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Over the past few decades, tremendous efforts have been devoted to developing various techniques for fringe analysis, and they can be broadly classified into two categories: (1) phase-shifting (PS) methods which require multiple fringe patterns to extract phase information and (2) spatial phase demodulation methods which allow phase retrieval from a single fringe pattern, such as the Fourier transform (FT), windowed Fourier transform (WFT), and wavelet transform (WT) methods. Compared with spatial phase demodulation methods, the multiple-shot phase-shifting techniques are generally more robust and can achieve pixel-wise phase measurement with higher resolution and accuracy. Furthermore, the phase-shifting measurements are quite insensitive to non-uniform background intensity and fringe modulation. Nevertheless, due to their multi-shot nature, these methods are difficult to apply to dynamic measurements and are more susceptible to external disturbance and vibrations. Thus, for many applications, phase extraction from a single fringe pattern is desired, which falls under the purview of spatial fringe analysis.
Here, we demonstrate experimentally for the first time, to our knowledge, that the use of convolutional neural networks can substantially enhance the accuracy of phase demodulation from a single fringe pattern. Deep learning is a powerful machine learning technique that employs artificial neural networks with multiple layers of increasingly richer functionality. The effectiveness of the proposed method is verified using carrier fringe patterns under the scenario of fringe projection profilometry. Experimental results demonstrate its superior performance in terms of high accuracy and edge-preserving over two representative single-frame techniques: Fourier transform profilometry and windowed Fourier profilometry.
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