Phase Unwrapping Algorithms Implementation in MATLAB

In this article, we explore MATLAB-based implementations for solving phase unwrapping problems. We provide comprehensive coverage of two distinct phase unwrapping algorithms. The first algorithm implements quality-guided path-following phase unwrapping, a widely-used method that demonstrates strong performance in practical applications through systematic pixel processing based on quality metrics. The second algorithm implements Goldstein's branch-cut method, an innovative approach that effectively addresses challenges traditional methods struggle with, particularly through strategic branch cut placement to resolve phase inconsistencies. We delve into the fundamental principles and implementation details of both algorithms, including key MATLAB functions such as phase gradient calculations, quality map generation, and path integration techniques for the quality-guided method, while for Goldstein's method we examine residue identification, branch cut formation, and phase correction mechanisms. The implementation involves careful handling of phase derivatives using MATLAB's gradient functions and intelligent path planning using priority queues based on quality metrics. Furthermore, we conduct comparative analysis of these algorithms' strengths and limitations in real-world applications, discussing computational efficiency, noise resilience, and handling of discontinuous phases. We also propose potential enhancements including adaptive thresholding mechanisms and hybrid approaches that combine both methods' advantages. These insights aim to advance research and application outcomes in phase unwrapping technology, particularly for interferometry, medical imaging, and optical measurement systems.