Optimized phase compensation in wavelet transform for deformed fringe patterns and its application to CFRP structures

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Abstract This paper derives an optimized phase compensation method for wavelet transform (WT) based on the principles of Windowed Fourier Transform and WT. Starting from the mechanisms of WT and phase compensation, the intermediate parameters of the cost function approach are transferred to the phase correction stage. This process enables a more accurate estimation of the wavelet ridges, thereby providing a more reliable wavelet window function and enhancing the final phase resolution accuracy. Using varying amounts of deformation as test sets, the proposed method is validated on deformed fringe patterns and compared with theoretical phase fields. The results show that the proposed method, namely wavelet transform with cost-function-aided phase correction and parameter transfer (WT-CPCT), reduces the average root mean square error (RMSE) of the phase difference by 34.0% compared with the traditional WT method and by 1.4% compared with proposed wavelet transform with cost-function-aided phase correction but without parameter transfer (WT-CPC). Under different noise levels, WT-CPCT also maintains stable RMSE values and outperforms the comparison methods. Furthermore, phase extraction and comparative analyses are conducted on the woven structure of carbon fiber reinforced polymer blades using sampling moiré, windowed Fourier ridge, and the proposed WT-CPCT method. The results show that the proposed method provides stable wrapped phase distributions and good phase continuity near blade edges. These results demonstrate that the proposed method is effective for deformed fringe images and further improves the performance of WT-based phase analysis.

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