Qinghua Wang

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.

This study proposes the FT-moiré inversion method for accurately measuring and analyzing the atomic arrays in thin films and invisible substrates. The atomic arrays at the bottom of the structure cannot be directly observed in a scanning tunneling microscope (STM), but only the moiré pattern generated by their interference is visible. To overcome this limitation, the FT-moiré inversion method retrieves the characteristic parameters and compares the possibilities of all the interference combinations of moiré patterns in multilayer atomic structures, identifies the correct two atomic species, and then analyzes them to obtain the periodic characteristics of the potentially invisible atomic arrangements. The validity and accuracy of the FT-moiré inversion method are verified. Moreover, the FT-moiré inversion method is successfully applied to analyze the distortion distributions of thin-film atoms and invisible substrate atoms in the Fe₂N–Cu(111) atomic structure. This method can probe underlying atomic features in structures that are not visible with STM and can be generalized to other atomic structure studies of thin films and substrates to achieve improved optoelectronic and mechanical properties through precise detection of lattice defects and tuning of strain fields.