Neural network-based phase extraction method for digital moiré fringes in single-grating displacement measurement systems

This study proposes a novel method for phase extraction from digital moiré fringe patterns in single-grating displacement measurement systems using deep learning. The method creates grating images with a specially designed two-dimensional cosine image superimposed to artificially create digital moiré fringes. This design guarantees that the sampled image information contains an integer number of complete moiré fringe periods, eliminating phase extraction errors that are caused by spectral leakage. Phase detection is then carried out with a trained neural network, eliminating the need for complicated signal decomposition algorithms and extensive parameter adjustments or error compensations. Experimental comparisons with variational mode decomposition-based methods show that the proposed method has better phase extraction accuracy and robustness. Based on a single-grating configuration, this study proposes a low-cost and high-precision solution for nanoscale displacement measurement.