小波在空域和频域上均具有良好的局域化性能,适合于非平稳信号分析。在传统的小波变换轮廓术中,对基小波进行尺度伸缩,即调整子小波的中心频率,去匹配局部条纹,以获取对应的相位信息。但仅在局部位置对Morlet小波进行尺度伸缩不能最佳地提取局部相位信息。详细分析了振荡波形随高斯窗宽变化的复Morlet小波在条纹分析中的特点,提出了一种改进的小波处理方法。将所提方法的相位重建结果与基于代价函数的小波方法的相位重建结果进行比较。结果表明:所提方法综合了不同窗宽的复Morlet小波优点,具有更可靠的脊提取结果;所提的优化小波脊提取方法在条纹分析中具有更好的抑噪能力,提高了小波变换轮廓术的测量精度;计算机模拟和实验均验证了所提方法的有效性。

Wavelets are suitable for analyzing non-stationary signals because of their good localized capabilities in both space domain and frequency domain. In traditional wavelet transform profilometry, the scaling of the mother wavelet, which moves the center frequency of the daughter wavelet, can be used to meet local signals for acquiring phase information. It is not accurate enough to extract the local phase information just changing the scale of the complex Morlet wavelet in the local position. To solve this problem, we discuss the characteristics of complex Morlet wavelets with different Gaussian window widths in fringe analysis and propose an improved wavelet processing method. The phase reconstruction results of the proposed method was compared with those of the wavelet processing by employing a cost function. The results show that the proposed method combines merits of the complex Morlet wavelets with different Gaussian window widths, which gives more reliable ridge information. The measurement accuracy of the wavelet transform profilometry is improved by employing optimized wavelet ridge extraction technique because it has stronger noise suppression ability in fringe analysis. The validity of the proposed method is verified by computer simulations and experiments.