2D Wavefront Phase Unwrapping Algorithm Implementation

Phase unwrapping is a critical technique for recovering true physical information from two-dimensional wavefront phase data. In optical measurement and interferometry, directly acquired phase data often exhibits wrapping phenomena due to periodic characteristics (phase values are constrained between -π and π). Through phase unwrapping algorithms, these truncated phase values can be expanded into continuous physical quantities, accurately reflecting characteristics such as surface height, topography, or refractive index distribution of measured objects. Implementation typically involves detecting phase jumps by calculating differences between adjacent pixels and adding multiples of 2π to remove discontinuities.

Common unwrapping methods include path-following algorithms (like Goldstein's branch-cut method), least-squares approaches, and global solutions based on Fourier transforms. The core challenge lies in eliminating phase jumps while maintaining local data consistency. Code implementation often requires handling noise through pre-processing filters and using quality-guided path following to avoid error propagation. High-quality phase unwrapping results are essential for precision optical inspection, biomedical imaging, and industrial surface defect analysis. Key functions in implementation typically involve phase gradient calculation, residue detection, and integration path optimization.