Branch-cut algorithm with second-order residues in phase unwrapping

Area of Science:

• Optical Metrology
• Computational Imaging
• Phase Measurement

Background:

• Phase unwrapping is crucial for 3D surface reconstruction from fringe projection systems.
• Conventional branch-cut algorithms face challenges with residue handling and accuracy.
• Existing methods often rely on specific residue charge matching, limiting applicability.

Purpose of the Study:

• To introduce a novel branch-cut algorithm for phase map unwrapping.
• To address limitations in conventional phase unwrapping techniques.
• To enhance the accuracy of relating phase behavior to surface characteristics.

Main Methods:

• Development of a novel branch-cut algorithm for phase map unwrapping.
• Computation of second-order residues with vortex phase structures from wrapped phase data.
• Utilizing a second-order derivative that incorporates the wrap cycle.
• Identifying consistent vorticity direction in phase vortex structures.

Main Results:

• The algorithm successfully exposes second-order residues with vortex phase structures.
• A consistent vorticity direction was observed in these vortex structures.
• The method facilitates branch-cut connections between residues irrespective of charge.
• Demonstrated high accuracy in simulations and practical experiments.

Conclusions:

• The novel branch-cut algorithm offers a significant advancement in phase map unwrapping.
• It overcomes limitations of traditional methods by connecting residues regardless of charge.
• The algorithm provides an accurate approach for analyzing phase-to-surface characteristic relationships.