提高基于Morlet小波“脊”处理方法的相位解调精度研究  

Study of Profilometry Measurement Precision Improvement Based on Morlet Wavelet Transform

作　　者：郑毅[1] 陈文静[1] 钟敏[1] 谌秋菊[1] 

机构地区：[1]四川大学电子信息学院

出　　处：《激光与光电子学进展》2014年第11期148-155,共8页Laser & Optoelectronics Progress

摘　　要：Morlet由于具有很好的空域和频域局域能力,是小波变换轮廓术中最常用的小波之一。通过计算Morlet小波与变形条纹之间的相似度,可以从Morlet小波"脊"中获得条纹的相位信息,从而重建被测物体的三位面形。在Morlet小波"脊"方法中,相位表达式的推导利用了相位函数的一阶泰勒近似,在物体高度变化率大的区域,重建面形的误差大。针对这个不足,提出了基于相位二阶泰勒展开的小波变换轮廓术,推导了"脊"相位的表达式:在已有的小波变换轮廓术的相位表达式中,引入了一个相位的二阶修正项,提高了物体高度变化大的区域的测量精度。计算机仿真和实验结果表明,所提方法可以提高小波变换"脊"方法恢复物体面形的精度。Morlet wavelet, which has the good localization characteristics both in the spatial and frequency domain, is commonly used to demodulate the phase map of the fringe pattern in wavelet transform profilometry by calculating the similarity between parts of the fringe pattern and the wavelet function. The phase information can be extracted by finding out the＂ridge＂information of the wavelet transform coefficients. Furthermore, the reconstructed surface of the tested object is obtained by the extracted the phase information and combining the system parameters of the measurement system. However, when the wavelet ＂ridge＂ method is used to demodulate the phase map, a first- order Taylor approximation is introduced to deduce the phase analytical description of the deformed fringe from the wavelet coefficients at the＂ridge＂position, which causes a big phase error in the areas with high height variation rate. Aiming at the shortage of the method, an improved Morlet wavelet transform＂ridge＂method based on a second-order Taylor expansion is presented. The detailed phase analytical expression from the wavelet transform coefficients at the position of＂ridge＂is given as well.Compared with the conventional wavelet ＂ridge＂ method employing the first Taylor approximation, the improved method has higher accuracy, especially around the zone with higher height variation rate, because a correction related to the second derivative of the tested object is introduced. Computer simulations and experiments verify our analysis.

关 键 词：测量 Morlet小波变换 精度提高 泰勒展开 相位 光学三维测量 

分 类 号：O438[机械工程—光学工程]