| A vital task of fringe pattern analysis is to extract the phase distribution of interferograms in which certain physical quantities are concealed. Because of its robustness, the two-dimensional continuous wavelet transform (2D-CWT) technique has drawn a lot of attentions in recent years, and becomes one of the most important techniques in fringe pattern analysis. Hence, the dissertation investigates the theory of the 2D-CWT thoroughly, and elaborates the proposed algorithms based on the 2D-CWT technique to extract the phase distribution of interferograms efficiently and accurately. Both computer simulation and real experiments are conducted to verify the validity and effectiveness of the proposed algorithms as well.;First, when analyzes the interferogram whose phase distribution is non-monotonic by using the 2D-CWT technique, the phase ambiguity issue is inevitable. To cope with the phase ambiguity issue, in this dissertation, a phase determination rule is proposed according to the phase distribution continuity, and a frequency-guided scheme is employed to obtain the correct phase distribution following a conventional 2D-CWT analysis.;However, the processing of 2D-CWT is usually time-consuming. In order to speed up the 2D-CWT analysis, the dissertation introduces a concept called the cover map. The cover map is constructed by discretizing the continuous dilation and rotation parameters. Then an algorithm is proposed based on the discretized parameters so as to substantially reduce the processing time without affecting the analysis accuracy.;In addition, the dissertation evaluates the performance of different kinds of mother wavelets for the 2D-CWT technique being used in optical fringe pattern analysis. Based upon the investigation, a 2D modulated Mexican hat wavelet is introduced to improve the performance of the 2D-CWT analysis.;Finally, in fringe pattern analysis, a technique is highly demanded to automatically analyze the interferograms that contain complex fringes and high-level noise as well as defects. In this dissertation, a hybrid technique is proposed to combine the concepts of the 2D-CWT technique and the phase-shifting technique. The novel technique takes the advantages of the two existing techniques, and has the ability to accurately and automatically analyze multiple phase-shifted complex interferograms involving noise and defects. |
