摘要
S变换结合了短时傅里叶变换和小波变换的优点,是一种无损可逆的非平稳信号时频分析方法,具有线性、多分辨率、逆变换唯一,且与傅里叶变换保持着直接联系等特点。针对基于"脊"分析原理的S变换轮廓术中,相位采用一阶泰勒展开描述时存在的不足,提出了更为精确的二阶泰勒展式的相位描述方法。通过严格的理论分析,得到了更准确的相位场的计算公式,弥补了采用一阶泰勒展式描述相位的不足,大大提高了S变换"脊"方法重建三维面形的精度。完成了相应的计算机模拟和实验验证,并将S变换三维重建效果与以前的基于相位一阶展式的结果进行了对比。
S Transform combines the advantages of the windowed Fourier transform and the wavelet transform. It is a kind of nondestructive and reversible time-frequency analysis method for the non-stationary signals with the characteristics of the linearity, multi-resolution and the only one inverse transformation existing. In addition, it has direct relationship with Fourier transform. Due to the shortage of the phase description based on the 1st-order Taylor expansion in the S transform “ridge” method, a more accuracy phase expression based on the 2nd-order Taylor expansion is proposed. According to the strictly theoretical analysis, a more accuracy calculation expression formula of the phase field is gotten and corresponding computer simulation and experiment are finished, which enriches the theory of S transform and improves the measurement accuracy of S transform. The three-dimensional （3D） reconstruction results based on the 1st-order Taylor expansion are also compared with that based on our method in S transform “ridge” method. The simulations and experiments show that the reconstruction of the surface from the 2nd-order Taylor expansion has higher measurement precision.
出处
《光学学报》
EI
CAS
CSCD
北大核心
2013年第6期149-156,共8页
Acta Optica Sinica
基金
国家自然科学基金(61177010)
四川省学术和技术带头人培养资金(2012DTPY011)资助课题
关键词
测量
S变换
条纹分析
泰勒展开
三维面形重建
measurement
S transform
fringe pattern analysis
Taylor expansion
3D reconstruction
