激光与光电子学进展, 2015, 52 (11): 110701, 网络出版: 2015-11-09
利用Hilbert 变换提高傅里叶变换轮廓术的测量范围和精度 下载: 1204次
Improve Measurement Range and Accuracy of Fourier Transform Profilometry by Hilbert Transform
傅里叶光学 傅里叶变换轮廓术 三维面形重建 频谱分析 希尔伯特变换 Fourier optics Fourier transform profilometry 3D shape reconstruction spectral analysis Hilbert transform
摘要
采用傅里叶变换轮廓术(FTP)进行三维面形测量时,变形条纹图零频分量的扩展对FTP 的测量范围和精度存在影响。消除变形条纹图的零频分量后,FTP 的测量范围可以提高3 倍。根据希尔伯特(Hilbert)变换具有90°相移和使直流分量为零的性质,提出通过两次分段Hilbert 变换抑制条纹零频分量的新方法。由于条纹背景分布是一个慢变函数,每半个周期内的局部背景分布可以看做常数,所以两次分段Hilbert 变换可以很好抑制条纹中零频分量对基频分量的影响,有利于减小测量误差。给出的理论分析、计算机模拟以及实验证明了所提方法的有效性。
Abstract
In the Fourier transform profilometry (FTP), the existence and expanding of zero frequency component of the deformed fringe pattern has an influence on the measurement range and accuracy of Fourier transform profilometry. After eliminating the zero frequency component of the deformed fringe, the measurement range of FTP will be three times of that of the traditional FTP. According to Hilbert transform having the nature of 90°phase shift and the direct current (DC) component becoming zero, a new method based on piecewise Hilbert transform is proposed to suppress zero frequency component of the fringe pattern. The zero frequency component of the fringe can be suppressed well because the background of the fringe is a slowly varying function and background distribution in each half period of the fringe should be regarded as constant. So, the proposed method can suppress the zero frequency component of the fringe well. The proposed method enlarges the measurement range of FTP and reduces its measurement error. In the paper, the theoretical analysis is given. Computer simulations and experimental results demonstrate the effectiveness of the proposed method.
骆凤, 陈文静, 苏显渝. 利用Hilbert 变换提高傅里叶变换轮廓术的测量范围和精度[J]. 激光与光电子学进展, 2015, 52(11): 110701. Luo Feng, Chen Wenjing, Su Xianyu. Improve Measurement Range and Accuracy of Fourier Transform Profilometry by Hilbert Transform[J]. Laser & Optoelectronics Progress, 2015, 52(11): 110701.