Two-frequency phase-shifting method vs. Gray-coded-based method in dynamic fringe projection profilometry: A comparative review

• Published in: Optics and lasers in engineering 2022-06, Vol.153, p.106995, Article 106995
• Main Authors: Wu, Zhoujie, Guo, Wenbo, Zhang, Qican
• Format: Article
• Language: English
• Subjects: 3D shape measurement; Fringe projection profilometry; Gray code; Temporal phase unwrapping; Two-frequency phase shifting
• ISSN: 0143-8166; 1873-0302
• DOI: 10.1016/j.optlaseng.2022.106995

•This paper provides a detailed comparison of two typical temporal phase unwrapping methods including the two-frequency phase-shifting method and the Gray-coded-based method.•The basic principles and recent developments of the six approaches (hierarchical, number-theoretical and heterodyne approaches in two-frequency phase-shifting method; traditional Gray code approach, complementary Gray code approach and Gray code approach with tripartite phase unwrapping (Tri-PU) in Gray-coded-based method) are reviewed.•The performance of six approaches on measuring anti-noise ability, efficiency and robustness to motion are compared in detail based on proposed rigorous noise-induced error model and motion-induced error model.•Theoretical analysis, numerical simulation and experimental results are consistent and demonstrate that (a) Gray-coded-based method has better anti-noise ability than two-frequency phase-shifting method; (b) two-frequency phase-shifting method is more efficient than Gray-coded-based method when the number of encoding fringe periods exceeds 8; (c) hierarchical approach and Gray-coded approach with Tri-PU have best performance to resist motion-induced error in their respective types of methods.•Comparative results can give a helpful guidance to choose the “best” approach in different application scenes and quantitatively determine the projected fringe periods and imaging or projecting speed in dynamic measurement for FPP. Two-frequency phase-shifting phase unwrapping and Gray-coded-based phase unwrapping are two typical temporal phase unwrapping methods to recover discontinuous or spatially isolated surfaces in fringe projection profilometry (FPP). But in dynamic measurement, environmental noise, required number of patterns and inter-frame motion affect the performance of these two methods on measuring anti-noise ability, efficiency and robustness in varying degrees. So, it is a challenge to quantitatively compare these methods’ abilities and determine the optimum one with appropriate system parameters and under a certain condition. In this paper, a detailed comparative study is conducted for the two-frequency phase-shifting method including hierarchical, number-theoretical and heterodyne approaches and the Gray-coded-based method including traditional Gray code approach, complementary Gray code approach and Gray code approach with tripartite phase unwrapping (Tri-PU). First, the principles of six approaches are reviewed; then, their anti-noise ab