Research and Development of Two-dimensional Windowed Fourier Transform Based Phase Unwrapping Algorithms for Interference Fringe Analysis

• Main Authors: Kuan-Yu Hsu, 徐冠宇
• Other Authors: 李世光
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/48496782676978504215

碩士 === 國立臺灣大學 === 應用力學研究所 === 103 === The main application scenario of this thesis is using Michelson interferometer as the non-destructive testing method, which measures tiny deformation of objects by retrieving the phase of the interference fringes generated due to deformation. To retrieve the deformation induced phase, we measure the interference fringe first and then analyze the phase by a process called phase-unwrapping. Trying to take advantages of the rapid development of CCD/CMOS, which provides a platform to significantly increase the spatial modulation frequency, Fourier transform based phase-unwrapping algorithm was adopted in this thesis. Trying to remove the bottleneck associated with phase-unwrapping, Fourier spectrum of interference fringe obtained with pre-introduced spatial carrier frequency so as to distinguish the correct direction of object deformation, was adopted. This approach first proposed by Mitsuo Takeda in 1981 is similar to the Doppler interferometer that solves the directional ambiguity by providing a frequency shift. The only difference lies on either temporal or spatial frequency was pre-introduced. It is with this pre-introduced spatial frequency shift, retrieving the phase information by using only one interference fringe (intensity map) becomes feasible. More specifically, the above-mentioned approach circumvent the disadvantages associated with phase-shifting algorithms such as the 5,1 phase-shifting algorithm, etc. that require more than one image to analyze the phase information. It is to be noted that retrieve phase map from intensity map with a single intensity map not only saves valuable computation time but also provides us with a platform for dynamic measurement as high-speed camera can be used to record the time-varying interference fringes (intensity maps) first and then compute phase map after the deformation is completed. Furthermore, in dealing with problems related to valid or effective functional domain (domain with valid interference fringes) and regions with vastly different signal-to-noise ratios (SNR), Windowed Fourier Transform (WFT) first proposed by Qian Kemao in 2004 was also introduced in this thesis. For phase unwrapping, this study used Least-Squares method to get the information of measured object rapidly. It is to be noted that this method leads to the use of Fourier transform to solve a Poisson’s equation with Neumann boundary conditions. As Fourier transform algorithm was used in converting the intensity map to the phase map and then perform phase-unwrapping, these algorithms developed in this thesis provides us with an opportunity to adopt the many attempts over the last 50 years in speeding up the computation time associated with Fourier transform. Some of these methods include Fast Fourier Transform (FFT), Sparse Fast Fourier Transform (SFFT) and hardware solution such as Graphic Processing Unit (GPU), etc. All of which can then be integrated to develop an ultrafast phase analysis system, which can found applications potentials ranging from in-situ real-time optical field measurement, production-need driven automatic optical inspection (AOI), etc. This works completed throughout this research include setting the Michelson interferometer, integrating MATLAB and LabVIEW to transfer experimentally induced optical intensity map to computers for signal post-processing, etc. To verify the overall effectiveness of this system, this study analyzed the phase information by measuring the mirror and stainless steel deformation by using the Michelson interferometer set up. The results of unwrapped phase matched the object deformation, successfully validated the accuracy and the feasibility of integrating these algorithms in this thesis.