title: Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis.
abstract: This paper theoretically discusses modulus of two-dimensional (2D) wavelet transform (WT) coefficients, calculated by using two frequently used 2D daughter wavelet definitions, in an optical fringe pattern analysis. The discussion shows that neither is good enough to represent the reliability of the phase data. The differences between the two frequently used 2D daughter wavelet definitions in the performance of 2D WT also are discussed. We propose a new 2D daughter wavelet definition for reliability-guided phase unwrapping of optical fringe pattern. The modulus of the advanced 2D WT coefficients, obtained by using a daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter that represents the reliability of the retrieved phase data. Computer simulation and experimentation show the validity of the proposed method.
authors.affiliation: Laboratory of Information Optics and Opto-Electronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China.
authors.forename: Sikun
authors.initials: S
authors.lastname: Li
authors.forename: Xiangzhao
authors.initials: X
authors.lastname: Wang
authors.forename: Xianyu
authors.initials: X
authors.lastname: Su
authors.forename: Feng
authors.initials: F
authors.lastname: Tang