The Simplest Spatial Phase Unwrapping Algorithm in Phase Measuring Profilometry

In phase measuring profilometry, spatial phase unwrapping algorithms are required to recover the phase information of target objects. Although various algorithms exist for this purpose, the simplest and most commonly used approach is the continuous phase unwrapping algorithm. This method leverages phase continuity by constraining phase differences within the range of $[-\pi, \pi]$ and performs phase unwrapping through phase difference integration. From an implementation perspective, this typically involves calculating wrapped phase differences between adjacent pixels, checking for phase jumps exceeding $\pi$, and adding multiples of $2\pi$ to maintain continuity. However, this algorithm may fail under certain conditions, such as when dealing with objects featuring significant height variations or discontinuities. Consequently, improved algorithms have been developed, including multi-frequency phase unwrapping techniques that use different wavelength patterns to resolve ambiguity, and image segmentation-based approaches that partition the phase map into continuous regions before unwrapping. While these advanced methods provide more accurate phase recovery, they also introduce increased implementation complexity and computational overhead.