Research Of Mode Decomposition Method In Fourier Transform Profilometry

Fourier Transform Profilometry(FTP)has been widely used in industrial measurement as a fast optical non-destructive testing method,but its measurement accuracy is easily affected by the environment.It is difficult to extract the fundamental frequency information because the complex background light will cause zero frequency and fundamental frequency overlap in the spectrum of the fringe pattern.Although the traditional band-pass filtering method can extract the fundamental frequency information we want,its extraction accuracy is restricted by the window shape and window size,and it cannot be adaptive.In order to improve the measurement accuracy and to adapt to complex environments,this Thesis pays more attention to the extraction of the fundamental frequency in the Fourier domain of the fringe pattern.The fundamental frequency components extraction has always been a research hotspot of FTP.After comparing the Bidimensional Empirical Mode Decomposition(BEMD)method,the Hilbert transform method and the two-dimensional Variational Mode Decomposition(2DVMD)method,a method based on Singular Value Decomposition(SVD)was applied and improved from one-dimensional perspective.The improved SVD-EMD model is more robust.From two-dimensional perspective,we improved the 2DVMD method to a 2DVMD-BEMD model which is an effective decomposition method.Then the inverse Fourier Transform and the phase unwrapping algorithm are performed to the extracted fundamental frequency component,it can effectively recover the abrupt change information of the measured object.Numerical simulations and experimental results show that FTP based on 2DVMD method can reconstruct the details of the measured object more effectively than FTP based on filtering method,and even achieve the accuracy of PMP method.Considering the defect recovery cannot be performed well when the defect direction is perpendicular to the fringe direction,we project the orthogonal composite fringe pattern on the surface of the object and the deformed fringe can be decomposed into the horizontal and vertical part by 2DVMD method.By fusing the two parts phase information,it can easily recover the surface defect of the measured object.Through experiments and error analysis,it is found that FTP based on 2DVMD method is more conducive to recovering the surface of the object.The phase extraction from orthogonal composite fringe based on 2DVMD method is more conducive to recovering the detail information of the object.Both of them illustrate that the effect of 2DVMD method is far better than that of filtering method.