从小波变换的基本原理出发,分析采用一维复Morlet小波变换在解调具有双载频分量的倾斜条纹图中存在的问题,利用二维小波变换具有方向选择的特点,提出采用由一系列二维复Morlet小波构造出的二维Fan小波对此类条纹图进行解调的方法。并对比了二者在处理倾斜变形条纹(含两个载频分量)的能力。结果表明,二维Fan小波变换由于在进行尺度伸缩的同时,还具有多个角度上的方向特性,可以提取特定方向上的信号,在解调倾斜变形条纹图中包含的相位信息中具有优势,可以更好地获取有用信息。

Based on the basic principle of wavelet transform,the shortage of one-dimensional complex Morlet wavelet transform in demodulating the tilt fringe pattern with two carrier frequencies was analyzed. Then the method of two-dimensional (2-D) fan wavelet made up of a series of 2-D complex Morlet wavelet was proposed to demodulate such patterns. We compared the two methods through processing deformed fringe patterns with two carrier frequencies. The results show 2-D fan wavelet has better ability to obtain the useful information because it can analyze the signals by adjusting both the scaling factor and rotation angle to reach the optimal match between the singles and wavelet functions. That is,2-D Fan wavelet has advantages to dispose two-frequency components grating patterns because of its multiple-directional property.