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Neural network-based phase extraction method for digital moiré fringes in single-grating displacement measurement
Optics Express
|February 20, 2026
Summary
This study introduces a deep learning method for accurate phase extraction in displacement measurement. It uses artificial moiré fringes for precise nanoscale measurements with a single grating.
Area of Science:
- Optics and Photonics
- Machine Learning Applications
- Metrology
Background:
- Digital moiré fringe patterns are crucial for displacement measurement.
- Traditional phase extraction methods can suffer from spectral leakage and require complex algorithms.
- Single-grating systems offer a cost-effective approach to displacement measurement.
Purpose of the Study:
- To develop a novel, deep learning-based phase extraction method for digital moiré fringe patterns.
- To improve accuracy and robustness in nanoscale displacement measurements.
- To eliminate errors caused by spectral leakage in single-grating systems.
Main Methods:
- Artificial generation of digital moiré fringes by superimposing a 2D cosine image onto grating images.
- Ensuring integer periods of moiré fringes in sampled data to prevent spectral leakage.
- Utilizing a trained neural network for phase detection, bypassing complex signal decomposition.
Main Results:
- The proposed deep learning method achieves superior phase extraction accuracy compared to variational mode decomposition.
- The method demonstrates enhanced robustness in displacement measurements.
- Successful implementation in a single-grating configuration for nanoscale measurements.
Conclusions:
- The novel deep learning approach provides a low-cost, high-precision solution for nanoscale displacement measurement.
- Artificial moiré fringe generation effectively eliminates phase extraction errors.
- The method simplifies the measurement process by avoiding complex algorithms and parameter tuning.

