缩窗口傅里叶变换来优化基频的准确提取；在相移法中，采用软件的方法利用希尔伯特变换来实现物理上的相移，并结合了求平均相位斜率的的方法有效去除载波相位成份。两种方法的共同优点都是只需要拍摄单幅条纹图像，操作简单，计算复杂度不高，有利于快速测量，具有良好的应用前景。

关键词: 频移法, 相移法, 伸缩窗口傅里叶变换, 希尔伯特变换