A deep learning approach for small-step high-precision phase calculation in fringe projection: integrating phase unwrapping and compound error correction

Haoyue Liu, Xiaodong Zhang,
A deep learning approach for small-step high-precision phase calculation in fringe projection: integrating phase unwrapping and compound error correction,
Measurement,
Volume 256, Part D,
2025,
118480,
ISSN 0263-2241,
https://doi.org/10.1016/j.measurement.2025.118480.
(https://www.sciencedirect.com/science/article/pii/S0263224125018391)
Abstract: Fringe projection profilometry is widely used for 3D measurement, with its accuracy primarily determined by phase calculations. A major challenge is balancing measurement speed and precision. Achieving higher precision often requires additional fringe patterns (i.e., more phase-shifting steps), reducing speed and potentially introducing temporal errors. Thus, achieving small-step, high-precision phase calculation is crucial for improving performance. Existing methods, including traditional algorithms and deep learning approaches, often treat phase unwrapping and error correction separately, neglecting their interdependence. Additionally, these methods are generally limited in generalizability and focus on single-phase errors, while real-world scenarios involve multiple coexisting errors. To address these challenges, we present a deep learning-based approach for small-step, high-precision phase calculation that unifies phase unwrapping and error correction. Due to significant variations in error magnitudes, we use a joint training strategy with two networks: Net1, based on the lightweight ERFNet-Lite architecture to minimize GPU memory usage, and Net2, incorporating a novel global multi-scale attention (GMSA) module within the GMSA-UNet to address compound phase errors. Experimental results demonstrate that our algorithm performs phase unwrapping using three-step phase-shifting input, achieving accuracy comparable to eight-step methods, while effectively mitigating errors caused by system nonlinearity, specular reflections, and shadows. Both simulated and real-world experiments validate its effectiveness and feasibility, with generalization tests confirming its robustness.
Keywords: Fringe projection; Phase unwrapping; Compound phase error; Attention mechanism; Computer graphic