Phase retrieval for noisy fringe pattern by using empirical mode decomposition and Hilbert Huang transform

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To address the issue of the intermittent noise in optical fringe pattern, an adaptive method of noise reduction is given based on empirical mode decomposition (EMD) and Hilbert Huang transform (HHT), and then the wrapped phase is obtained by performing the Hilbert transform on the refined pattern. Firstly, the signal of the fringe pattern is decomposed into several intrinsic mode functions (IMFs). With the instantaneous frequencies and marginal spectra of each IMF obtained by HHT, the criterion of identifying the noise IMF is determined. Then, it is judged whether a mode-mixing problem, which is the frequent problem in traditional EMD, appears in each noise IMF. If the problem appears, the "noise," which is designed according to the signal adaptively, is added to the original signal, and then the obtained new signal is decomposed again. The process will be repeated until there is no mode mixing in the noise IMF. Finally, the wrapped phase is obtained by performing a Hilbert transform on the refined pattern with noise and background components removed. The proposed method can solve the mode-mixing problem effectively. It can reduce most of the noise and maintain a large amount of detailed phase information simultaneously. Simulation and compared experiments show the efficiency, robustness, and accuracy of the proposed method.